Case Solutions Corporate Finance Ross, Westerfield, Westerfield, Jaffe, and Jordan 11th edition 10/20/2015 Prepared by: Brad Jordan ni!ersity of "entu#$y Joe S%olira Bel%ont ni!ersity
C-2 CASE SOLUTIONS
C-2 CASE SOLUTIONS
CHAPTER 31 CASE C-3
CHAPTER 2 CASH FLOWS AT WARF COMPUTERS The operating cash flow for the company co mpany is: (NOTE: All All numbers are in thousands of dollars) OCF E!"T # $epreciation % Current ta&es OCF '*+* # ,+ % -*. OCF '/01 To calculate the cash flow from assets we need to find the capital spending and change in net wor2ing capital3 The capital spending for the year was: Capital spending Ending net fi&ed assets % !eginning net fi&ed assets # $epreciation
Net capital spending
'1-*/ 04,+ '/*.1
And the change in net wor2ing capital was: Change in net working capital Ending N5C % !eginning N5C
Change in N5C
'//1. 4/, '/
6o the cash flow from assets was: Cash flow from assets
Operating cash flow % Net capital spending % Change in N5C Cash flow from assets
'/01 /*.1 / ',,4
The cash flow to creditors was: Cash flow to creditors
"nterest paid % Net New !orrowing Cash flow to Creditors
'/10 1/ '/*-
The cash flow to stoc2holders was: Cash flow to stockholders
$i7idends paid
'4
% Net new e8uity raised
% (%./)
Cash flow to 6toc2holders
'1,1
The accounting cash flow statement of cash flows for the year was: 6tatement of Cash Flows
Operations Net income $epreciation $eferred ta&es Changes in assets and liabilities Accounts recei7able "n7entories Accounts payable Accrued e&penses Other Total cash flow from operations
'//-0 ,+ /0/ (,+) 1, (/.,) (/,) '/,-
"n7esting acti7ities Ac8uisition of fi&ed assets 6ale of fi&ed assets Total cash flow from in7esting acti7ities
'(/,+) ,4 '(/*.1)
Financing acti7ities 9etirement of debt roceeds of long;term debt $i7idends 9epurchase of stoc2 roceeds from new stoc2 issues Total cash flow from financing acti7ities
'(/40) + (4) (--) /. '(1/)
Change in cash (on balance sheet)
'-/
CHAPTER 31 CASE C-5
Answers to questions 1& The firm had positi7e earnings in an accounting sense (N" < *) and had positi7e cash flow from operations and a positi7e cash flow from assets3 The firm in7ested '/ in new net wor2ing capital and '/*.1 in new fi&ed assets3 The firm was able to return '1,1 to its stoc2holders and '/*- to creditors3 2& The financial cash flows present a more accurate picture of the company since it accurately reflects interest cash flows as a financing decision rather than an operating decision3 '& The e&pansion plans loo2 li2e they are probably a good idea3 The company was able to return a significant amount of cash to its shareholders during the year but a better use of these cash flows may ha7e been to retain them for the e&pansion3 This decision will be discussed in more detail later in the boo23
CHAPTER 3 RATIOS AND FINANCIAL PLANNING AT EAST COAST YACHTS 1&
The calculations for the ratios listed are: Current ratio '/.+10** = '/1*1** Current ratio 30, times >uic2 ratio ('/.+10** % --01**) = '/1*1** >uic2 ratio 3,1 times Total asset turno7er '/*4***** = '//01*,4** Total asset turno7er /3+* times "n7entory turno7er '/,+-***** = '--01** "n7entory turno7er 3, times 9ecei7ables turno7er '/*4***** = '.4/*+** 9ecei7ables turno7er 1.3-+ times Total debt ratio ('//01*,4** % .4.+,-**) = '//01*,4** Total debt ratio 3,4 times $ebt%e8uity ratio ('/1*1** # 1-,*****) = '.4.+,-** $ebt%e8uity ratio 340 times E8uity multiplier '//01*,4** = '.4.+,-**
E8uity multiplier /340 times "nterest co7erage '1*4*** = '104/*** "nterest co7erage 0340 times rofit margin '/.+-+** = '/*4***** rofit margin 3*0. or 03.? 9eturn on assets '/.+-+** = '//01*,4** 9eturn on assets 3/1. or /13.? 9eturn on e8uity '/.+-+** = '.4.+,-** 9eturn on e8uity 3-- or -3-?
CHAPTER 31 CASE C-7
2&
9egarding the li8uidity ratios East Coast @achts current ratio is below the median industry ratio3 This implies the company has less li8uidity than the industry in general3 owe7er the current ratio is abo7e the lower 8uartile so there are companies in the industry with lower li8uidity than East Coast @achts3 The company may ha7e more predictable cash flows or more access to short;term borrowing3 The turno7er ratios are all higher than the industry medianB in fact all three turno7er ratios are abo7e the upper 8uartile3 This may mean that East Coast @achts is more efficient than the industry in using its assets to generate sales3 The financial le7erage ratios are all below the industry median but abo7e the lower 8uartile3 East Coast @achts generally has less debt than comparable companies but is still within the normal range3 The profit margin for the company is about the same as the industry median the 9OA is slightly higher than the industry median and the 9OE is well abo7e the industry median3 East Coast @achts seems to be performing well in the profitability area3 O7erall East Coast @achts performance seems good although the li8uidity ratios indicate that a closer loo2 may be needed in this area3
!elow is a list of possible reasons it may be good or bad that each ratio is higher or lower than the industry3 Note that the list is not e&hausti7e but merely one possible e&planation for each ratio3 Ratio Current ratio
>uic2 ratio Total asset turno7er
"n7entory turno7er 9ecei7ables turno7er
(ood !etter at managing current accounts3 !etter at managing current accounts3 !etter at utiliing assets3
!etter at in7entory management possibly due to better procedures3 !etter at collecting recei7ables3
Total debt ratio
ess debt than industry median means the company is less li2ely to e&perience credit problems3
$ebt;e8uity ratio
ess debt than industry median means the company is less li2ely to e&perience credit problems3
E8uity multiplier
ess debt than industry median means the company is less li2ely to e&perience credit problems3
"nterest co7erage
ess debt than industry median means the company is less li2ely to e&perience credit problems3
rofit margin
The D is slightly abo7e the industry median so it is performing better than many peers3 Company is performing abo7e many of its peers3 Company is performing abo7e many of its peers3
9OA 9OE
Bad Day be ha7ing li8uidity problems3
Day be ha7ing li8uidity problems3 Assets may be older and depreciated re8uiring e&tensi7e in7estment soon3 Could be e&periencing in7entory shortages3 Day ha7e credit terms that are too strict3 $ecreasing recei7ables turno7er may increase sales3 "ncreasing the amount of debt can increase shareholder returns3 Especially notice that it will increase 9OE3 "ncreasing the amount of debt can increase shareholder returns3 Especially notice that it will increase 9OE3 "ncreasing the amount of debt can increase shareholder returns3 Especially notice that it will increase 9OE3 "ncreasing the amount of debt can increase shareholder returns3 Especially notice that it will increase 9OE3 Day be able to better control costs3
Assets may be old and depreciated relati7e to industry3 rofit margin and ED could still be increased which would further increase 9OE3
"f you created an "n7entory = Current liabilities ratio East Coast @achts would ha7e a ratio that is lower than the industry median3 The current ratio is below the industry median while the 8uic2 ratio is abo7e the industry median3 This implies that East Coast @achts has less in7entory to current liabilities than the industry median3 !ecause the cash ratio is lower than the industry median East Coast @achts has less in7entory than the industry median but more accounts recei7able3
CHAPTER 31 CASE C-9
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To calculate the internal growth rate we first need to find the 9OE and the retention ratio so: 9OE Net income = Total e8uity 9OE '/.+-+** = '.4.+,-** 9OE 3-- or -3-? b Addition to 9E = Net income b '///*1,44 = '/.+-+** b 30* or 0*?
6o the sustainable growth rate is: 6ustainable growth rate (9OE G b) = H/ % (9OE G b)I 6ustainable growth rate H3--(30*)I = H/ % 3--(30*)I 6ustainable growth rate 34* or 34*? The sustainable growth rate is the growth rate the company can achie7e with no e&ternal financing while maintaining a constant debt%e8uity ratio3 At the sustainable growth rate the pro forma statements ne&t year will be: Income statement '.4*/+0
6ales COJ6 Other e&penses $epreciation E!"T "nterest Ta&able income Ta&es (,*?)
/+-11,-0 1*4-/-.0 -+04*** '1+000,+ 104/*** '1,41-0,+ /140,-44
Net income
'*4-*,4
$i7idends Add to 9E
'-+4, /,-0+.
Balance sheet
Assets Current Assets Cash Accounts rec3 "n7entory Total CA
',*1+*4 0-,.1. +/,./11 '/4,,00-*
iabilities K E8uity Current iabilities Accounts ayable '+.0.0+, Notes ayable /0-0,,+ Total C '-*11 ong;term debt
'1-,*****
'..+**** -+-00,. '0,.0,.
Fi&ed assets Net KE
'/,01/0
6hareholder E8uity Common stoc2 9etained earnings Total E8uity
Total Assets
'/,,/0*411
Total KE
6o the EFN is: EFN Total assets % Total liabilities and e8uity EFN '/,,/0*411 % /1-+-*-.0 EFN '01/*0The ratios with these pro forma statements are: Current ratio '/4,,00-* = '-*11 Current ratio 30, times >uic2 ratio ('/4,,00-* % +/,./11) = '-*11 >uic2 ratio 3,1 times Total asset turno7er '.4*/+0 = '/,,/0*411 Total asset turno7er /3+* times "n7entory turno7er '/+-11,-0 = '+/,./11 "n7entory turno7er 3, times 9ecei7ables turno7er '.4*/+0 = '0-,.1. 9ecei7ables turno7er 1.3-+ times Total debt ratio ('/,,/0*411 % 0,.0,.) = '/,,/0*411 Total debt ratio 3,+ times $ebt%e8uity ratio ('-*11 # 1-,*****) = '0,.0,. $ebt%e8uity ratio 3+, times
'/1-+-*-.0
CHAPTER 31 CASE C-11
E8uity multiplier '/,,/0*411 = '0,.0,. E8uity multiplier /34, times "nterest co7erage '1+000,+ = '104/*** "nterest co7erage /*3 times rofit margin '*4-*,4 = '.4*/+0 rofit margin 3*+*4 or +3*4? 9eturn on assets '*4-*,4 = '/,,/0*411 9eturn on assets 3/,., or /,3.,? 9eturn on e8uity '*4-*,4 = '0,.0,. 9eturn on e8uity 3+1 or +31? The only ratios that changed are the debt ratio the interest co7erage ratio profit margin return on assets and return on e8uity3 The debt ratio changes because long;term debt is assumed to remain fi&ed in the pro forma statements3 The other ratios change slightly because interest and depreciation are also assumed to remain constant as well3 )&
ro forma financial statements for ne&t year at a * percent growth rate are: Income statement 6ales '.1*+**** COJ6 /0+1**** Other e&penses 1*1*,** $epreciation -+04*** E!"T '10-.*-** "nterest 104/*** Ta&able income '11+.4-** Ta&es (,*?) /1.,1+,*
Net income
'*1/.0-*
$i7idends Add to 9E
'-*4.1/+ /,*,,
Balance sheet
Assets Current Assets Cash Accounts rec3 "n7entory Total CA
'14,0* 0*44-* 04.0-* '/+4++,,*
iabilities K E8uity Current iabilities Accounts ayable '+101,* Notes ayable /0///* Total C '..+,1-* ong;term debt
'1-,*****
'..+**** -+.*, '01+*.*,
Fi&ed assets Net KE
'//000,,*
6hareholder E8uity Common stoc2 9etained earnings Total E8uity
Total Assets
'/,*0-.++*
Total KE
'/1.0+4,*
6o the EFN is: EFN Total assets % Total liabilities and e8uity EFN '/,*0-.++* % /1.0+4,* EFN ',40-,0+ 5&
Now we are assuming the company can only build in amounts of '. million3 5e will assume that the company will go ahead with the fi&ed asset ac8uisition3 "n this case the pro forma financial statement calculation will change slightly3 To estimate the new depreciation charge we will find the current depreciation as a percentage of fi&ed assets then apply this percentage to the new fi&ed assets3 The depreciation as a percentage of assets this year was: $epreciation percentage '-+04*** = '/*/,+/** $epreciation percentage 3*-0+ or -30+? The new le7el of fi&ed assets with the '. million purchase will be: New fi&ed assets '/*/,+/** '/*/,+/** # .****** '/-,+/** '/-,+/** 6o the pro forma depreciation as a percentage of sales will be: ro forma depreciation 3*-0+('/-,+/**) ro forma depreciation '+.01-,4
CHAPTER 31 CASE C-13
5e will will use this amount in the pro forma income statement3 6o the pro forma income statement will be: Income statement 6ales '.1*+**** COJ6 /0+1**** Other e&penses 1*1*,**
$epreciation E!"T "nterest Ta&able income Ta&es (,*?)
