$
otal otal interest earned
&%0)9.1* 0.12
o, "uch is interest earned on interest? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
$
3nterest earned earned on the interest
1%&&$.1* 0.12
Explanation:
he $*%)00 invest"ent ,ill gro, to a future value of $9%))9.1* 4= FV 9 = $*%)00 × (1 + 0.09 95% assu"