+.01-,4 '1.4..4./ 104/*** '1/-,4./ /+-.4+*
Net income
'/44+40/
$i7idends Add to 9E
'.04*. /1.*+0/4
The pro forma balance sheet will remain re main the same e&cept for the fi&ed asset and e8uity accounts3 The fi&ed asset account will increase by '. million rather than the growth rate of sales3 Balance sheet
Assets Current Assets Cash Accounts rec3 "n7entory Total CA
'14,0* 0*44-* 04.0-* '/+4++,,*
iabilities K E8uity Current iabilities Accounts ayable '+101,* Notes ayable /0///* Total C '..+,1-* ong;term debt
'1-,*****
'..+**** -0./11/4 '01*411/4
Fi&ed assets Net KE
'/-,+/**
6hareholder E8uity Common stoc2 9etained earnings Total E8uity
Total Assets
'/,.,-4-,*
Total KE
'/1.*00-04
6o the EFN is: EFN Total assets % Total liabilities and e8uity EFN '/,.,-4-,* % /1.*00-04 EFN '/*14/4-/ 6ince the fi&ed assets ha7e increased at a faster percentage than sales the capacity utiliation for ne&t year will decrease3
CHAPTER 4 THE MBA DECISION 1&
Age is ob7iously an important factor3 The younger an indi7idual is the more time there is for the (hopefully) increased salary to offset the cost of the decision to return to school for an D!A3 The cost includes both the e&plicit costs such as tuition as well as the opportunity cost of the lost salary3
2&
erhaps the most important non8uantifiable factors would be whether or not he is married and if he has any children3 5ith a spouse and=or children he may be less inclined to return for an D!A since his family may be less amenable to the time and money constraints imposed by classes3 Other factors would include his willingness and desire to pursue an D!A Lob satisfaction and how important the prestige of a Lob is to him him regardless of the salary3 salary3
'&
e has three choices: remain at his current Lob pursue a 5ilton D!A or pursue a Dt3 erry D!A3 "n this analysis room and board costs are irrele7ant since presumably they will be the same whether he attends college or 2eeps his current Lob3 5e need to find the afterta& 7alue of each so: Remain at current current job:
Afterta& salary '-.***(/ % 3-) Afterta& salary ',+/** is salary will grow at 1 percent per year so the present 7alue of his afterta& af terta& salary is: M C H/ H/ = (r % % g )I )I % H/ = ( r % % g )I )I G H(/ # g ) = (/ # r )I )It M ',+/**H/ = (3*-1 % 3*1)I % H/ = (3*-1 % 3*1)I G H(/ # 3*1) = (/ # 3*-1)I ,* M '/*,,0+310 Wilton MBA:
Costs: The direct costs will occur today and in one year and include tuition boo2s and supplies health insurance and the room and board increase3 6o the total direct costs are: M of direct e&penses ('0**** # 1*** # 1*** # ***) # ('0**** # 1*** # 1*** # ***) = /3*-1 M of direct e&penses '/./10031
CHAPTER 31 CASE C-15
The financial benefits are the bonus to be paid in years and the future salary3 M of afterta& bonus paid in years '****(/ % 31/) = /3*-1 M of afterta& bonus paid in years '//30 Afterta& salary '//****(/ % 31/) Afterta& salary '0.4** is salary will grow at , percent per year3 5e must also remember that he will now only wor2 for 1+ years so the present 7alue of his afterta& salary is: M C H/ = (r % g )I % H/ = ( r % g )I G H(/ # g ) = (/ # r )It M '0.4**H/ = (3*-1 % 3*,)I % H/ = (3*-1 % 3*,)I G H(/ # 3*,) = (/ # 3*-1)I 1+ M '/+-+*/3,/ 6ince the first salary payment will be recei7ed three years from today so we need to discount this for two years to find the 7alue today which will be: M '/+-+*/3,/ = /3*-1 M '/-,+.,3*. 6o the total 7alue of a 5ilton D!A is: Malue %'/./10031 # //30 # /-,+.,3*. Malue '/.*41003., Mount err! MBA:
The direct costs will occur today and include tuition boo2s and supplies health insurance and the room and board increase3 6o the total direct costs are: Total direct costs '+.*** # ,.** # 1*** # *** Total direct costs '4,.** Note this is also the M of the direct costs since they are all paid today3 The financial benefits are the bonus to be paid in / year and the future salary3 M of afterta& bonus paid in / year '/+***(/ % 34) = /3*-1 M of afterta& bonus paid in / year '/*3.+ is afterta& salary at his new Lob will be: Afterta& salary '4***(/ % 34) Afterta& salary '-.1*
is salary will grow at 13. percent per year3 5e must also remember that he will now only wor2 for 14 years so the present 7alue of his afterta& salary is: M C H/ = (r % g )I % H/ = ( r % g )I G H(/ # g ) = (/ # r )It M '-.1*H/ = (3*-1 % 3*1.)I % H/ = (3*-1 % 3*1.)I G H(/ # 3*1.) = (/ # 3*-1)I 14 M '/.*4/-.3+6ince the first salary payment will be recei7ed two years from today we need to discount this for one year to find the 7alue today which will be: M '/.*4/-.3+- = /3*-1 M '/,/40134 6o the total 7alue of a Dount erry D!A is: Malue %'4,.** # /*3.+ # /,/40134 Malue '/110,.3+0 )&
e is somewhat correct3 Calculating the future 7alue of each decision will result in the option with the highest present 7alue ha7ing the highest future 7alue3 Thus a future 7alue analysis will result in the same decision3 owe7er his statement that a future 7alue analysis is the correct method is wrong since a present 7alue analysis will gi7e the correct answer as well3
5&
To find the salary offer he would need to ma2e the 5ilton D!A as financially attracti7e as the as the current Lob we need to ta2e the M of his current Lob add the costs of attending 5ilton and the M of the bonus on an afterta& basis3 Note this assumes that the singing bonus is constant3 6o the necessary M to ma2e the 5ilton D!A the same as his current Lob will be: M '/*,,0+310 # /./10031 % //30 M '//+1+43++ This M will ma2e his current Lob e&actly e8ual to the 5ilton D!A on a financial basis3 6ince the salary will not start for 1 years we need to find the 7alue in years so that it is the present 7alue of growing annuity3 6o: Malue in years '//+1+43++(/3*-. ) Malue in years '/1100-3. 6ince his salary will still be a growing annuity the afterta& salary needed is: M C H/ = (r % g )I % H/ = ( r % g )I G H(/ # g ) = (/ # r )It '/1100-3. C H/ = (3*-1 % 3*,)I % H/ = (3*-1 % 3*,)I G H(/ # 3*,) = (/ # 3*-1)I 1+ C '.,.*03, This is the afterta& salary3 6o the preta& salary must be: reta& salary '.,.*03, = (/ % 31/) reta& salary '0+44.344
CHAPTER 31 CASE C-17
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The cost (interest rate) of the decision depends on the ris2iness of the use of the funds not the source of the funds3 Therefore whether he can pay cash or must borrow is irrele7ant3 This is an important concept which will be discussed further in capital budgeting and the cost of capital in later chapters3
CHAPTER 5 BULLOCK GOLD MINING 1&
An e&le spreadsheet is:
CHAPTER 31 CASE C-19
2&
6ince the NM of the mine is positi7e the company should open the mine3 5e should note it may be ad7antageous to delay the mine opening because of real options a topic co7ered in more detail in a later chapter3
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There are many possible 7ariations on the M!A code to calculate the paybac2 period3 !elow is a M!A program from http:==www37bae&press3com=2b=getarticle3phpP2bQid.3 Function A@!ACR(in7est finflow) $im & As $ouble 7 As $ouble $im c As "nteger i As "nteger & Abs(in7est) i/ c finflow3Count $o &&;7 7 finflow3Cells(i)3Malue "f & 7 Then A@!ACR i E&it Function Else"f & S 7 Then i;/ &=7 A@!ACR # E&it Function End "f ii#/ oop Until i < c A@!ACR Vno paybac2V End Function
CHAPTER 6, Case #1 B+-+S. ( To analye this proLect we must calculate the incremental cash flows generated by the proLect3 6ince net wor2ing capital is built up ahead of sales the initial cash flow depends in part on this cash outflow3 6o we will begin by calculating sales3 Each year the company will sell .***** tons under contract and the rest on the spot mar2et3 The total sales re7enue is the price per ton under contract times .***** tons plus the spot mar2et sales times the spot mar2et price3 The sales per year will be:
Contract 6pot Total
"ear # ',1****** 4,**** '.,****
"ear $ ',1****** /1+-**** '.-+-****
"ear % ',1****** /00/**** '-*0/****
"ear & ',1****** -41**** ',441****
The current afterta& 7alue of the land is an opportunity cost3 The initial outlay for net wor2ing capital is the re8uired net wor2ing capital percentage times @ear / sales or: "nitial net wor2ing capital 3*.('.,****) '-/*** 6o the cash flow today is:
E8uipment and N5C Total
%'4.****** %-.***** %-/*** %'/*,//***
Now we can calculate the OCF each year3 The OCF is:
6ales MC FC $ep3 E!T Ta& N" # $ep3 OCF
"ear # '.,*** * /4**** ,/*****
"ear $ '.-+-*** * /*+**** ,/*****
/1.0..** '/.1,,.* * .+1*4/* '4./1.4* /1.0..** '1*+4*4 *
1-..**
"ear %
'-*0/**** -1**** ,/***** /--/..**
'+,/,.** '/01-,.** 1/40./* -.4+./* './-44* '/*0-.44* 1-..** /--/..** '+,+,4 * '01+/,4*
"ear & ',441*** * /+4**** ,/*****
//+-..** '/.-0,.* * .4.-1/* '40/+/4* //+-..** '/.+1-4 *
"ear '
"ear (
'0*****
%'0***** %/*-*** %'/-0,*** *
%+**** '+**** *
%'/-0,***
'+****
CHAPTER 31 CASE C-21
@ears . and - are of particular interest3 @ear . has an e&pense of '30 million to reclaim the land and it is the only e&pense for the year3 Ta&es that year are a credit an assumption gi7en in the case3 "n @ear - the charitable donation is irrele7ant in itself since it is re8uired for the company to donate the land in order to recei7e the necessary permits3 owe7er the donation of the land does mean that the company will recei7e a ta& credit on the donation of the land so this ta& credit is rele7ant3 Ne&t we need to calculate the net wor2ing capital cash flow each year3 N5C is . percent of ne&t years sales so the N5C re8uirement each year is:
!eg3 N5C End N5C N5C CF
"ear # '-/*** +,1*** %'1/***
"ear $ '+,1*** 1*1..** %'/4.**
"ear % '1*1..** ,4-.** '.14***
"ear & ',4-.**
',4-.**
The last cash flow we need to account for is the sal7age 7alue3 The fact that the company is 2eeping the e8uipment for another proLect is irrele7ant3 The afterta& sal7age 7alue of the e8uipment should be used as the cost of e8uipment for the new proLect3 "n other words the e8uipment could be sold after this proLect3 Reeping the e8uipment is an opportunity cost associated with that proLect3 The boo2 7alue of the e8uipment is the original cost minus the accumulated depreciation or: !oo2 7alue of e8uipment '4.****** % /1.0..** % 1-..** % /--/..** % //+-..** !oo2 7alue of e8uipment '4-0+*** 6ince the mar2et 7alue of the e8uipment is '.0 million the e8uipment is sold at a gain to boo2 7alue so the sale will incur the ta&es of: Ta&es on sale of e8uipment ('4-0+*** % .0******)(31+) Ta&es on sale of e8uipment %'/*1+1-* And the afterta& sal7age 7alue of the e8uipment is: Afterta& sal7age 7alue '.0****** % /*1+1-* Afterta& sal7age 7alue ',--0/-,*
6o the net cash flows each year including the operating cash flow net wor2ing capital and afterta& sal7age 7alue are:
)ime * /
Cash flow %'/*,//*** +.+*4* ++444*
1 , . -
04*,4* 0*-40+1* %/-0,*** +****
6o the capital budgeting analysis for the proLect is: aybac2 period 1 # '.*,1,1* = '0*-40+1* aybac2 period 131. years " ('+.+*4* = /3/ # '++444* = /3/ # '04*,4* = /3/ 1 # '0*-40+1* = /3/ , % '/-0,*** = /3/. # '+**** = /3/ -) = '/*,//*** rofitability inde& /3*10/ The NM is: NM %'/*,//*** # '+.+*4* = /3/ # '++444* = /3/ # '04*,4* = /3/ 1 # '0*-40+1* = /3/ , % '/-0,*** = /3/ . # '+**** = /3/ NM '1+.0+-,3./ The e8uation for "99 is: * %'/*,//*** # '+.+*4* = (/ # "99) # '++444* = (/ # "99) # '04*,4* = (/ # "99) 1 # '0*-40+1* = (/ # "99), % '/-0,*** = (/ # "99) . # '+**** = (/ # "99) Using a spreadsheet or financial calculator the "99 for the proLect is: "99 /13,.? Note although the sign changes if the cash flows indicate up to 1 "99s a glance at the NM profile shows only one real "993 "n the final analysis the company should accept the proLect since the NM is positi7e3
CHAPTER 6, Case #2 (33.W++" R+S, C&
CHAPTER 31 CASE C-23
The cash flow to start the proLect is the '/-* million e8uipment cost and the '4 million re8uired for net wor2ing capital yielding a total cash outflow today of '/-4 million3 The research and de7elopment costs and the mar2eting test are sun2 costs3 5e can calculate the future cash flows on a nominal basis or a real basis3 6ince the depreciation is gi7en in nominal 7alues we will calculate the cash flows in nominal terms3 The same solution can be found using real cash flows3 6ince the price and 7ariable costs increase by / percent and the inflation rate is 13. percent the nominal growth in both 7ariables is: (/ # R) (/ # r )(/ # h) R H(/3*/)(/3*1.)I % / R 3*,+ or ,3+? To analye this proLect we must calculate the incremental cash flows generated by the proLect3 5e will calculate the real cash flows although using nominal cash flows will result in the same NM3 The sales of new automobiles will grow by 3. percent per year and there are four tires per car3 6ince the company e&pects to capture // percent of the mar2et the number of tires sold in the OED mar2et will be:
Automobiles sold Tires for automobiles sold 6uperTread tires sold
"ear #
"ear $
"ear %
"ear &
-*****
-1..***
-./1+0.
--0-0
,+*****
.,****
-*...**
-0*-+++
0+***
04-**
+--/*.
4100.+
The number of tires sold in the replacement mar2et will grow at percent per year and Joodwee2 will capture + percent of the mar2et3 6o the number of tires sold in the replacement mar2et will be:
Total tires sold in mar2et 6uperTread tires sold
"ear #
"ear $
"ear %
"ear &
1******
1-,****
114+**
114.+-.-
.-****
-//**
--1,,
0/--4
The tires will be sold in each mar2et at a different price3 The price will increase each year at the rate calculated earlier so the price each year will be:
"ear #
"ear $
"ear %
"ear &
OED
',/3**
',30-
',,3.4
',-3.*
9eplacement
'-3**
'-,3--
'-03,
'0*31/
Dultiplying the number of tires sold in each mar2et by the respecti7e price in that mar2et the re7enue each year will be:
OED mar2et 9eplacement mar2et Total
"ear #
"ear $
"ear %
"ear &
'///+,+***
'//4..1+1+
'/004*.0,
'/1-.4,0+-
/.+0****
/-++0.+
/04.0+0/+
/4/*/,.-*
'0*.-+***
'++1+/1--
'1*01-44
'10-*41,-
Now we can calculate the incremental cash flows each year3 5e will calculate the nominal cash flows3 $oing so we find: "ear #
"ear $
"ear %
"ear &
'0*.-+***
'++1+/1--
'1*01-44
'10-*41,-
/.11.***
/-1.1*/+.
/-14/.++
/-0-0.+
D2t3 and general costs
,1******
,,140.**
,.+,*,/4
,011*1
$epreciation
+-,***
14/+,***
04+,***
/44+,***
E!T
'./1.***
',/-4-+*
'-4-4*,.
'4--0.+-
Ta&
*.,*+**
/-.*0+0
0+./-/+
10*-0*1,
Net income
'1*+//**
',0-/+*+
',/000,0
'..-**../
OCF
'.1-0.**
'-14,.+*+
'-40-/,0
'0..+,../
9e7enue Mariable costs
Net wor2ing capital is a percentage of sales so the net wor2ing capital re8uirements will change e7ery year3 The net wor2ing capital cash flows will be: "ear #
"ear $
"ear %
"ear &
!eginning
'4******
',*.+.**
',1.0*.
',-/*.14,
Ending
,*.+.**
,1.0*.
,-/*.14,
%'1/.+.**
%'-0**.
%'+,+/+4
N5C cash flow
',-/*.14,
The boo2 7alue of the e8uipment is the original cost minus the accumulated depreciation3 The boo2 7alue of e8uipment each year will be:
!oo2 7alue of e8uipment
"ear #
"ear $
"ear %
"ear &
'/10/1-***
'404.***
'-44-+***
',44+,***
6ince the mar2et 7alue of the e8uipment is '., million the e8uipment is sold at a gain to boo2 7alue so the sale will incur the ta&es of: Ta&es on sale of e8uipment (',44+,*** % -.******)(3,*) %'-**-,** And the afterta& sal7age 7alue of the e8uipment is: Afterta& sal7age 7alue '-.****** % -**-,** Afterta& sal7age 7alue '.+441-**
CHAPTER 31 CASE C-25
6o the net cash flows each year including the operating cash flow net wor2ing capital and afterta& sal7age 7alue are:
)ime * /
Cash flow %'/-4****** *4**** -/01+*1
1 ,
--4/11+ /+*-+1.,.
6o the paybac2 period for the proLect is: aybac2 period 1 # '/+04.4 = '/+*-+1.,. aybac2 period 13/* years The discounted cash flows are:
)ime * / 1 ,
*iscounted cash flow %'/-4****** /4,040/+ ,0-,+,,. ,.++.0 /*4-/1*.
$iscounted paybac2 period 1 # '..4+--// = '/*4-/1*. $iscounted paybac2 period 13./ years The re8uired return for the proLect is in nominal terms so the profitability inde& is: rofitability inde& ('*4****=/3/1, # '-/01+*1=/3/1, # '--4/11+=/3/1,1 # '/+*-+1.,.=/3/1,,) = '/-4****** rofitability inde& /31/. The e8uation for "99 is: * %'/-4****** # '*4****=(/ # "99) # '-/01+*1=(/ # "99) # '--4/11+=(/ # "99) 1 # '/+*-+1.,.=(/ # "99) , Using a spreadsheet or financial calculator the "99 for the proLect is: "99 ,3*,? NM %'/-4****** # '*4****=/3/1, # '-/01+*1=/3/1, # '--4/11+=/3/1, 1 # '/+*-+1.,.=/3/1, , NM '.10,-4,30, "n the final analysis the company should accept the proLect since the NM is positi7e3
CHAPTER 7 B4 B+R, C The company is faced with the option of when to har7est the lumber3 5hate7er har7est cycle the company chooses it will follow that cycle in perpetuity3 6ince the forest was planted * years ago the options a7ailable in the case are ,*; ,.; .* and ..;year har7est cycles3 No matter what har7est cycle the company chooses it will always thin the timber * years after har7ests and replants3 The cash flows will grow at the inflation rate so we can use the real or nominal cash flows3 "n this case it is simpler to use real cash flows although nominal cash flows would yield the same result3 6o the real re8uired return on the proLect is: (/ # R) (/ # r )(/ # h) /3/* (/ # r )(/3*10) r 3*-*+ or -3*+? The conser7ation funds are e&pected to grow at a slower rate than inflation so the real return for the conser7ation fund will be: (/ # R) (/ # r )(/ # h) /3/* (/ # r )(/3*1) r 3*-.4 or -3.4? The company will thin the forest today regardless of the har7est schedule so this first thinning is not an incremental cash flow but future thinning is part of the analysis since the thinning schedule is determined by the har7est schedule3 The cash flow from the thinning process is: Cash flow from thinning Acres thinned G Cash flow per acre Cash flow from thinning .***('/***) Cash flow from thinning '.****** The real cost of the conser7ation fund is constant but the e&pense will be ta& deductible so the afterta& cost of the conser7ation fund will be: Afterta& conser7ation fund cost (/ % 31.)('.****) Afterta& conser7ation fund cost '/-.** For each analysis the re7enue and costs are: 9e7enue H∑ (? of grade)(har7est per acre)(7alue of board grade)I(acres har7ested)(/ % defect rate) Tractor cost (Cost D!F)(D!F per acre)(acres) 9oad cost (Cost D!F)(D!F per acre)(acres) 6ale preparation and administration (Cost D!F)(D!F acre)(acres)
CHAPTER 31 CASE C-27
E&ca7ator piling broadcast burning site preparation and planting costs are the cost of each per acre times the number of acres3 These costs are the same no matter what the har7est schedule since they are based on acres not D!F3
Now we can calculate the cash flow for each har7est schedule3 One important note is that no depreciation is gi7en in the case3 6ince the har7est time is li2ely to be short the assumption is that no depreciat depreciation ion is attributa attributable ble to the har7est3 This implies implies that operating operating cash flow is e8ual to net income3 Now we can calculate the NM of each har7est schedule3 The NM of each har7est schedule is the NM of the first har7est the NM of the thinning the NM of all future har7ests minus the present 7alue of the conser7ation conser7ation fund costs3 costs3 &+,!ear har-est schedule:
9e7enue
',*1.4/1.
Tractor cost
4+0****
9oad
1..***
6ale preparation K admin
/-4***
E&ca7ator piling !roadcast burning 6ite preparation lanting costs
0.**** /.***** 0.*** //.***
E! E !" T
'/.4./1.
Ta Ta&es
0..+40
Net income (OCF)
'/,*1-+1+
The M of the first har7est in * years is: MFirst '/,*1-+1+=(/ # 3*-*+) * MFirst ',1/.*4+ Thinning will also occur on a ,*;year schedule with the ne&t thinning ,* years from today3 The effecti7e ,*;year interest rate for the proLect is: ,*;year proLect interest rate H(/ # 3*-*+) ,*I % / ,*;year proLect interest rate 4.+3/0? 5e also need the ,*;year interest rate for the conser7ation fund which will be: ,*;year conser7ation interest rate H(/ # 3*-.4) 3 *-.4) ,*I % / ,*;year conser7ation interest rate //+13+0? 6ince we ha7e the cash flows from each thinning and the ne&t thinning will occur in ,* years we can find the present 7alue of future thinnings on this schedule which will be: MThinning '.******=43.+/0 '.******=43.+/0 MThinning './+.3+*
CHAPTER 31 CASE C-29
The operating cash flow from each har7est on the ,*;year schedule is '/,*1-+1+ so the present 7alue of the cash flows from the har7ests are: Mar7est H('/,*1-+1+=43.+/0)I = (/ # 3*-*+) 3 *-*+) * Mar7est ',.*1,.34, Now we can find the present 7alue of the conser7ation fund deposits3 The present 7alue of these deposits is at @ear * is: MConser7ation %'/-.** % '/-.**=//3+1+0 MConser7ation %'/0--3 And the 7alue today is: MConser7ation %'/0--3=(/ # 3*-.4) * MConser7ation %',4/+3. 6o the NM of a ,*;year har7est schedule is: NM ',1/.*4+ # ./+.3+* ./+.3+* # ,.*1,.34, ,.*1,.34, % ,4/+3. NM '.1+*+03-1 &',!ear har-est schedule:
9e7enue Tractor cost
',0*./-** //,+****
9oad
,/*****
6ale preparation K admin
/,0-***
E&ca7ator piling !roadcast burning 6ite preparation lanting costs
0.**** /.***** 0.*** //.***
E! E !" T
'.+4.-**
Ta Ta&es
4*-1,-*
Net income (OCF)
'/-+1/,*
The M of the first har7est in . years is: MFirst '/-+1/,* = (/ # 3*-*+) . MFirst '1+.41* Thinning will also occur on a ,.;year schedule with the ne&t thinning ,. years from today3 The effecti7e ,.;year interest rate for the proLect is: ,.;year proLect interest rate H(/ # 3*-*+) ,.I % / ,.;year proLect interest rate /1/3//?
5e also need the ,.;year interest rate for the conser7ation fund which will be: ,.;year conser7ation interest rate H(/ # 3*-.4) 3 *-.4) ,.I % / ,.;year conser7ation interest rate /---31+? 6ince we ha7e the cash flows from each thinning and the ne&t thinning will occur in ,. years we can find the present 7alue of future thinnings on this schedule which will be: MThinning '.******=/13/// MThinning '10+,0*3,The operating cash flow from each har7est on the ,.;year schedule is '/-+1/,* so the present 7alue of the cash flows from the har7ests are: Mar7est H('/-+1/,*=/13////)I = (/ # 3*-*+) . Mar7est '4/-,,3*, Now we can find the present 7alue of the conser7ation fund deposits3 The present 7alue of these deposits at @ear . is: MConser7ation %'/-.** % '/-.**=/-3--1+ MConser7ation %'/0./3-0 And the 7alue today is: MConser7ation %'/0./3-0=(/ # 3*-.4) . MConser7ation %'1,4,/30 6o the NM of a ,.;year har7est schedule is: NM '1+.41* # 10+,0*3,10+,0*3,- # 4/-,,3*, 4/-,,3*, % 1,4,/30 NM ',,++/*13* '+,!ear har-est schedule:
9e7enue Tractor cost
',4-44,,* ///****
9oad
,1.***
6ale preparation K admin
/..0***
E&ca7ator piling !roadcast burning 6ite preparation lanting costs
0.**** /.***** 0.*** //.***
E! E !" T
'0-*0,,*
Ta Ta&es
4---*,
Net income (OCF)
'/04,,+1-
CHAPTER 31 CASE C-31
The M of the first har7est in 1* years is: MFirst '/04,,+1-=(/ # 3*-*+) 1* MFirst '1*.+.41 Thinning will also occur on a .*;year schedule with the ne&t thinning .* years from today3 The effecti7e .*;year interest rate for the proLect is: .*;year proLect interest rate H(/ # 3*-*+) .*I % / .*;year proLect interest rate /+*+3.? 5e also need the .*;year interest rate for the conser7ation fund which will be: .*;year conser7ation interest rate H(/ # 3*-.4) .*I % / .*;year conser7ation interest rate 11*3,? 6ince we ha7e the cash flows from each thinning and the ne&t thinning will occur in .* years we can find the present 7alue of future thinnings on this schedule which will be: MThinning '.******=/+3*+. MThinning '0-,-431, The operating cash flow from each har7est on the .*;year schedule is '/04,,+1- so the present 7alue of the cash flows from the har7ests are: Mar7est H('/04,,+1-=/+3*+.I = (/ # 3*-*+) 1* Mar7est '/-4//3, Now we can find the present 7alue of the conser7ation fund deposits3 The present 7alue of these deposits is at @ear 1* is: MConser7ation %'/-.** % '/-.**=131*, MConser7ation %'/-4,013.1 And the 7alue today is: MConser7ation %'/-4,013.1=(/ # 3*-.4) 1* MConser7ation %',4+-3+4 6o the NM of a .*;year har7est schedule is: NM '1*.+.41 # 0-,-431, # /-4//3, % ,4+-3+4 NM '1,04/4-3,.
'',!ear har-est schedule:
9e7enue Tractor cost
/-0****
9oad
,..***
6ale preparation K admin
/-4***
E&ca7ator piling !roadcast burning 6ite preparation lanting costs
'.*.0+-1
0.**** /.***** 0.*** //.***
E!"T
'4/11+-1
Ta&es
/*/4-+.
Net income (OCF)
'/+410*//
The M of the first har7est in 1. years is: MFirst '/+410*//=(/ # 3*-*+) 1. MFirst ',*11++ Thinning will also occur on a ..;year schedule with the ne&t thinning .. years from today3 The effecti7e ..;year interest rate for the proLect is: ..;year proLect interest rate H(/ # 3*-*+) ..I % / ..;year proLect interest rate ,-13/*? 5e also need the ..;year interest rate for the conser7ation fund which will be: ..;year conser7ation interest rate H(/ # 3*-.4) ..I % / ..;year conser7ation interest rate 1,13-*? 6ince we ha7e the cash flows from each thinning and the ne&t thinning will occur in .. years we can find the present 7alue of future thinnings on this schedule which will be: MThinning '.******=,3-1/* MThinning '*44.340 The operating cash flow from each har7est on the ..;year schedule is '/+410*// so the present 7alue of the cash flows from the har7ests are: Mar7est H('/+410*//=,3-1/*I = (/ # 3*-*+) 1. Mar7est '40.0.3- Now we can find the present 7alue of the conser7ation fund deposits3 The present 7alue of these deposits is at @ear 1. is: MConser7ation %'/-.** % '/-.**=13,1-* MConser7ation %'/-0.*43+0
CHAPTER 31 CASE C-33
And the 7alue today is: MConser7ation %'/-4.*43+0=(/ # 3*-.4) 1. MConser7ation %'/04.*3++ 6o the NM of a ..;year har7est schedule is: NM ',*11++ # *44.340 # 40.0.3- % /04.*3++ NM '-+-**+3+. The company should use a ,*;year har7est schedule since it has the highest NM3 Notice that when the NM began to decline it continued declining3 This is e&pected since the growth in the trees increases at a decreasing rate3 6o once we reach a point where the increased growth cannot o7ercome the increased effects of compounding har7esting should ta2e place3 There is no point further in the future which will pro7ide a higher NM3
CHAPTER 8 6C( +S C3S 4C-7S +8PS3 PS W- B3. SS+ A rule of thumb with bond pro7isions is to determine who the pro7isions benefit3 "f the company benefits the bond will ha7e a higher coupon rate3 "f the bondholders benefit the bond will ha7e a lower coupon rate3
1&
a.
A bond with collateral will ha7e a lower coupon rate3 !ondholders ha7e the claim on the collateral e7en in ban2ruptcy3 Collateral pro7ides an asset that bondholders can claim which lowers their ris2 in default3 The downside of collateral is that the company generally cannot sell the asset used as collateral and they will generally ha7e to 2eep the asset in good wor2ing order3
b.
The more senior the bond is the lower the coupon rate3 6enior bonds get full payment in ban2ruptcy proceedings before subordinated bonds recei7e any payment3 A potential problem may arise in that the bond co7enant may restrict the company from issuing any future bonds senior to the current bonds3
c.
A sin2ing fund will reduce the coupon rate because it is a partial guarantee to bondholders3 The problem with a sin2ing fund is that the company must ma2e the interim payments into a sin2ing fund or face default3 This means the company must be able to generate these cash flows3
2&
d.
A pro7ision with a specific call date and prices would increase the coupon rate3 The call pro7ision would only be used when it is to the companys ad7antage thus the bondholders disad7antage3 The downside is the higher coupon rate3 The company benefits by being able to refinance at a lower rate if interest rates fall significantly that is enough to offset the call pro7ision cost3
e.
A deferred call would reduce the coupon rate relati7e to a call pro7ision without a deferred call3 The bond will still ha7e a higher rate relati7e to a plain 7anilla bond3 The deferred call means that the company cannot call the bond for a specified period3 This offers the bondholders protection for this period3 The disad7antage of a deferred call is that the company cannot call the bond during the call protection period3 "nterest rates could potentially fall to the point where it would be beneficial for the company to call the bond yet the company is unable to do so3
f.
A ma2e;whole call pro7ision should lower the coupon rate in comparison to a call pro7ision with specific dates since the ma2e;whole call repays the bondholder the present 7alue of the future cash flows3 owe7er a ma2e;whole call pro7ision should not affect the coupon rate in comparison to a plain 7anilla bond3 6ince the bondholders are made whole they should be indifferent between a plain 7anilla bond and a ma2e;whole bond3 "f a bond with a ma2e;whole pro7ision is called bondholders recei7e the mar2et 7alue of the bond which they can rein7est in another bond with similar characteristics3 "f we compare this to a bond with a specific call price in7estors rarely recei7e the full mar2et 7alue of the future cash flows3
g.
A positi7e co7enant would reduce the coupon rate3 The presence of positi7e co7enants protects bondholders by forcing the company to underta2e actions that benefit bondholders3 E&les of positi7e co7enants would be: the company must maintain audited financial statementsB the company must maintain a minimum specified le7el of wor2ing capital or a minimum specified current ratioB the company must maintain any collateral in good wor2ing order3 The negati7e side of positi7e co7enants is that the company is restricted in its actions3 The positi7e co7enant may force the company into actions in the future that it would rather not underta2e3
h.
A negati7e co7enant would reduce the coupon rate3 The presence of negati7e co7enants protects bondholders from actions by the company that would harm the bondholders3 9emember the goal of a corporation is to ma&imie shareholder wealth3 This says nothing about bondholders3 E&les of negati7e co7enants would be: the company cannot increase di7idends or at least increase beyond a specified le7elB the company cannot issue new bonds senior to the current bond issueB the company cannot sell any collateral3 The downside of negati7e co7enants is the restriction of the companys actions3
i.
E7en though the company is not public a con7ersion feature would li2ely lower the coupon rate3 The con7ersion feature would permit bondholders to benefit if the company does well and also goes public3 The downside is that the company may be selling e8uity at a discounted price3
j3
The downside of a floating rate coupon is that if interest rates rise the company has to pay a higher interest rate3 owe7er if interest rates fall the company pays a lower interest rate3
6ince the coupon bonds will ha7e a coupon rate e8ual to the @TD they will sell at par3 6o the number of coupon bonds to sell will be: (NOTE: The te&t has a typo3 The coupon rate on the coupon bonds should be 03. percent3) Coupon bonds to sell '.******* = '/*** .****
CHAPTER 31 CASE C-35
The price of the *;year ero coupon bond when it is issued will be: ero coupon price '/*** = /3*10. ,* '431, 6o the number of ero coupon bonds the company will need to sell is: ero coupon bonds to sell '.******* = '431, /+*/'&
At maturity the principal payment for the coupon bonds will be: Coupon bond principal payment at maturity .****('/***) '.******* The principal payment for the ero coupon bonds at maturity will be: ero coupon bond payment at maturity /+*/-('/***) '/+*/-***
)&
One of the main considerations is timing of the cash flows3 The annual coupon payment on the coupon bonds will be: Annual coupon bond payments .****('/***)(3*-.) '1.**** 6ince the interest payments are ta& deductible the afterta& cash flow from the interest payments will be: Afterta& coupon payments '1.****(/ % 31.) '//.** E7en though interest payments are not actually made each year the implied interest on the ero coupon bonds is ta& deductible3 The 7alue of the ero coupon bonds ne&t year will be: Malue of ero in one year '/***=/3*10. 1+ ',-3+6o the growth on the ero coupon bond was: ero coupon growth ',-3+- % 431, '/03. This increase in 7alue is ta& deductible so it reduces ta&es e7en though there is no cash flow for interest payments3 6o there is a positi7e cash flow created ne&t year in the amount of: ero cash flow /+*/-('/03.)(31.) '/11-4431 This cash flow will increase each year since the 7alue of the ero coupon bond will increase by a greater dollar amount each year3
5&
"f the Treasury rate is ,3+* percent the ma2e;whole call price in 0 years is: '103.*(/ % H/=(/ # 3*-)I- = 3*-) # '/***H/ = (/ # 3*-) -I '//.31+ And if the Treasury rate is +3* percent the ma2e;whole call price in 0 years is: '103.*(/ % H/=(/ # 3*,1)I- = 3*,1) # '/***H/ = (/ # 3*,1) -I '4/,34*
*&
The in7estor is not necessarily made whole with the ma2e;whole call pro7ision but is made close to whole3 Assume a company issues a bond with a ma2e;whole call of the Treasury rate plus 3. percent3 Further assume this is the correct a7erage spread for the companys bond o7er the life of the bond3 Although the spread is correct on a7erage it is not correct at e7ery specific time3 The spread o7er the Treasury rate 7aries o7er the life of the bond and is higher when the bond has a longer time to maturity3 To see this consider at the e&treme the spread for any bond abo7e the Treasury yield at maturity is ero3 6o if the bond is called early in its life the spread abo7e the Treasury is li2ely to be too low3 This means the in7estor is more than made whole3 "f the bond is called late in its life the spread is too high3 This means the interest rate used to calculate the present 7alue of the cash flows is too high which results in a lower present 7alue3 Thus the bondholder is made less than whole3 "n practical terms this difference is li2ely to be small and it will almost always result in a higher price paid to the bondholder when compared to a traditional call feature3
CHAPTER 31 CASE C-37
9&
There is no definiti7e answer to which type of bond the company should issue3 "f the intermediate cash flows for the coupon payments will be difficult a ero coupon bond is li2ely to be the best solution3 owe7er the ero coupon bond will re8uire a larger payment at maturity3 As for the type of call pro7ision a ma2e;whole call pro7ision is generally better for bondholders therefore the coupon rate of the bond will li2ely be lower to sell the bond at par 7alue3 Again there is a tradeoff3
CHAPTER 9 S3C" 3 R( -+R S4S+S 1&
The total di7idends paid by the company were '-,****3 6ince there are 1***** shares outstanding the total earnings for the company were: Total earnings 1*****('.31.) '/-*.*** This means the payout ratio was: ayout ratio '-,****='/-*.*** 314++ or 143++? 6o the retention ratio was: 9etention ratio / % 314++ 3-*/ or -*3/? Using the retention ratio the companys growth rate is: g 9OE G b 3/(3-*/) 3/-1 or /3-1?
Now we can 7alue the company using the entire di7idend payment3 The total 7alue of the companys e8uity under these assumptions is: Total e8uity 7alue $ / = (9 % g) Total e8uity 7alue '-,****(/3/-1) = (3/+ % 3/-1) Total e8uity 7alue '/1,/1+-346o the 7alue per share is: Malue per share '/1,/1+-34- = 1***** Malue per share ',,30/ 2&
6ince Nautilus Darine Engines had a write off which affected its earnings per share we need to recalculate the industry E63 6o the industry E6 is:
"ndustry E6 ('/3/4 # /3- # 3*0) = 1 '/3./ Using this industry E6 the industry payout ratio is: "ndustry payout ratio '3,,='/3./ 3+4+ or +34+?
CHAPTER 31 CASE C-39
6o the industry retention ratio is "ndustry retention ratio / % 3+4+ 30/* or 0/3*? This means the industry growth rate is: "ndustry g 3//(30/*) 3*0+/ or 03+/? The company will continue to grow at its current pace for fi7e years before slowing to the industry growth rate3 6o the total di7idends for each of the ne&t si& years will be: $/ $ $1 $, $. $-
'-,****3**(/3/-1) '0*+*03,+ '0*+*03,+(/3/-1) '+//+/03+, '+//+/03+,(/3/-1) '4/,1/4311 '4/,1/4311(/3/-1) '/*40-3+ '/*40-3+(/3/-1) '//.40+3,/ '//.40+3,/(/3*0+/) '/.*1+,3**
The total 7alue of the stoc2 in @ear . with the industry re8uired return will be: 6toc2 7alue in @ear . '/.*1+,3** = (3/. % 3*0+/) '/014.1*+34 This means the total 7alue of the stoc2 today is: Malue of stoc2 today '0*+*03,+=/3/. # '+//+/03+,=/3/. # '4/,1/4311=/3/.1 # '/*40-3+=/3/., # ('//.40+3,/ # /014.1*+34) = /3/. . Malue of stoc2 today '//-..0,43,+ And the 7alue per share of the stoc2 today is: Malue per share '//-..0,43,+ = 1***** Malue per share '1+3+. '&
Using the re7ised industry E6 the industry E ratio is: "ndustry E '/+3*+ = '/3./ /3** Using the original stoc2 price assumption 9agans E ratio is: 9agan E (original assumptions) ',,30/ = '.31. +31Using the re7ised assumptions 9agans E '1+3+. = '.31. 03Ob7iously 9agans E is lower than the industry a7erage3 Ji7en that the growth rate for the company is higher than the industry this is une&pected3 The reason is that the company pays out a higher di7idend than the industry3
)&
ere we must ma2e an assumption3 5e ha7e two estimates of the re8uired return3 6ince we are assuming the growth rate follows the growth rate assumption in >uestion we will use the industry a7erage re8uired return assumed in that 8uestion as well3 The total earnings of the company which would be paid out as a di7idend as a cash cow are: Total earnings (/.**** shares)('.31.) Total earnings '/-*.*** 6o the 7alue of 9agan as a cash cow is: Cash cow 7alue '/-*.*** = 3/. '/*0***** The total stoc2 7alue with growth from >uestion is '//-..0,43,+ so the percentage of the 7alue of the company not attributable to growth opportunities is: ercentage of 7alue not attributable to growth opportunities '/*0***** = '//-..0,43,+ 34/+* 6o the percentage of the companys 7alue attributable to growth opportunities is: ercentage of 7alue attributable to growth opportunities / % 34/+* 3*+* or +3*?
5&
Again we will assume the results in >uestion are correct3 The growth rate of the company we calculated in this 8uestion was the industry growth rate of 03+/ percent3 6ince the growth rate is: g 9OE G b
"f we assume the payout ratio remains constant the 9OE is: 3*0+/ 9OE(3-*/) 9OE 3/44 or /344? *&
The most ob7ious solution is to retain more of the companys earnings and in7est in profitable opportunities3 This strategy will not wor2 if the return on the companys in7estment is lower than the re8uired return on the companys stoc23
CHAPTER 10 A JOB AT EAST COAST YACHTS 1&
The biggest ad7antage the mutual funds ha7e is instant di7ersification3 The mutual funds ha7e a number of assets in the portfolio3
2&
!oth the A9 and EA9 are infinite3 The match is instantaneous so the number of periods in a year is infinite3
CHAPTER 31 CASE C-41
'&
The ad7antage of the acti7ely managed fund is the possibility of outperforming the mar2et which the fund has done on a7erage o7er the past ten years3 The maLor disad7antage is the li2elihood of underperforming the mar2et3 "n general most mutual funds do not outperform the mar2et for an e&tended period of time and finding the funds that will outperform the mar2et in the future beforehand is a daunting tas23 One factor that ma2es outperforming the mar2et e7en more difficult is the management fee charged by the fund3
,3
The returns are the most 7olatile for the small cap fund because the stoc2s in this fund are the ris2iest3 This does not imply the fund is bad Lust that the ris2 is higher and therefore the e&pected return is higher3 @ou would want to in7est in this fund if your ris2 tolerance is such that you are willing to ta2e on the additional ris2 in e&pectation of a higher return3 The higher e&penses of the fund are e&pected3 "n general small cap funds ha7e higher e&penses in large part due to the greater cost of running the fund including researching smaller stoc2s3
5&
The 6harpe ratio for each of the mutual funds and the company stoc2s are: !ledsoe 6K .** "nde& Fund (43/+? % 13) = *3,1? 340 !ledsoe 6mall;Cap Fund (/,3/? % 13) = .3/1? 3,1,. !ledsoe arge Company 6toc2 Fund (+3.+? % 13) = 13+? 3.4 !ledsoe !ond Fund (-3,.? % 13) = 43+.? 3144 East Coast @achts 6toc2 (/-? % 13) = -.? 3/4-4 The 6harpe ratio is most applicable for a di7ersified portfolio and is least applicable for the company stoc23
*&
This is a 7ery open;ended 8uestion3 The asset allocation depends on the ris2 tolerance of the indi7idual3 owe7er most students will be young so in this case the portfolio allocation should be more hea7ily weighted toward stoc2s3 "n any case there should be little if any money allocated to the company stoc23 The principle of di7ersification indicates that an indi7idual should hold a di7ersified portfolio3 "n7esting hea7ily in company stoc2 does not create a di7ersified portfolio3 This is especially true since income comes from the company as well3 "f times get bad for the company employees face layoffs or reduced wor2 hours3 6o not only does the in7estment perform poorly but income may be reduced as well3 5e only ha7e to loo2 at employees of Enron or 5orldCom to see the potential for problems with in7esting in company stoc23 At most . to /* percent of the portfolio should be allocated to company stoc23 Age is a determinant in the decision3 Older indi7iduals should be less hea7ily weighted toward stoc2s3 A commonly used rule of thumb is that an indi7idual should in7est /** minus their age in stoc2s3 Unfortunately this rule of thumb tends to result in an underin7estment in stoc2s3
CHAPTER 11 A JOB AT EAST COAST YACHTS, PART 2 1&
There should be little if any money allocated to the company stoc23 The principle of di7ersification indicates that an indi7idual should hold a di7ersified portfolio3 "n7esting hea7ily in company stoc2 does not create a di7ersified portfolio3 This is especially true since income also comes from the company3 "f times get bad for the company employees face layoffs or reduced wor2 hours3 6o not only does the in7estment perform poorly but income may be reduced as well3 5e only ha7e to loo2 at employees of Enron or 5orldCom to see the potential for problems with in7esting in company stoc23 At most . to /* percent of the portfolio should be allocated to company stoc23
2&
This is not the portfolio with the least ris23 !y adding stoc2s a ris2ier asset the o7erall ris2 of the portfolio will decline3 This will be demonstrated in the ne&t 8uestions3
'&
5e can use the e8uations for the e&pected return of the portfolio and the portfolio standard de7iation that is: E(9 ) / EE(9 E) # / $E(9 $)
σ ( / E σ E # / $ σ $ # / E / $σEσ$ρ$E)/= Using these e8uations and e8uity portfolio weights from ero to /** percent at inter7als of /* percent we get the following portfolio e&pected returns and standard de7iations:
CHAPTER 31 CASE C-43
5eight of stoc2 fund *? /*? *? 1*? ,*? .*? -*? 0*? +*? 4*? /**?
ortfolio E(9) -3,.? -3--? -3++? 03*4? 031*? 03.? 0301? 034,? +3/.? +310? +3.+?
ortfolio standard de7iation 43+.**? 43./+? 43+**-? /*3-,+,? //34,/0? /13..1-? /.31+,1? /031-,+? /43,,41? /3-*00? 13+**?
The graph of the opportunity set of feasible portfolios will loo2 li2e the following:
Investment Opportunity Set 10% 9% 8% 7% 6%
Portfolio Expected Return
5% 4% 3% 2% 1% 0% 8% 10% 12% 14% 16% 18% 20% 22% 24% 26%
Portfolio Standard Deviation
)&
Now we can use 6ol7er to ma&imie this e&pression by changing the weight of the e8uity input cell3 The constraint is that the standard de7iation of the portfolio is e8ual to the standard de7iation of the bond fund3 Using 6ol7er the weight of the large cap stoc2 fund and bond fund in this portfolio is: / E 3*+ / $ 304/+
6o the e&pected return and standard de7iation of this portfolio is: E(9) 3*+(3*+.+) # 304/+(3*-,.) E(9) 3*-+4 or -3+4?
σ H3*+(31+) # 304/+(3*4+.) # (3*+)(304/+)(31+)(3*4+.)(3/.)I /= σ 3*4+. or 43+.? This is the e&act same standard de7iation as the bond fund but the e&pected return is about one;half percent higher3
CHAPTER 31 CASE C-45
5&
To find the weights of each asset in the minimum 7ariance portfolio we begin with the e8uation for the 7ariance of the portfolio3 Using 6 to represent the large company fund and ! to represent the bond fund the 7ariance of a portfolio of two assets e8uals:
σ : / 6 σ 6 # / ! σ ! # / 6 / !ρ6! 6ince the weights of the assets must sum to one we can write the 7ariance of the portfolio as:
!
σ : / 6 σ 6 # (/ % / 6)σ
# / 6(/ % / 6)σ6σ!ρ6!
To find the minimum for any function we find the deri7ati7e and set the deri7ati7e e8ual to ero3 Finding the deri7ati7e of the 7ariance function setting the deri7ati7e e8ual to ero and sol7ing for the weight of the stoc2 fund we find:
dW p=d / 6 / 6σ 6 % (/ % / 6 )W! # W6W! ρ6! % , / 6W6W!ρ6! * 6ol7e for / 6 to get:
/ 6 (σ ! % σ6σ!ρ6!) = (σ 6 # σ ! % σ6σ!ρ6!)
Using this e&pression we find the weight of the stoc2 fund must be: / 6 H3*4+. % (31+)(3*4+.)(3/.)I = H31+ # 3*4+. % (31+)(3*4+.)(3/.)I / 6 3/*,/
This implies the weight of the bond fund is: / ! / % / 6 / ! / % 3/*,/ / ! 3+4.4
The e&pected return of this portfolio is: E(9) 3/*,/(3*+.+) # 3+4.4(3*-,.) E(9) 3*--0 or -3-0? The 7ariance of the portfolio is:
σ : / 6 σ 6 # / ! σ ! # / 6 / !σ6σ!ρ6!
σ : (3/*,/)(31+) # (3+4.4)(3*4+.) # (3/*,/)(3+4.4)(31+)(3*4+.)(3/.)
σ : 3**4*.4 And the standard de7iation is:
σ 3**4*.4/= σ 3*4. or 43.?
CHAPTER 31 CASE C-47
5ith these returns and 7ariances the minimum 7ariance portfolio is important because no in7estor would e7er hold a portfolio with a greater weight in bonds3 "f an in7estor increases the weight of bonds in the portfolio the ris2 of the portfolio increases and the e&pected return decreases3 The result is illustrated in >uestion ,3 *&
5e can find the 6harpe optimal portfolio by using 6ol7er3 To use 6ol7er we input the 6harpe ratio in a cell3 The 6harpe ratio is:
E(9) − 9 f W:
6harpe ratio
5e also need to recognie that the weight of debt in the portfolio is one minus the weight of e8uity3 6ubstituting the e8uations for the e&pected return of the portfolio and the standard de7iation of the portfolio we get: / E E(9 E ) + (/ − / E )E(9 $ ) − 9 f
6harpe ratio
( / E W E
+
(/ − / E ) W $
+
/ E (/ − / E )W E W $ X E$ )
/=
Now we can use 6ol7er to ma&imie this e&pression by changing the weight of e8uity input cell3 $oing so we find the weight of e8uity in the 6harpe optimal portfolio is /430- percent3 This 8uestion can also be sol7ed directly3 The goal is to ma&imie the 6harpe ratio so we can use the e&pression for the 6harpe ratio set the deri7ati7e e8ual to ero and sol7e for the weight of e8uity (or debt)3 $oing so the resulting e&pression for the weight of e8uity in the 6harpe optimal portfolio is: HE(9 E ) − 9 f IW $
/ E
HE(9 E ) − 9 f IW $
+
−
HE(9 $ ) − 9 f IW E
HE(9 $ ) − 9 f IW E W $ X E$ −
HE(9)E
−
9 f
+
E(9) $
−
9 f IW E W $ X E$
Using this e8uation we find the weight of e8uity in the 6harpe optimal portfolio is: / E
H3*+.+ − 3*1I3*4+. H3*+.+ − 3*1*I3*4+ .
+
H3*-,. − 3*1*I(31 +)(3*4+.) (3/.)
H3*-,. − 3*1/*I31+
/ E 3/40-
and the weight of debt is: / $ / % 3/40 / $ 3+*,
−
−
H3*+.+ − 3*1* + 3*-,. − 3*1*I(31 +)(3*4+.) (3/.)
6o the e&pected return and standard de7iation of the 6harpe optimal portfolio is: E(9) 3/40-(3*+.+) # 3+*,(3*-,.) E(9) 3*-+0 or -3+0?
σ H3/40-(31+) # 3+*,(3*4+.) # (3/40-)(31+)(3+*,)(3*4+.)(3/.)I /= σ 3*404 or 4304? The 6harpe ratio of the 6harpe optimal portfolio is:
3*-+0 − 3*1* 6harpe ratio
3*404
6harpe ratio 310./ The 6harpe optimal portfolio is the best ris2y portfolio for all in7estors because it deli7ers a greater reward;to;ris2 ratio than any other portfolio3 "f a line is drawn from the ris2;free rate to the 6harpe optimal portfolio it shows the best combination of portfolios a7ailable to an y in7estor3 "n7estors can change the le7el of ris2 by altering the percentage of their in7estment in the ris2;free asset and the 6harpe optimal portfolio3 This line is the 6ecurity Dar2et ine3
CHAPTER 12 THE FAMA-FRENCH MULTI-FACTOR MODEL AND MUTUAL FUND RETURNS 01)2: )he e3ample below shows the results for returns between 1ctober $+#+ and 4eptember $+#'. )he actual answer to the case will change based on current market conditions. 1&
For a large;company stoc2 fund we would e&pect the beta for the mar2et ris2 premium to be near one since large company returns account for a large part of the total mar2et return on a mar2et;7alue basis3 5e would e&pect the betas for the 6D! and D ris2 factors to be low and possibly negati7e since large company stoc2 returns are not highly related to small company stoc2 returns and large company stoc2s tend to be more oriented toward 7alue stoc2s3
2&
The following shows the results of the regression estimates for the period between October */* and 6eptember */.3 The actual answer to the case will change based on current mar2et returns3 5idelit! Magellan:
Regression 4tatistics *340--14 Dultiple 9 , 9 68uare *34.1*++-
CHAPTER 31 CASE C-49
AdLusted 9 68uare 6tandard Error Obser7ations
/ *34.*.0./1 1 *3**+0/,.1 -*
ANOMA 9egression 9esidual Total
"ntercept D2t;9F 6D! D
df
1 ..4
44 *3*+-,* *3**,. *3*4*--
Coefficients ;*3**//3*++/*3*-4/ ;*3/1*-
4tandard 2rror *3**/* *3*1.,*3*.01*3*-1//
M4 *3*++* *3****+
t 4tat ;/3040,. 1*3-4*4* /3*4-0* ;3*4-,
4ignificanc 5 e 5 1043,1-4 13-4,+E;10
,-alue *3*00-*3***** *300,0 *3*,*4
5idelit! 6ow,riced 4tock 5und:
Regression 4tatistics Dultiple 9 *340*4, 9 68uare *34,01 AdLusted 9 68uare *3414-0 6tandard Error *3**+-+ Obser7ations -*3*****
ANOMA 9egression 9esidual Total
"ntercept D2t;9F 6D! D
df 13***** .-3***** .43*****
44 *3*-414 *3**, *3*01-/
Coefficient s *3***-. *34.0, *3//, *3*41./
4tandard 2rror *3**//4 *3*1.1* *3*.0// *3*-+1
M4 *3*1/1 *3****+
4ignificanc 5 e 5 1*0341*/ *3*****
t 4tat *3.,1+1 03/14, /34-..* /3,++10
,-alue *3.++0/ *3***** *3*.,1 *3/,-
Baron 4mall Cap 5und:
Regression 4tatistics Dultiple 9 *34-.+, 9 68uare *341+, AdLusted 9 68uare *344, 6tandard Error *3*//,0 Obser7ations -*3*****
ANOMA 9egression 9esidual Total
"ntercept D2t;9F 6D!
df 13***** .-3***** .43*****
44 *3/*14 *3**010 *3/*40-
Coefficient s ;*3**/,0 /3*/,., *3.+-1*
4tandard 2rror *3**/.+ *3*,--+ *3*0..
M4 *3*1,/1 *3***/1
t 4tat ;*344-0 /301,01 030-104
4ignificance 5 5 .43+1-0 *3*****
,-alue *31.-.1 *3***** *3*****
6ower 7'8 ;*3**,-1 *34/*1 *3,1.*
CHAPTER 31 CASE C-51
D
;*3/1.
*3*+1*+
;/3,0--
*3/,-,,
;*3++0+
'&
This answer will depend on the returns used by the students3
)&
"f the mar2et is efficient all assets should ha7e an alpha of ero3 "n this case none of the three funds has a statistically significant positi7e alpha at the . percent le7el so the e7idence pro7ided here against mar2et efficiency is limited3
5&
Once adLusting for ris2 we cannot say any of these three funds performed better since all three alphas are not significantly different from ero at the . percent le7el of confidence although the alpha for the Fidelity Dagellan Fund is significantly negati7e at the /* percent le7el so it may ha7e had the worst performance gi7en its le7el of ris23
CHAPTER 13 COST OF CAPITAL FOR SWAN MOTORS 01)2: )he e3ample below shows the results during 0o-ember $+#$. )he actual answer to the case will change based on current market conditions. 1&
The boo2 7alue of the companys liabilities and e8uity can be found from a number of sources3 5e went to http:==www3sec3go7 and found Teslas Form /*8 dated 6eptember 1* */.3 Teslas Form /*8 showed the following:
The boo2 7alue of e8uity is '/1/. million on the balance sheet3 owe7er for a more current boo2 7alue we multiplied the number of shares outstanding by the boo2 7alue per share on @ahooY Finance3 For the boo2 7alue of debt we used the following note in the /*8:
"n the notes the company issued '+** million of */4 bond the issued another '/* million3 For the */ bond the company initially issued '/3 billion the issued another '/+* million3 The total numbers do not match the balance sheet debt but we will use these numbers nonetheless3 "t is li2ely
CHAPTER 31 CASE C-53
that the company has repurchased some of the outstanding debt but any repurchase is not noted in the /*83 2&
5e need 7arious pieces of information to estimate the cost of e8uity3 5e can use the di7idend growth model or the CAD so we will attempt to use both3 The following information is necessary for our calculations3 5e gathered all the information from finance3yahoo3com3 The screen shots below show this information3 Dar2et price '13Dar2et capitaliation '1*3/- billion 6hares outstanding /43+* million Dost recent di7idend '* !eta /3,* 1;month Treasury bill rate 3*-?
CHAPTER 31 CASE C-55
Tesla has ne7er paid a di7idend so we cannot use the di7idend growth model to estimate the cost of e8uity3 5e do ha7e the information to estimate the cost of e8uity with the CAD3 Using the mar2et ris2 premium of 0 percent from the te&tboo2 we get: 9 E 9 f # βHE(9 D) % 9 fI 9 E 3***- # /3,*H3*0I 9 E 3*4+- or 43+-? '&
!elow are the top /* competitors in the automobile industry by mar2et capitaliation at the time: Company
!eta
Ford Jeneral Dotors onda Toyota Fiat Chrysler Mol2swagen $aimlerChrysler Ford
*340 /3,, *30, *3., *3,4 /340 /3.. *340
"ndustry A7erage
/3/*
5e should ma2e an important note here: All of the competitors listed may not be direct competitors3 First since Tesla manufactures only electric cars it could be an entirely different industry3 Additionally Tesla primarily sells only in the United 6tates so it is largely immune from the currency ris2 faced by many of the abo7e auto companies3 Finally since se7eral of the companies listed are based o7erseas and only ha7e A$9s listed on U363 e&changes they may not be comparable3 "n this case we ha7e chosen to use all the companies listed3
Using the industry a7erage beta the cost of e8uity is: 9 E 9 f # βHE(9 D) % 9 fI 9 E 3***- # /30*H3*0I 9 E 030-? !ecause Teslas beta is so different from the industry beta a decision must be made as to the correct cost of e8uity3 will use the cost of e8uity using Teslas beta3 )&
To get the yield to maturity on Teslas bonds we went to finra; mar2ets3morningstar3com=!ondCenter=3 5e gathered the following information:
Tesla has a con7ertible bond that matures *-=*/=*/+3 !ecause the con7ertible feature is so deep in the money the bond is priced near the con7ersion 7alue resulting in a 7ery large negati7e yield to maturity3 5e ha7e chosen to ignore this bond in our analysis3 "f you clic2 on the lin2 for each bond the website pro7ides information concerning the bond including the face amount of the issue3 6o the weighted a7erage cost of debt for Tesla using both the boo2 7alue and the mar2et 7alue is:
1=/=*/4 1=/=*/ Total
Book -alue 9millions
ercent of total
;uoted price
'4* /1+* '1**
*3,* *3-* /3**
4,31,0 43-.
Market -alue 9millions
'+-0344 /0+3. '/,-3
ercent "ield to of total Maturit!
*3,* *3-* /3**
3*+? 30.,?
Book -alues
Market -alues
*3+/? /3-.? 3,-?
*3+? /3-,? 3,-?
"t is irrele7ant whether we use boo2 or mar2et 7alues to calculate the cost of debt for Tesla3 The weighted a7erage cost of debt using boo2 7alue weights is 3,- percent and using mar2et 7alue weights we get 3,- percent3 5&
Using boo2 7alue weights the total 7alue of Tesla is: M '1******** # '/1--*** M '1---*** 6o the 5ACC based on boo2 7alue weights is: 5ACC RE( 2 =< ) # R$( *=< )(/ % ) ) 5ACC (3*4+-)('/13--='1--3--) # (3*,-)('1**='1-3--)(/ % 31.) 5ACC 3*,- or ,3-?
CHAPTER 31 CASE C-57
Using the mar2et 7alue weights the total 7alue of Tesla is: M '/,-/0,** # '1*/-*1+*** M '11*-.,.,** 6o the 5ACC based on mar2et 7alue weights is: 5ACC RE(E=M) # R$( *=< )(/ % ) ) 5ACC (3*4+-)(' 1*/-*1+*** ='11*-.,.,**) # (3*,-)(' /,-/0,** ='11*-.,.,**)(/ % 31.) 5ACC 3*41+ or 431+? The cost of capital for Tesla using boo2 7alue weights and mar2et 7alue weights is dramatically different since Tesla has a mar2et;to;boo2 ratio of about 3+3 *&
The biggest potential problem with 6D" using Teslas cost of capital is that 6D" operates stores that generate the companys sales3 Tesla generates sales almost e&clusi7ely from its internet site3 This could potentially be a ris2 factor that affects the cost of capital3 Another factor that could affect the cost of capital is Teslas access to capital since it is a public company while 6wan Dotors is pri7ate3
CHAPTER 14 YOUR 401k ACCOUNT AT EAST COAST YACHTS 1&
!efore the fact you would e&pect that mutual funds managers would be able to outperform the mar2et3 This is due in part to the $arwinian nature of the business3 Jood performing fund managers are richly rewarded and poor performing fund managers are fired often 7ery 8uic2ly3 "n reality we should e&pect that less than .* percent of all e8uity mutual funds would outperform the mar2et3 This does not depend on the le7el of mar2et efficiency3 Consider the following 8uestion: 5hat percentage of in7estors will outperform the mar2et in a gi7en yearP Answer: Fifty percent3 5hile there could be one really poor in7estor who ta2es all of the losses in a gi7en year in general to get the mar2et a7erage we would e&pect one;half of in7estors would outperform the mar2et and one;half would underperform the mar2et3 After all the mar2et a7erage return has to be the a7erage return of all in7estors a7erage return3 This is definitely true if we consider the weighted a7erage return that is the a7erage return of in7estors weighted by the dollar amount of the in7estment3 5e would e&pect more than .* percent of mutual funds would underperform the mar2et because of the e&penses charged by the mutual funds3 Consider the large;cap stoc2 fund with an e&pense ratio of /3.* percent3 The fund must e&ceed the mar2et return by /3.* percent before fees in order to achie7e a return after fees e8ual to the mar2et return3 5hether the mar2et is efficient or inefficient is irrele7ant unless mutual funds managers are the best in7estors in the mar2et and all other in7estors including pri7ate money managers pension fund managers indi7iduals etc3 are the bad in7estors in the mar2et3
CHAPTER 31 CASE C-59
5e should also consider that mutual funds managers may be able to outperform the mar2et before e&penses3 5hether they can outperform the mar2et on an after;e&pense basis becomes a 8uestion of whether mutual fund managers can e&tract economic rents from the stoc2 mar2et3 The e7idence tends to support the idea that they cannot3 "n general research has found that mutual fund managers underperform the mar2et after e&penses by the a7erage e&pense ratio3 This means that mutual funds as a whole tend to ha7e the mar2et a7erage return before e&penses so they do not appear to be able to outperform the mar2et3 2&
The results in the graph tend to support the idea of mar2et efficiency3 Consider the case of the Fidelity Dagellan Fund one of the largest acti7ely managed e8uity mutual funds at the time this was written3 The total assets of the fund at the time this was written was about '3, billion3 6o the 8uestion is this: 5hat would Fidelity pay for one year to increase the return of the Dagellan Fund by 3*/ percentP "f we multiply the fund assets by 3*/ percent we get: ',********(3***/) ',****3 6o if Fidelity can increase the return of this one fund by only 3*/ percent per year it should be willing to pay up to '3, million for that year3 Ji7en the amount mutual fund companies would be willing to spend for research and the $arwinian nature of the industry we would e&pect that mutual fund managers should be able to outperform the mar2et3 5hile there ha7e been notable e&ceptions such as eter ynchs tenure at Dagellan as a whole mutual fund managers do not seem to be able to outperform the mar2et3 As a result if the Zbest[ and definitely best;financed in7estors cannot outperform the mar2et the results support the concept of mar2et efficiency3
'&
Ji7en that the e7idence presented tends to support mar2et efficiency you should in7est in the 6K .** inde& fund3 owe7er this is not the entire answer3 !y in7esting the entire e8uity portion of your account in the 6K .** inde& your portfolio is not di7ersified since the 6K .** inde& includes only large;cap stoc2s3 Therefore part of your e8uity in7estment should probably be in the small cap fund for di7ersification purposes3 Note that a small cap inde& fund may be the best option but there is no small cap inde& fund a7ailable in the ,*/2 account3
CHAPTER 16 S+P-+S3 R+ +S+ R+CP;3 1&
"f 6tephenson wishes to ma&imie the o7erall 7alue of the firm it should use debt to finance the ',. million purchase3 6ince interest payments are ta& deductible debt in the firms capital structure will decrease the firms ta&able income creating a ta& shield that will increase the o7erall 7alue of the firm3
2&
6ince 6tephenson is an all;e8uity firm with // million shares of common stoc2 outstanding worth ',+3.* per share the mar2et 7alue of the firm is: Dar2et 7alue of e8uity ',+3.*(//******) Dar2et 7alue of e8uity '.11.***** 6o the mar2et 7alue balance sheet before the land purchase is: Market -alue balance sheet
'&
Assets
'.11.*****
E8uity
'.11.*****
Total assets
'.11.*****
$ebt K E8uity
'.11.*****
a.
As a result of the purchase the firms pre;ta& earnings will increase by '/* million per year in perpetuity3 These earnings are ta&ed at a rate of ,* percent3 Therefore after ta&es the purchase increases the annual e&pected earnings of the firm by: Earnings increase '/*******(/ % 3,*) Earnings increase '-****** 6ince 6tephenson is an all;e8uity firm the appropriate discount rate is the firms unle7ered cost of e8uity so the NM of the purchase is: NM %',.****** # ('-****** = 3/*.) NM '//,+.0
CHAPTER 31 CASE C-61
b.
After the announcement the 7alue of 6tephenson will increase by '//,+.0 the net present 7alue of the purchase3 Under the efficient;mar2et hypothesis the mar2et 7alue of the firms e8uity will immediately rise to reflect the NM of the proLect3 Therefore the mar2et 7alue of 6tephensons e8uity after the announcement will be: E8uity 7alue '.11.***** # //,+.0 E8uity 7alue '.,.-,+.0 Market -alue balance sheet
Old assets
'.11.*****
NM of proLect
//,+.0
Total assets
'.,.-,+.0
E8uity
'.,.-,+.0
$ebt K E8uity
'.,.-,+.0
6ince the mar2et 7alue of the firms e8uity is '.,.-,+.0 and the firm has // million shares of common stoc2 outstanding 6tephensons stoc2 price after the announcement will be: New share price '.,.-,+.0 = //****** New share price ',43-* 6ince 6tephenson must raise ',. million to finance the purchase and the firms stoc2 is worth ',43-* per share 6tephenson must issue: 6hares to issue ',.****** = ',43-* 6hares to issue 4*0/+0 c.
6tephenson will recei7e ',. million in cash as a result of the e8uity issue3 This will increase the firms assets and e8uity by ',. million3 6o the new mar2et 7alue balance sheet after the stoc2 issue will be: Market -alue balance sheet
Cash
' ,.******
Old assets
.11.*****
NM of proLect Total assets
//,+.0 '.4*-,+.0
E8uity
'.4*-,+.0
$ebt K E8uity
'.4*-,+.0
The stoc2 price will remain unchanged3 To show this 6tephenson will now ha7e: Total shares outstanding //****** # 4*0/+0 Total shares outstanding //4*0/+0 6o the share price is: 6hare price '.4*-,+.0 = //4*0/+0 6hare price ',43-*
d.
The proLect will generate '/* million of additional annual preta& earnings fore7er3 These earnings will be ta&ed at a rate of ,* percent3 Therefore after ta&es the proLect increases the annual earnings of the firm by '- million3 6o the afterta& present 7alue of the earnings increase is: MroLect '-****** = 3/*. MroLect '.0/,+.0 6o the mar2et 7alue balance sheet of the company will be: Market -alue balance sheet
Old assets M of proLect Total assets )&
a.
'.11.***** .0/,+.0 '.4*-,+.0
E8uity
'.4*-,+.0
$ebt K E8uity
'.4*-,+.0
Dodigliani;Diller roposition " states that in a world with corporate ta&es: < 6 < = # t C B
As was shown in >uestion 1 6tephenson will be worth '.4*-,+.0 if it finances the purchase with e8uity3 "f it were to finance the initial outlay of the proLect with debt the firm would ha7e ',. million worth of 0 percent debt outstanding3 6o the 7alue of the company if it financed with debt is: < 6 '.4*-,+.0 # 3,*(',.******) < 6 '1*+-,+.0 b.
After the announcement the 7alue of 6tephenson will immediately rise by the present 7alue of the proLect3 6ince the mar2et 7alue of the firms debt is ',. million and the 7alue of the firm is '-*+-,+.0 we can calculate the mar2et 7alue of 6tephensons e8uity3 6tephensons mar2et; 7alue balance sheet after the debt issue will be: Market -alue balance sheet
Malue unle7ered Ta& shield Total assets
'.4*-,+.0 /+****** '-*+-,+.0
$ebt
' ,.******
E8uity
.-1-,+.0
$ebt K E8uity
'-*+-,+.0
6ince the mar2et 7alue of 6tephensons e8uity is '.-1-,+.0 and the firm has // million shares of common stoc2 outstanding 6tephensons stoc2 price after the debt issue will be: 6toc2 price '.-1-,+.0 = //****** 6toc2 price './3, 5&
"f 6tephenson uses e8uity in order to finance the proLect the firms stoc2 price will remain at ',43-* per share3 "f the firm uses debt in order to finance the proLect the firms stoc2 price will rise to './3, per share3 Therefore debt financing ma&imies the per share stoc2 price of the firms e8uity3
CHAPTER 31 CASE C-63
CHAPTER 17 McKENZIE CORPORATION’S CAPITAL BUDGETING 1&
5e assume the '.0***** is spent immediately so we can ignore time 7alue of money considerations3 "f we include the time 7alue of money the numerical solutions will change slightly but the analysis will remain the same3 The e&pected 7alue of the company in one year without e&pansion is: M 31*('*******) # 3.*('.******) # 3*(',1******) M '0/***** And the e&pected 7alue of the company in one year with e&pansion is: M 31*('******) # 3.*('1******) # 3*('.******) M '11****** The companys stoc2holders appear to be better off with e&pansion since the e&pected NM of the proLect is positi7e3 The difference in the e&pected 7alue of the company with and without e&pansion is '.4*****3 "f the re8uired in7estment is '.0***** the e&pansion creates a positi7e increase in e&pected 7alue for current shareholders3 owe7er as further analysis will show stoc2holders are actually worse off3
2&
The 7alue of the companys debt with low economic growth is the 7alue of the company because the company 7alue is less than the face 7alue of the debt3 "n both other economic states the 7alue of the debt is the face 7alue of the debt3 6o the e&pected 7alue of debt in one year without e&pansion is: M$ 31*('*******) # 3.*('.******) # 3*('.******) M$ '1.***** And the 7alue of the companys debt in one year with e&pansion is: M$ 31*('******) # 3.*('.******) # 3*('.******) M$ ',/*****
'&
The 7alue of the companys e8uity with low economic growth is ero both with and without e&pansion since the company 7alue will be less than the face 7alue of the debt3 The 7alue of e8uity with normal growth or high growth is the 7alue of the company minus the '.****** face 7alue of debt3 6o the e&pected 7alue of the e8uity without e&pansion is: ME 31*('*) # 3.*('*) # 3*('/+******) ME '1-***** And the 7alue of e8uity with e&pansion is: ME 31*('*) # 3.*('0******) # 3*('0******) ME '+4***** The 7alue e&pected for bondholders from the e&pansion is the difference in the e&pected 7alue of debt3 6o with e&pansion the companys bondholders gain: !ondholder gain ',/***** % 1.***** !ondholder gain '-***** And the 7alue e&pected for stoc2holders is: 6toc2holder gain '+4***** % 1-***** 6toc2holder gain '.1***** The stoc2holder 7alue increases by '.1***** but the e&pansion was funded entirely by e8uity so the e&pected NM of e&pansion for stoc2holders is actually: 6toc2holder NM %'.0***** # .1***** 6toc2holder NM %',*****
)&
Assuming bondholders are fully informed and they act rationally they will e3pect the stoc2holders to act in their best interest and not e&pand so the price of the bonds will not change3 "f the e&pansion is announced the price of the bonds will increase3
5&
"f they dont e&pand nothing will happen since it is already priced into the bond3 "f the company announces the e&pansion they signal they are willing to sacrifice for the bondholders so the company will recei7e a lower interest rate in the future3
*&
"t is a stronger signal that stoc2holders are not acting in their best interest if the e&pansion is financed with cash on hand3 "f the company issues new e8uity the e&pected loss in stoc2 7alue is shared proportionally by the new in7estors so the current stoc2holders will not bear the entire loss in stoc2 7alue alone3 !y e&panding with cash on hand current stoc2holders are bearing the entire e&pected loss in stoc2 7alue3
CHAPTER 18
CHAPTER 31 CASE C-65
THE LEVERAGED BUYOUT OF CHEEK PRODUCTS, INC. "n this le7eraged buyout the debt le7el of the company changes through time3 6ince the debt le7el changes through time the AM method is appropriate for e7aluating the !O3 The steps we must underta2e are: 6tep /: Calculating the present 7alue of unle7ered cash flows for the first fi7e years3 6tep : Calculating the present 7alue of the unle7ered cash f lows beyond the first fi7e years3 6tep 1: Calculating the present 7alue of interest ta& shields for the first fi7e years3 6tep ,: Calculating the present 7alue of interest ta& shields beyond the first fi7e years3 6tep /: Calculating the present 7alue of unle7ered cash flows for the first fi7e years3 The income statement presented does not include interest so it is the proLected unle7ered cash flows of the company3 To find the cash flows each year we find the operating cash flow by adding depreciation bac2 to net income3 Ne&t we subtract any capital e&penditures changes in net wor2ing capital and add the asset sales3 6o the unle7ered cash flows each year will be:
6ales Costs $ep E!T Ta& Net income Capital e&penditures Change in N5C Asset sales Unle7ered cash flows
$+#' '0,43** 01/3** ,+.3** '/.113** -/13* '4/43+*
$+#( '1*+13** 4.43** ./-3** '/-*+3** -,13* '4-,3+*
$+#> '113** /**43** .103** '/00-3** 0/*3,* '/*-.3-*
$+#? '1,**3** /*4/3** .-,3** '/0,.3** -4+3** '/*,03**
$+#7 '1.143** //,43** .0.3** '/+/.3** 01,3** '/*+43**
'04 '(/) '/,/4
', '(/+-) '/*+
'1*, '/*/
'1*+ '4.
'1*, '/*+
'---3+*
',.3+*
'//403-*
'/*+3**
'/.3**
6ince these are unle7ered cash flows we need to discount at the unle7ered cost of e8uity3 !ecause the company currently has no debt the re8uired return on assets is e8ual to the cost of e8uity3 6o using this discount rate we find the present 7alue of the unle7ered cash flows for the ne&t fi7e years will be: M '---3+* = /3/, # ',.3+* = /3/, # '//403-* = /3/,1 # '/*+ = /3/, , # '/. = /3/, . M '-,**3,+
6tep : Calculating the present 7alue of the unle7ered cash f lows beyond the first fi7e years3 The assumption gi7en is that the cash flows will grow at 13. percent into perpetuity3 Again we discount these cash flows at the unle7ered return on e8uity3 6o the 7alue of these cash flows in @ear . will be: Unle7ered CF 7alue in @ear . H'/.(/ # 3*1.)I = (3/, % 3*1.) Unle7ered CF 7alue in @ear . '/1,/3/, The 7alue today of this terminal 7alue is: M '/1,/3/, = /3/, . M '-,*43-* 6tep 1: Calculating the present 7alue of interest ta& shields for the first fi7e years3 The interest ta& shield each year is the interest paid times the ta& rate3 To find the present 7alue of the interest ta& shield we need to discount these at the preta& cost of debt so the present 7alue of the interest ta& shield for the first fi7e years is: M ('/40)(3,*) = /3/. # ('/+.4)(3,*) = /3/. # ('.4)(3,*) = /3/. 1 # ('.-)(3,*) = /3/., # ('-/,)(3,*) = /3/. . M '1//3+4 6tep ,: Calculating the present 7alue of interest ta& shields beyond the first fi7e years3 Finally we must calculate the 7alue of ta& shields associated with debt used to finance the operations of the company after the first fi7e years3 The assumption gi7en in the case is that debt will be reduced and maintained at . percent of the 7alue of the firm from that date forward3 Under this assumption it is appropriate to use the 5ACC method to calculate a terminal 7alue for the firm at the target capital structure3 This in turn can be decomposed into an all;e8uity 7alue and a 7alue from ta& shields3 Note that we need to use the interest rate on the debt beyond @ear . in these calculations3 "f the capital structure changes after the first fi7e years the le7ered cost of e8uity can be found with Dodigliani;Diller roposition "" with corporate ta&es: R4 R* # ( B=4 )( R* % R B)(/ % t C) R4 3/, # (3.)(3/, % 3*+)(/ % 3,*) R4 3/,4* or /,34*?
Now we can calculate the 5ACC for the company beyond @ear .3 The 5ACC at this point will be: R5ACC H B = ( B # 4 )I(/ % t C) R B # H4 = ( B # 4 )I R4 R5ACC H3.I(/ % 3,*)(3*+) # H/ = /3.I(3/,4*) R5ACC 3/1/ or /13/?
5e can use the 5ACC to calculate the terminal 7alue of the le7ered company which will be: < H'/.(/ # 3*1.)I = (3/1/ % 3*1.) < '/1,0*3*-
CHAPTER 31 CASE C-67
Using Dodigliani;Dillers 7aluation of a le7ered firm: < < U # t C B
we can 7alue the interest ta& shield as: '/1,0*3*- '/1,/3/, # "nterest ta& shield "nterest ta& shield '//+34 This is the 7alue of the interest ta& shield beyond @ear .3 $iscounting this at the cost of debt o7er the first fi7e years we find the 7alue today is: / M '//+34 = /3/. . M '--3,0 5e ha7e 7alued all future cash flows of the company3 The 7alue of the unle7ered cash flows today is: Malue of unle7ered CF '-,**3,+ # -,*43-* Malue of unle7ered CF '/+/*3*+ And the 7alue of the interest ta& shield today is: Malue of interest ta& shield '1//3+4 # --3,0 Malue of interest ta& shield '1+1+316o the total 7alue of the company today is: Malue of company today '/+/*3*+ # 1+1+31Malue of company today '/--,+3,, 6o the most the group should offer per share is: rice '/--,+3,, = ,. rice '143/0
CHAPTER 19 ELECTRONIC TIMING, INC. 1&The 7alue of the company will decline by the amount of the di7idend3 "gnoring ta&es shareholders wealth will not be affected because the stoc2 price will drop by the amount of the di7idend payment3
/ A good argument can be made that since post;*/4 debt le7els are proportional to firm 7alue the ta& shields are as ris2y as the firm and should be discounted at the rate R*3
2&
The 7alue of the company could increase or decrease3 "f the company is o7er;le7ered paying off debt can lower the interest rate on debt and decrease financial distress costs3 "f there are no financial distress costs capital structure theory argues that increasing debt can increase the 7alue of the company because of the interest ta& shield3
'&
The E ratio will fall and the 9OA and 9OE will increase but the changes are irrele7ant3
)&
A regular dividend payment is something the company should probably not undertake. A company rarely begins regular dividend payments that it will be unable to continue in the future. Cessation of dividend payments is 7iewed as a negati7e signal by the mar2et3
5&
The implication is that the company should not retain earnings unless the 9OE of the new proLect is greater than the shareholders re8uired return on e8uity3 This is an intuiti7e result3 6hareholders want the company to retain earnings for future growth if the earnings will earn a greater return than shareholders re8uire3 "f the return on the retained earnings is lower than shareholders re8uired return the company is lowering shareholder 7alue3
6.
The decision does depend on the organizational form of the company. Money paid to shareholders of a corporation are dividends, and currently taxed at the lower dividend tax rate. Money paid to the owners of an LLC is considered income, and taxed at the applicable personal income tax rate.
CHAPTER 20 EAST COAST YACHTS GOES PUBLIC 1&
The main difference in the costs is the reduced possibility of underpricing in a $utch auction3 As to which is better we dont actually 2now3 "n theory the $utch auction should be better since it should eliminate underpricing3 owe7er as Joogle shows underpricing can still e&ist in a $utch auction3 5hether the underpricing is as se7ere in a $utch auction as it would be in a traditional underwritten offer is un2nown3
2&
There is no way to calculate the optimum sie of the "O so whether $an is correct or arissa is correct will only be told in time3 The disad7antages of raising the e&tra cash in the "O include the agency costs of e&cess cash3 The e&tra cash may encourage management to act carelessly3 The e&tra cash will also earn a small return unless in7ested in income producing assets3 At best cash and short; term in7estments are a ero NM in7estment3 The ad7antages of the increased "O sie include the increased li8uidity for the company and the lower probability that the company will ha7e to go bac2 to the primary mar2et in the near term future3 The increased sie will also reduce the costs of the "O as a percentage of funds raised although this may not be a large ad7antage3
'&
The underwriter fee is 0 percent of the amount raised or: Underwriter fee '+.******(3*0) Underwriter fee '.4.****
CHAPTER 31 CASE C-69
6ince the company must currently pro7ide audited financial statements due to the bond co7enants the audit costs are not incremental costs and should not be included in the calculation of the fees3 6o the sum of the other fees is: Total other fees '/+***** # /.*** # **** # /***** # +.** # ..*** # 0.*** Total other fees '.,1.** This means the total fees are: Total fees '.4.**** # .,1.** Total fees '+,41.** The net amount raised is the "O offer sie minus the underwriter fee or: Net amount raised '+.****** % .4.**** Net amount raised '04*.**** 6o the fees as a percentage of the net amount to the company are: Fee percentage '+,41.** = '04*.**** Fee percentage 3/*0, or /*30,?
)&
!ecause of legal repercussions you should not pro7ide specific ad7ice on which option the employees should choose3 There are ad7antages and disad7antages to each3 "f the employee tenders the stoc2 to be sold in the "O the employee will lose out on any underpricing3 This could be a significant cost3 owe7er if the employee retains the stoc2 he=she must hold the stoc2 for the loc2up period typically /+* days3 Additionally during the loc2up period the employee is legally prohibited from hedging the price ris2 of the stoc2 with any deri7ati7es3 And hea7y selling by insiders is considered a negati7e signal by the mar2et3 Another ris2 in not selling in the "O is that after the loc2up period e&pires the employees may be considered insiders subLect to 6EC restrictions on selling stoc23
CHAPTER 21 THE DECISION TO LEASE OR BUY AT WARF COMPUTERS 1&
The decision to buy or lease is made by loo2ing at the incremental cash flows3 The incremental cash flows from leasing the machine are the security deposit the lease payments the ta& sa7ings on the lease the lost depreciation ta& shield the sa7ed purchase price of the machine and the lost sal7age 7alue3 The sal7age 7alue of the e8uipment in four years will be: Afterta& sal7age 7alue ',,**** % ',,****(31.) Afterta& sal7age 7alue '+-*** This is an opportunity cost to 5arf Computers since if the company leases the e8uipment it will not be able to sell the e8uipment in four years3 The lease payments are due at the beginning of each year so the incremental cash flows are: "ear +
6a7ed purchase
"ear #
"ear $
"ear %
'1-*****
ost sal7age 7alue
%'+-***
ost dep3 ta& shield
%',/44.+
%'.-**0*
%'/+--*-
6ecurity deposit
%/****
ease payment
%41.***
%41.***
%41.***
%41.***
10.*
10.*
10.*
10.*
'0+.*
%'/*00*+
%'//-0+*
%'04,1.-
Ta& on lease payment Cash flow from leasing The afterta& cost of debt is:
Afterta& cost of debt 3//(/ % 31.) Afterta& cost of debt 3*0/. or 03/.? And the NA of the lease is:
"ear &
%411-/****
%'/-41--
CHAPTER 31 CASE C-71
NA '0+.* % '/*00*+ = /3*0/. % '//-0+* = /3*0/. % '04,1.- = /3*0/. 1 % '/-41-- = /3*0/., NA '1/0.13. The company should lease the e8uipment3
2&
The boo2 7alue of the e8uipment in @ear will be: !oo2 7alue '1-***** % '1-*****(31111 # 3,,,.) !oo2 7alue '0444* 6o the afterta& sal7age 7alue in @ear will be: Afterta& sal7age 7alue '//,,*** # ('0444* % /,,****)(31.) Afterta& sal7age 7alue '//.40 6o the NA of the lease under the new terms would be: "ear +
6a7ed purchase
"ear #
'1-*****
ost sal7age 7alue
%'//.40
ost dep3 ta& shield ease payment Ta& on lease payment Cash flow from leasing
"ear $
%',/44.+ %/-.****
%/-.****
.00.**
.00.**
'.0.**
%'/,4,.+
%.-**0*
%'/00-*,
6o the NA of the lease under these terms is: NA '.0.** % '/,4,.+ = /3*0/. % '/00-*, = /3*0/. NA %',/4/3-* The NA of the lease is negati7e under these terms so it appears the terms are less fa7orable for the lessee3 owe7er the lease will li2ely be classified as an operating lease3 The lease is now for two years which is less than 0. percent of the e8uipments life3 Using the companys cost of debt the present 7alue of the lease payments is: M of lease payments '/-.**** # '/-.**** = /3// M of lease payments '1/1-,+-3,4 This is less than 4* percent of the price of the e8uipment3 As long as the lease contract does transfer ownership to the lessee at the end of the contact or allow for a purchase at a bargain price the FA6 /1 conditions for a capital lease are not met3 As such the reason for suggesting the re7ised lease terms is unethical on Nic2s part3 Also notice that the 8uestion also states that if the lease is renewed in two years the lessor will allow for the increased lease payments made o7er the first two years3 This is also an indication that the re7ision is for less than ethical reasons3
CHAPTER 31 CASE C-73
'&
)&
a.
The inclusion of a right to purchase the e8uipment will ha7e no effect on the 7alue of the lease3 "f the company does not purchase the e8uipment it can go on the mar2et and purchase identical e8uipment at the same price3
b.
The right to purchase the e8uipment at a fi&ed price will ha7e increase the 7alue of the lease3 "f the company can purchase the e8uipment at the end of the lease at below mar2et 7alue it will sa7e money or at a minimum can purchase the e8uipment at the fi&ed price and resell it in the open mar2et3 This is a real option therefore has 7alue to the lessee3 "t is a call option on the e8uipment3 As such it must ha7e a 7alue until it e&pires or is e&ercised3 "t is also important to note that this would li2ely ma2e the lease contract a capitalied lease3
c.
The right to purchase the e8uipment at a bargain price is also a real option for the lessee and will increase the 7alue of the lease3 "t is a call option and therefore will ha7e 7alue until it e&pires or is e&ercised3 This contract condition will definitely ensure the lease is classified as a capitalied lease3
The cancellation option is also a real option3 The cancellation option is a put option on the e8uipment3 "t will increase the 7alue of the lease since the lessee will only e&ercise the option when it is to the lessees ad7antage3
CHAPTER 22 CLISSOLD INDUSTRIES OPTIONS 1&
6ince the !lac2%6choles model uses the standard de7iation of the underlying asset and there is only one underlying asset no matter how many stri2e prices are a7ailable we would only e&pect to see one implied standard de7iation3
2&
To find the implied 7olatility for an option you can set up a spreadsheet to calculate the option price3 The 6ol7er function in E&cel will allow you to input the desired price and will sol7e for the desired un2nown 7ariable3 5e did this (the spreadsheet is a7ailable) and the implied standard de7iation for each of the options is:
'&
Stri$e Pri#e
3ption Pri#e
%plied Standard .e!iation
'.*
'/30+
0.3*,?
..
/*3/,
0*34-
-*
0344
-+3/
-.
.3+/
-13
There are two possible e&planations3 The first is model misspecification3 Although the !lac2% 6choles option pricing model is widely acclaimed it is possible that the model specifications are incorrect3 One potential 7ariable that is incorrectly specified is the assumption of constant 7olatility3
"n fact the 7olatility of the underlying stoc2 is itself 7olatile and will increase or decrease o7er time3 The !lac2%6choles model may also ignore important 7ariables3 For e&le Fisher !lac2 describes trades he Dyron 6choles 9obert Derton and others made when the model was first de7eloped (!lac2 Fisher /4+4 Zow we came up with the option pricing formula[ )he @ournal of ortfolio Management 5inter ,;+3) As in any potential arbitrage opportunity they purchased underpriced assets in this case warrants on National Jeneral stoc23 Unfortunately soon after they too2 this position American Financial announced a tender offer for National Jeneral which sharply reduced the 7alue of the warrants3 The mar2et had already priced the potential tender offer in the warrant price while this 7ariable was not accounted for in the !lac2%6choles model3 A second possible e&planation is li8uidity3 At; or near;the;money options tend to be more li8uid than deep in;the;money or deep out;of;the;money options3 6ince options that are not near;the;money are less li8uid the price should carry a li8uidity premium3 )&
The M"\ is a benchmar2 for stoc2 mar2et 7olatility3 The M"\ is based on option prices which reflect in7estors] consensus 7iew of future e&pected stoc2 mar2et 7olatility3 $uring periods of mar2et turmoil both option prices and the M"\ tend to rise3 5hen the mar2et is calmer in7estor fear option prices and the M"\ decline3
5&
The M"\ uses eight different 6K /** "nde& (OE\) option series to represent the implied 7olatility of a hypothetical OE\ option with e&actly 1* days to e&piration3
CHAPTER 23 EXOTIC CUISINES’ EMPLOYEE STOCK OPTIONS 1&
5e can use the !lac2%6choles e8uation to 7alue the employee stoc2 options3 5e need to use the ris2;free rate that is the same as the maturity as the options3 6o assuming e&piration in three years the 7alue of the stoc2 options per share of stoc2 is: d / Hln('03/.=',*) # (3*1+ # 3-* =) × 1I = (3-* × d 3.-, % (3-* ×
1 ) 3.-,
1 ) %30++
N(d /) 3-*/ N(d ) 3/-4 utting these 7alues into the !lac2;6choles model we find the option 7alue is: C '03/.(3-*04) % (',*e %3*1+(1))(3/-4)
CHAPTER 31 CASE C-75
C '+3.+
Assuming e&piration in /* years the 7alue of the stoc2 options per share of stoc2 is: d / Hln('03/.=',*) # (3*,, # 3-* =) × /*I = (3-* × d 340-, % (3-* ×
/* ) 340-,
/* ) %34/*
N(d /) 3+1. N(d ) 3/0+. utting these 7alues into the !lac2%6choles model we find the option 7alue is: C '03/.(3+1.-) % (',*e %3*,,(/*))(3/0+.) C '/+3*4 2&
5hether you should e&ercise the options in three years depends on se7eral factors3 A primary factor is how long you plan to stay with the company3 "f you are planning to lea7e ne&t wee2 you should e&ercise the options3 A second factor is how the option e&ercise will affect your ta&es3
'&
The fact that the employee stoc2 options are not traded decreases the 7alue of the options3 A basic way to understand this is to realie that an option always has 7alue since ignoring the premium it can ne7er lose money3 The right to sell an option also has to ha7e 7alue3 "f the right to sell is remo7ed it decreases the price of the option3
)&
The rationale for employee stoc2 options is to reduce agency costs by better aligning employee and shareholder interests3 Mesting re8uires employees to wor2 at a company for a specified time which means the employee actions are actually part of the company performance3 Mesting is also a Zgolden handcuff[3 The employee is less li2ely to lea7e the company if in;the;money employee stoc2 options will 7est soon3
5&
The e7aluation of the argument for or against repricing is open;ended3 There are 7alid reasons on both sides of the discussion3 9epricing increases the 7alue of the employee stoc2 option3 Consider an e&treme: A company announces the employee stoc2 options will be worth a minimum of '/* at e&piration3 6ince all 7alues less than '/* are no longer possible the 7alue of the option increases3
*&
Employee stoc2 options increase in 7alue if the stoc2 price increasesB howe7er the stoc2 price can increase because of a general mar2et increase3 Consider a company of a7erage ris2 in a bull mar2et that has a large return for se7eral years3 The companys stoc2 should closely mirror the mar2et return e7en though most of the stoc2 price increase is due to the general mar2et increase3 6imilarly if the mar2et falls the companys stoc2 will li2ely fall as well e7en if the company is doing well3 A better method of 7aluing employee stoc2 options might be to reward employees for company performance in e&cess of the mar2et performance adLusted for the companys le7el of ris23
CHAPTER 24 S&S AIR’S CONVERTIBLE BOND 1&
Chris is suggesting a con7ersion price of ',. because it means the stoc2 price will ha7e to increase before the bondholders can benefit from the con7ersion3 E7en though the company is not publicly traded the con7ersion price is important3 First the company may go public in the future3 The case does not discuss whether the company has plans to go public and if so how soon it might go public3 "f the company does goes public the bondholders will ha7e an acti7e mar2et for the stoc2 if they con7ert3 6econd e7en if the company does not go public the bondholders could potentially ha7e an e8uity interest in the company3 This e8uity interest can be sold to the original owners or someone else3 The potential problem with pri7ate e8uity is that the mar2et is not as li8uid as the mar2et for a public company3 This illi8uidity lowers the 7alue of the stoc23 5e can use the E ratio to estimate the current stoc2 price3 $oing so we get: =E rice=E6 /03.* rice='/30. rice '1*3-1
2&
The floor 7alue is the ma&imum of the con7ersion 7alue and the intrinsic 7alue3 The con7ersion 7alue of the bond is gi7en as '-+*3.-3 The intrinsic 7alue of the bond is: "ntrinsic 7alue '.(M"FA,?*) # '/***(M"F,?*)
CHAPTER 31 CASE C-77
"ntrinsic 7alue '0*13// 6o the floor 7alue of the bond is '0*13//3 This means that if the company offered bonds with the same coupon rate and no con7ersion feature they would be able to sell them for '0*13//3 '&
The con7ersion ratio of the bonds is: Con7ersion ratio '/***=',. 3 6o each bond can be con7erted to 3 shares of stoc23
)&
The con7ersion premium is the increase in stoc2 price necessary to ma2e the con7ersion option possible3 6ince the stoc2 is currently selling for '1*3-1 and the con7ersion price is ',. the con7ersion premium of the bond is: Con7ersion premium (',. % 1*3-1) = '1*3-1 Con7ersion premium 3,-4, or ,-34,?
5&
The option 7alue of a con7ertible bond is defined as the difference between the mar2et 7alue of the bond and the ma&imum of its straight 7alue and con7ersion 7alue3 6ince the bond is sold at par 7alue the option 7alue is: Option 7alue Dar2et 7alue % Da&H6traight 7alue Con7ersion 7alueI Option 7alue '/*** % Da&H'0*13// '-+*3.-I Option 7alue '/*** % 0*13// Option 7alue '4-3+4
*&
Todds argument is wrong because it ignores the fact that if the company does well bondholders will be allowed to participate in the companys success3 "f the stoc2 price rises to '.* bondholders are effecti7ely allowed to purchase stoc2 at the con7ersion price of ',.3
9&
Dar2s argument is incorrect because the company is issuing debt with a lower coupon rate than they would ha7e been able to otherwise3 "f the company does poorly it will recei7e the benefit of a lower coupon rate3
<&
9econciling the two arguments re8uires that we remember our central goal: to increase the wealth of the e&isting shareholders3 Thus with *%* hindsight we see that issuing con7ertible bonds will turn out to be worse than issuing straight bonds and better than issuing common stoc2 if the company prospers3 The reason is that the prosperity has to be shared with bondholders after they con7ert3 "n contrast if a company does poorly issuing con7ertible bonds will turn out to be better than issuing straight bonds and worse than issuing common stoc23 The reason is that the firm will ha7e benefited from the lower coupon payments on the con7ertible bonds3 !oth of the arguments ha7e a grain of truthB we Lust need to combine them3 Ultimately which option is better for the company will only be 2nown in the future and will depend on the performance of the company3 The table below illustrates this point3
Con-ertible bonds issued instead of straight bonds Con-ertible bonds issued instead of common stock
=&
f the #o%pany does poorly 6ow stock price and no con-ersion Cheap financing because coupon rate is lower (good outcome)3
E&pensi7e financing because firm could ha7e issued common stoc2 at high prices (bad outcome)3
f the #o%pany prospers igh stock price and con-ersion E&pensi7e financing because bonds are con7erted which dilutes e&isting e8uity (bad outcome)3 Cheap financing because firm issues stoc2 at high prices when bonds are con7erted (good outcome)3
The call pro7ision allows the company to redeem the bonds at the companys discretion3 "f the companys stoc2 appears to be poised to rise the company can call the outstanding bonds3 "t could be possible that the bondholders would benefit from con7erting the bonds at that point but it would eliminate the potential future gains to the bondholders3
CHAPTER 31 CASE C-79
CHAPTER 25 WILLIAMSON MORTGAGE, INC. 1&
^errys mortgage payments form a .;year annuity with monthly payments discounted at the long; term interest rate of .3. percent3 5e can sol7e for the payment amount so that the present 7alue of the annuity e8uals '.***** the amount of principal that he plans to borrow3 The monthly mortgage payment will be: '.***** C(M"FA.3.?=/1** ) C '1*0*3,,
2&
The most significant ris2 that she faces is interest rate ris23 "f the current mar2et rate of interest rises between today and the date the mortgage is sold the fair 7alue of the mortgage will decrease and Da& will only be willing to purchase the mortgage for a price less than '.*****3 "f this is the case she will not be able to loan ^erry the full '.***** promised3
'&
Treasury bond prices ha7e an in7erse relationship with interest rates3 As interest rates rise Treasury bonds become less 7aluableB as interest rates fall Treasury bonds become more 7aluable3 6ince ^ennifer will be hurt when interest rates rise she is also hurt when Treasury bonds decrease in 7alue3 "n order to protect herself from decreases in the price of Treasury bonds she should ta2e a short position in Treasury bond futures to hedge this interest rate ris23 6ince three;month Treasury bond futures contracts are a7ailable and each contract is for '/***** of Treasury bonds she would ta2e a short position in fi7e 1;month Treasury bond futures contracts in order to hedge her '.***** e&posure to changes in the mar2et interest rate o7er the ne&t three months
)&
a.
"f the mar2et interest rate is -3 percent on the date that ^ennifer meets with the Da& the fair 7alue of the mortgage is the present 7alue of an annuity that ma2es monthly payments of '1*0*3,, for . years discounted at -3 percent or: Dortgage 7alue '1*0*3,,(M"FA-3?=/1** ) Dortgage 7alue ',-0-143.,
b3
5&
An increase in the interest rate will cause the 7alue of the T;bond futures contracts to decrease3 The long position will lose and the short position will gain3 6ince ^ennifer is short in the futures the futures gain will offset the loss in 7alue of the mortgage3
a. "f the mar2et interest rate is ,3- percent on the date that ^ennifer meets with Da& the fair 7alue of the mortgage is the present 7alue of an annuity that ma2es monthly payments of '1*0*3,, for . years discounted at ,3- percent or:
Dortgage 7alue '1*0*3,,(M"FA,3-?=/1** ) Dortgage 7alue '.,-+*,3.4
b3
*&
An increase in the interest rate will cause the 7alue of the Treasury bond futures contracts to increase3 The long position will gain and the short position will lose3 6ince ^ennifer is short in the futures the futures loss will be offset by the gain in 7alue of the mortgage3
The biggest ris2 is that the hedge is not a perfect hedge3 "f interest rates change the fact that Treasury bond interest is semiannual while the mortgage payments are monthly may affect the relati7e 7alue of the two3 Additionally while a change in one of the interest rates will li2ely coincide with a change in the other interest rate the change does not ha7e to be the same3 For e&le the Treasury rate could increase * basis points and the mortgage rates could increase by ,* basis points3 The fact that this is not a perfect hedge simply means that the gain=loss from the futures contracts may not e&actly offset the loss=gain in the mortgage3 5e would e&pect especially gi7en the short;term nature of the hedge that the loss in one instrument would be similar to the gain in the other instrument3
CHAPTER 26 KEAFER MANUFACTURING WORKING CAPITAL MANAGEMENT 1&
The cash flow each 8uarter will consist of the sales collection minus the suppliers paid e&penses di7idends interest and capital outlays3 The cash flows for each 8uarter will be:
Collections from pre7ious 8uarter Collections from current 8uarter sales ayments to suppliers for pre7ious 8uarter ayments to suppliers for current 8uarter E&penses $i7idends and interest Outlay Net cash flow
Cash 5low ;# ;$ '-*0.**3** '0.10-+3**
;% '0+*,,,3**
;& '0-4.**3**
,1-143**
,./+1-3**
,,..**3**
,*4,+3**
%1.*,1-3**
%1-+1+3**
%1.00.*3**
%11+*1,3**
%.11*3** %40.,*3** %/+.***3**
%,40.*3** %1*+*0*3** %/+.***3**
%-,/.3. %+0*/*3** %/+.***3**
%',1+-3**
'444,-3**
%1.4+-3** %1*10.*3** %/+.***3** %14****3** %',-.,3**
Cash Balance ;#
;$
;%
'//-/++3,+
;&
CHAPTER 31 CASE C-81
!eginning cash balance Net cash inflow Ending cash balance Dinimum cash balance Cumulati7e surplus %deficit
'/****3** %,1+-3** '/-0-/,3** /1.***3** '1-/,3**
'/-0-/,3** 444,-3** '-0.-*3** /1.***3** '/1.-*3**
'-0.-*3** %,-.,3** '/*/+3** /1.***3** %'//14+3**
'/*/+3** //-/++3,+ '/10*-3,+ /1.***3** '*-3,+
The short;term financial plan loo2s li2e this:
Target cash balance Net cash inflow New short;term in7estments "ncome on short;term in7estments 6hort;term in7estments sold New short;term borrowing "nterest on short;term borrowing 6hort;term borrowing repaid Ending cash balance Dinimum cash balance Cumulati7e surplus %deficit !eginning short;term in7estments Ending short;term in7estments !eginning short;term debt Ending short;term debt
4hort,term 5inancial lan '/1.***3** '/1.***3** %,1+-3** 444,-3**
* 10.3** ,*//3** * * * '/1.***3** %/1.***3** '*
%/**1/3** 10.3** * * * * '/1.***3** %/1.***3** '*
'/1.***3** %,-.,3** * +0-3-/ /0.1/3** 0*1,,3,* * * '/1.***3** %/1.***3** '*
'0.***3** 0.***3** * '*
'0.***3** /0.1/3** * '*
'/0.1/3** * * '0*1,,3,*
'/1.***3** //-/++3,+ %,,44434. * * * %+,,3/1 %0*1,,3,* '/1.***3** %/1.***3** '* '* ,,44434. 0*1,,3,* '*
The interest calculations for each 8uarter and the net cash cost are: >/: >: >1: >,:
E&cess funds at start of 8uarter of E&cess funds at start of 8uarter of E&cess funds at start of 8uarter of 6hortage of funds at start of 8uarter of
'0.***3** '0.***3** '/0.1/3** '0*1,,3,*
Net cash cost >/ > >1 >,
'10.3** 10.3** +0-3-/ %+,,3/1
Cash generated by short;term financing
'0+3,0
earns earns earns costs
'10.3** '10.3** '+0-3-/ '+,,3/1
in income3 in income3 in income3 in interest3
CHAPTER 31 CASE C-83
2&
"f Reafer reduces its target cash balance to '4**** the cash flows each 8uarter will remain the same so they will not be repeated here3 The cash balance and short;term financial plan will be:
!eginning cash balance Net cash inflow Ending cash balance Dinimum cash balance Cumulati7e surplus %deficit
Target cash balance Net cash inflow New short;term in7estments "ncome on short;term in7estments 6hort;term in7estments sold New short;term borrowing "nterest on short;term borrowing 6hort;term borrowing repaid Ending cash balance Dinimum cash balance Cumulati7e surplus %deficit !eginning short;term in7estments Ending short;term in7estments !eginning short;term debt Ending short;term debt >/ : > : >1 : >, :
Cash Balance ;# ;$ '/****3** '/-0-/,3** %,1+-3** 444,-3**
;% '-0.-*3** %,-.,3**
;& '/*/+3** //-/++3,+
'/-0-/,3** 4****3** '00-/,3**
'/*/+3** 4****3** %'-+4+3**
'/10*-3,+ 4****3** ',0*-3,+
'4****3** //-/++3,+ %4*44-3,4 * * * %4+30 %,+4130 '4****3** %4****3** '* '* 4*44-3,4 ,+4130 '*
'-0.-*3** 4****3** '/00.-*3**
4hort,term 5inancial lan '4****3** '4****3** %,1+-3** 444,-3**
* -**3** ,/0+-3** * * * '4****3** %4****3** '*
%/**.,-3** -**3** * * * * '4****3** %4****3** '*
'4****3** %,-.,3** * //*301 *.,-3** ,+4130 * * '4****3** %4****3** '*
'/****3** /****3** * '*
'/****3** *.,-3** * '*
'*.,-3** * * ',+4130
E&cess funds at start of 8uarter of
'/****3**
earns
'-**3**
in income3
E&cess funds at start of 8uarter of
'/****3**
earns
'-**3**
in income3
E&cess funds at start of 8uarter of
'*.,-3**
earns
'//*301
in income3
6hortage of funds at start of 8uarter of
',+4130
costs
'4+30
in interest3
Net cash cost >/ > >1 >,
'-**3** -**3** //*301 %4+30
Cash generated by short;term financing
'**,3*/
CHAPTER 31 CASE C-85
'&
"f the sales growth rate is // percent the cash flows for each 8uarter will be: Cash 5low
Collections from pre7ious 8uarter Collections from current 8uarter sales ayments to suppliers for pre7ious 8uarter ayments to suppliers for current 8uarter E&penses $i7idends and interest Outlay Net cash flow
!eginning cash balance Net cash inflow Ending cash balance Dinimum cash balance Cumulati7e surplus %deficit
;# '-*0.**3**
;$ '00,0*-3**
;% '+*/13**
;& '04*+0.3**
,,+./,3**
,-,1+03**
,.0+0.3**
,1-,/3**
%1-*/0*311
%104/-3+1
%1-0-+03.*
%1,0,13+1
%-*11+3/0 %1*.+*.3** %/+.***3**
%.--+03.* %1/--03.* %/+.***3**
%04*4+3*1 %4,4+3.* %/+.***3**
%'..443.*
'/*0+-/3/0
%,.,/3/0 %1//+03.* %/+.***3** %14****3** %'10,/+3/0
Cash Balance ;# ;$ '/****3** '/.,0**3.*
;% '-.-/3-0
;& './,13.*
%10,/+3/0 './,13.* /1.***3** %'/*4+.-3.*
//0*//3-, '/,/..3/, /1.***3** '0/..3/,
'/1.***3** //0*//3-, %-1/*-3-1 * * * %-143/4 %.1-.3+ '/1.***3** %/1.***3** '* '* -1/*-3-1 .1-.3+ '*
%..443.* '/.,0**3.* /1.***3** '/40**3.*
/*0+-/3/0 '-.-/3-0 /1.***3** '/0.-/3-0
'//0*//3-,
The short;term financial plan loo2s li2e this:
Target cash balance Net cash inflow New short;term in7estments "ncome on short;term in7estments 6hort;term in7estments sold New short;term borrowing "nterest on short;term borrowing 6hort;term borrowing repaid Ending cash balance Dinimum cash balance Cumulati7e surplus %deficit !eginning short;term in7estments Ending short;term in7estments !eginning short;term debt Ending short;term debt
4hort,term 5inancial lan '/1.***3** '/1.***3** %..443.* /*0+-/3/0 * %/*+1-3/0 10.3** 10.3** .,4,3.* * * * * *
* '/1.***3** %/1.***3** '*
* '/1.***3** %/1.***3** '*
'/1.***3** %10,/+3/0 * 4/-3/+ /+11-3/0 .1-.3+ * * '/1.***3** %/1.***3** '*
'0.***3** 0.***3** * '*
'0.***3** /+11-3/0 * '*
'/+11-3/0 * * '.1-.3+
CHAPTER 31 CASE C-87
The interest calculations for each 8uarter and the net cash cost are: >/: >: >1: >,:
E&cess funds at start of 8uarter of E&cess funds at start of 8uarter of E&cess funds at start of 8uarter of 6hortage of funds at start of 8uarter of
'0.***3** '0.***3** '/+11-3/0 '.1-.3+
Net cash cost >/ > >1 >,
'10.3** 10.3** 4/-3/+ %-143/4
Cash generated by short;term financing
'/*-344
earns earns earns costs
'10.3** '10.3** '4/-3/+ '-143/4
in income3 in income3 in income3 in interest3
"f the sales growth rate is . percent the cash flows for each 8uarter will be: Cash 5low
Collections from pre7ious 8uarter Collections from current 8uarter sales ayments to suppliers for pre7ious 8uarter ayments to suppliers for current 8uarter E&penses $i7idends and interest Outlay Net cash flow
!eginning cash balance Net cash inflow Ending cash balance Dinimum cash balance Cumulati7e surplus %deficit
;# '-*0.**3**
;$ '01+1*3**
;% '0.+0-.3**
;& '0,+/.3**
,,0*3**
,14+.3**
,11/.3**
,*4..3**
%1,*0*/3-0
%1.0.43/0
%1,0+/3.*
%1+-,,3/0
%,--.3+1 %+40.3** %/+.***3**
%,+/3.* %44./3.* %/+.***3**
%,40,*30. %04*103.* %/+.***3**
%'4,03.*
'4*1*3+1
%4,1*3+1 %4.1/3.* %/+.***3** %14****3** %'..--.3+1
Cash Balance ;# ;$ '/****3** '/+*.03.* %4,03.* 4*1*3+1 '/+*.03.* '0..+311 /1.***3** /1.***3** ',..03.* '/10..+311
;% '0..+311 %..--.3+1 '/-+43.* /1.***3** %'//+/*03.*
;& '/-+43.* //,4.03.+ '/1/+.*3*+ /1.***3** %'1/,434
'//,4.03.+
The short;term financial plan loo2s li2e this:
Target cash balance Net cash inflow New short;term in7estments "ncome on short;term in7estments 6hort;term in7estments sold New short;term borrowing "nterest on short;term borrowing 6hort;term borrowing repaid Ending cash balance Dinimum cash balance Cumulati7e surplus %deficit !eginning short;term in7estments Ending short;term in7estments !eginning short;term debt Ending short;term debt
4hort,term 5inancial lan '/1.***3** '/1.***3** %4,03.* 4*1*3+1
* 10.3** 4*403.* * * * '/1.***3** %/1.***3** '*
%4,*.3+1 10.3** * * * * '/1.***3** %/1.***3** '*
'/1.***3** %..--.3+1 * +103*1 /-0,*.3+1 +0,340 * * '/1.***3** %/1.***3** '*
'0.***3** 0.***3** * '*
'0.***3** /-0,*.3+1 * '*
'/-0,*.3+1 * * '+0,340
'/1.***3** //,4.03.+ %-,+.3., * * * %/*,43*+ %+0,340 '/1.***3** %/1.***3** '* '* -,+.3., +0,340 '*
The interest calculations for each 8uarter and the net cash cost are: >/: >: >1: >,:
E&cess funds at start of 8uarter of E&cess funds at start of 8uarter of E&cess funds at start of 8uarter of 6hortage of funds at start of 8uarter of
'0.***3** '0.***3** '/-0,*.3+1 '+0,340
Net cash cost >/ > >1 >,
'10.3** 10.3** +103*1 %/*,43*+
Cash generated by short;term financing
'.1034.
earns earns earns costs
'10.3** '10.3** '+103*1 '/*,43*+
in income3 in income3 in income3 in interest3
CHAPTER 31 CASE C-89
)&
6ince the only period in which there is borrowing is the third period we can set the ending short; term debt in >uarter 1 e8ual to ero and use 6ol7er3 $oing so we find the necessary sales growth rate is / percent3 The short;term financial plan would be:
Collections from pre7ious 8uarter Collections from current 8uarter sales ayments to suppliers for pre7ious 8uarter ayments to suppliers for current 8uarter E&penses $i7idends and interest Outlay Net cash flow
Cash 5low ;# ;$ '-*0.**3** '+,,,44311
;% '+0,1+-311
;& '+-/.3**
,++4*3-0
.*-13-0
,44/.3**
,0/-/03-0
%14-/+3//
%,*-./34,
%,**+/3.*
%10+013+
%+1043*%1111..3** %/+.***3**
%04+/3.* %1,./.3.* %/+.***3**
%11/-./3/4 %1/..03.* %/+.***3**
%'4+1,,3.*
'/1,,.3*-
%-,14/30 %1,*1/3.* %/+.***3** %14****3** %'*0**.314
'//-+/*30*
Cash Balance
!eginning cash balance Net cash inflow Ending cash balance Dinimum cash balance Cumulati7e surplus %deficit
;# '/****3** %4+1,,3.* '///-..3.*
;$ '///-..3.* /1,,.3*',.4**3.-
;% ',.4**3.%*0**.314 '1++4.3/0
;& '1++4.3/0 //-+/*30* '/..0*.3+0
/1.***3** %'11,,3.*
/1.***3** '//*4**3.-
/1.***3** %'4-/*,3+1
/1.***3** '*0*.3+0
The short;term financial plan loo2s li2e this:
Target cash balance Net cash inflow New short;term in7estments "ncome on short;term in7estments 6hort;term in7estments sold New short;term borrowing "nterest on short;term borrowing 6hort;term borrowing repaid Ending cash balance Dinimum cash balance Cumulati7e surplus %deficit
4hort,term 5inancial lan '/1.***3** '/1.***3** %4+1,,3.* /1,,.3*-
!eginning short;term in7estments Ending short;term in7estments !eginning short;term debt Ending short;term debt
* 10.3** 404-43.* * * * '/1.***3** %/1.***3** '*
%/1,-*3*10.3** * * * * '/1.***3** %/1.***3** '*
'/1.***3** %*0**.314 * /*,+3/* *.4.034 * * * '/1.***3** %/1.***3** '*
'0.***3** 0.***3** * '*
'0.***3** *4-*3** '*
'*4-*3*1--300 * '*
'/1.***3** //-+/*30* %//-+43* /+31/ * * * * '/1.***3** %/1.***3** '* '1--300 /*,4/30+ * '*
The interest calculations for each 8uarter and the net cash cost are: >/: >: >1: >,:
E&cess funds at start of 8uarter of E&cess funds at start of 8uarter of E&cess funds at start of 8uarter of E&cess funds at start of 8uarter of
'0.***3** '0.***3** '*4-*3*'1--300
Net cash cost >/ > >1 >,
'10.3** 10.3** /*,+3/* /+31/
Cash generated by short;term financing
'/+/-3,/
earns earns earns earns
'10.3** '10.3** '/*,+3/* '/+31/
in income3 in income3 in income3 in income3
CHAPTER 27 CASH MANAGEMENT AT RICHMOND CORP.
CHAPTER 31 CASE C-91
1&
The amount the company will ha7e a7ailable is the future 7alue of the transfers which are an annuity3 The amount of each transfer is one minus the wire transfer cost times the number of transfers which is four since there are four ban2s times the amount of each transfer3 6o the total a7ailable in two wee2s will be: Amount a7ailable (/ % 3**),H'/+.***(FM"FA 3*-+?/,)I Amount a7ailable '/*1+./*,3/.
2&
The ban2 will accept the AC transfers from the four different ban2s so the company incurs a transfer fee from each collection center3 The future 7alue of the deposits will now be: Malue of AC H,('/+.*** % **)(FM"FA 3*0.?/, )I=/3***0. Malue of AC '/*14/-*+31The company should go ahead with the plan since the future 7alue is higher3
'&
To find the cost at which the company is indifferent we set the amount a7ailable we found in >uestion / e8ual to the cost e8uation we used in >uestion 3 6etting up this e8uation where \ stands for the AC transfer cost we find: H,('/+.*** % '\)(FM"FA3*0.?/,)I=/3***0. '/*1+./*,3/. \ '1/.3-0
CHAPTER 28 CREDIT POLICY AT BRAAM INDUSTRIES To decide on the optimal credit policy we need to calculate the NM of each policy3 5e will begin with the calculation of the NM of the current policy3 Current olic!
First we need to calculate the a7erage daily sales which are: A7erage daily sales '//-******=1-. A7erage daily sales '1/0+*+3 Now we need to calculate the daily interest rate: $aily interest rate (/ # 3*-) /=1-. % / 3*/.40?
Ne&t we need the a7erage daily costs3 5e will begin with the a7erage daily 7ariable costs which are ,. percent of sales3 6o the a7erage daily 7ariable costs are: A7erage daily 7ariable costs 3,.('//-******=1-.) A7erage daily 7ariable costs '/,1*/130* Under the current policy the default rate is 3/ percent so the a7erage daily defaults will be: A7erage daily defaults 3*/('//-******=1-.) A7erage daily defaults '--01340 The current policy has administrati7e costs e8ual to /3- percent of sales so the a7erage daily administrati7e costs are: A7erage daily administrati7e costs 3*/-('//-******=1-.) A7erage daily administrati7e costs '.*+,341 5e also need the appropriate interest rate for the collection period3 5ith a 3*/.40 percent daily interest rate the periodic rate for the 1+ day collection period is: "nterest rate (/ # 3***/.40 = 1-.) 1+ % / "nterest rate 3**-*4 or 3-*4? 6ince the credit policy will e&ist into perpetuity the NM is: NM %'/,1*/130* # ('1/0+*+3 % /,1*/130* % --01340 % .*+,341) = 3**-*4 NM '--.*4,03.
CHAPTER 31 CASE C-93
1ption #
Under Option / the a7erage daily sales are: A7erage daily sales '/1*******=1-. A7erage daily sales '1.-/-,31+ The a7erage daily 7ariable costs will be: A7erage daily 7ariable costs 3,.('/1*******=1-.) A7erage daily 7ariable costs '/-*01340 Under the Option / the default rate is 3- percent so the a7erage daily defaults will be: A7erage daily defaults 3*-('/1******* = 1-.) A7erage daily defaults '4-*30 Option / has administrati7e costs e8ual to 3, percent of sales so the a7erage daily administrati7e costs are: A7erage daily administrati7e costs 3*,('/1*******=1-.) A7erage daily administrati7e costs '+.,034. 5e also need the appropriate interest rate for the collection period3 5ith a 3*/.40 percent daily interest rate the periodic rate for the ,/ day collection period is: "nterest rate (/ # 3***/.40 = 1-.) ,/ % / "nterest rate 3**-.0 or 3-.0? 6ince the credit policy will e&ist into perpetuity the NM is: NM %'/-*01340 # ('1.-/-,31+ % /-*01340 % 4-*30 % +.,034.) = 3**-.0 NM '-4.+.1/3.1 1ption $
Under Option the a7erage daily sales are: A7erage daily sales '/4******=1-. A7erage daily sales '1.1,,3-The a7erage daily 7ariable costs will be: A7erage daily 7ariable costs 3,.('/4******=1-.) A7erage daily 7ariable costs '/.4*,/3/* Under the Option the default rate is 3 percent so the a7erage daily defaults will be: A7erage daily defaults 3*('/4******=1-.) A7erage daily defaults '000.31,
Option has administrati7e costs e8ual to /34 percent of sales so the a7erage daily administrati7e costs are: A7erage daily administrati7e costs 3*/4('/4******=1-.) A7erage daily administrati7e costs '-0/.3*0 5e also need the appropriate interest rate for the collection period3 5ith a 3*/.40 percent daily interest rate the periodic rate for the ./ day collection period is: "nterest rate (/ # 3***/.40=1-.)./ % / "nterest rate 3**+/+ or 3+/+? 6ince the credit policy will e&ist into perpetuity the NM is: NM %'/.4*,/3/* # ('1.1,,3-- % /.4*,/3/* % 000.31, % -0/.3*0) = 3**+/+ NM '/+,-,-/3., 1ption %
Under Option 1 the a7erage daily sales are: A7erage daily sales '/1******=1-. A7erage daily sales '1-/-,13+, The a7erage daily 7ariable costs will be: A7erage daily 7ariable costs 3,.('/1******=1-.) A7erage daily 7ariable costs '/-014301 Under the Option 1 the default rate is 3. percent so the a7erage daily defaults will be: A7erage daily defaults 3*.('/1******=1-.) A7erage daily defaults '4*,/3/* Option 1 has administrati7e costs e8ual to 3/ percent of sales so the a7erage daily administrati7e costs are: A7erage daily administrati7e costs 3*/('/1******=1-.) A7erage daily administrati7e costs '0.4,3. 5e also need the appropriate interest rate for the collection period3 5ith a 3*/.40 percent daily interest rate the periodic rate for the ,4 day collection period is: "nterest rate (/ # 3***/.40=1-.),4 % / "nterest rate 3**0+. or 30+.? 6ince the credit policy will e&ist into perpetuity the NM is: NM %'/-014301 # ('1-/-,13+, % /-014301 % 4*,/3/* % 0.4,3, = 3**0+. NM '1*,0*+/3*+
CHAPTER 31 CASE C-95
The company should choose Option / since it has the highest NM3 The default rate and administrati7e costs of Option are below those of Option 13 This is plausible3 Option e&tends the credit period while Option 1 e&tends the credit period and rela&es the credit policy3 The rela&ation of the credit policy will increase the default rate since it will include companies with lower credit ratings who are less li2ely to pay3 This in turn will increase the administrati7e costs of managing the delin8uent accounts3
CHAPTER 29 THE BIRDIE GOLF–HYBRID GOLF MERGER 1&
As with any other merger analysis we need to e&amine the present 7alue of the incremental cash flows3 The cash flow today from the ac8uisition is the ac8uisition cost plus the di7idends paid today or: Ac8uisition of ybrid $i7idends from ybrid Total
%'1.****** 4-****** %'.-******
Using the information pro7ided the cash flows to !irdie Jolf from ac8uiring ybrid Jolf for the ne&t fi7e years will be:
$i7idends from ybrid Ta&;loss carryforwards Terminal 7alue of e8uity Terminal 7alue of debt Total
"ear # ',+-,***
',+-,***
"ear $ '+/4***
"ear % '/+-,***
/-******
/-******
',/4***
'1,-,***
"ear & '-,4-***
"ear ' '1-./***
'-,4-***
.0-****** %/4****** '+*,./***
To discount the cash flows from the merger we must discount each cash flow at the appropriate discount rate3 The additional cash flows from the ta&;loss carry forwards and the proposed le7el of debt should be discounted at the cost of debt because they are determined with 7ery little uncertainty3 The terminal 7alue of the company is subLect to normal business ris2 and must be discounted at a normal rate3 The current weight of debt and weight of e8uity in ybrids capital structure is: w$ 3.* = (/ # 3.*) w$ 311 wE / % 311 wE 3-0 The beta for ybrids debt is:
β$ (3*+ % 3*-) = (3/1 % 3*-) β$ 34
CHAPTER 31 CASE C-97
Thus the o7erall beta for ybrid is:
β (311 G 34) # (3-0 G /31*) β 34 Now we can calculate the re8uired return for normal operations of ybrid which is: E(9 ) 3*- # 34-(3/1 % 3*-) E(9 ) 3/01 or /301? To find the discount rate for di7idends we need to find the new beta of e8uity for the merged ybrid3 The new debt%e8uity ratio is / which implies a weight of debt and a weight of e8uity e8ual to .* percent3 The new beta for e8uity must be:
β New HβOld % (w$%new G w$%oldI = wE%new β New H34- % (3.* G 311)I = 3.* β New /3.4 6o the discount rate for the di7idends to be paid in future is: E(9 $i7) 3*- # /3.4(3/1 % 3*-) E(9 $i7) 3/0/1 or /03/1? Now we can find the present 7alue of the future cash flows3 The present 7alue of each years cash flows along with the appropriate discount rate for each cash flow is: *iscoun t rate /03/1?
$i7idends Ta&;loss TM of e8uity TM of debt Total
"ear # '/0*4
+? /301? +?
"ear $
"ear %
'.40*0./ /10/0,/
'//.++-/1 /0*/1/-
"ear & '/,*0.1 /
"ear '
'/-..+4- 1/-1,,+1* %/1*-0/40,
'/0*4
'/4-++/0
',+44 4
'/,*0.1 /
'*1/+/+
And the NM of the ac8uisition is: NM %'.-****** # /0*4 # /4-++/0 # ,+444 # /,*0.1/ # *1/+/+ NM '../11*34-
2&
6ince the ac8uisition is a positi7e NM proLect the most !irdie would offer is to increase the current cash offer by the current NM or: ighest offer '1.****** # ../11*34ighest offer '100./11*34The highest share price is the total high offer price di7ided by the shares outstanding or: ighest share price '110./11*34- = .***** shares ighest share price '03-*
'&
To determine the current e&change ratio which would ma2e a cash offer and a share offer e8ui7alent we need to determine the new share price under the original cash offer3 The new share price of !irdie after the merger will be: New H'4, G //-***** # '../11*34-I = //-***** New '4-3* 6o the e&change ratio which would ma2e the cash offer and share offer e8ui7alent is: E&change ratio '-+30. = '4-3* E&change ratio 30/,0
)&
The highest e&change ratio !irdie would accept is an e&change ratio that results in a ero NM ac8uisition3 This implies the share price of !irdie remains unchanged after the merger so the e&change ratio is: E&change ratio '-+30. = '4, E&change ratio 301/,
CHAPTER 31 EAST COAST YACHTS GOES INTERNATIONAL 1&
The biggest ad7antage is the increased sales while the biggest ris2 is e&change rate ris23
2&
"f the dollar strengthens the profit will decline3 Con7ersely if the dollar wea2ens the profit will increase3
'&
The company will pay the sales commission out of gross sales so the after;commission sales in euros is: After;commission sales _+******(/ % 3*.)
CHAPTER 31 CASE C-99
After;commission sales _0-***** At the current e&change rate of '/31,=_ the E!T in euros will be con7erted to dollars in the amount of: $ollar E!T _0-*****('/31,=_) $ollar E!T '/*/+,*** East Coast @achts has production costs e8ual to +* percent of dollar sales at this e&change rate3 The total sales in dollars are: Total sales _+******('/31,=_) Total sales '/*0**** And the production costs are: roduction costs '/*0****(3+*) roduction costs '+.0-*** 6o the profit at the current e&change rate is: rofit '/*/+,*** % +.0-*** rofit '/-*+*** "f the e&change rate changes to '/3.=_ the euros will con7ert to: $ollar sales _0-*****('/3.=_) $ollar sales '4.***** 6ince the production costs are fi&ed the profit at this e&change rate will be: rofit '4.***** % +.0-*** rofit '4,***
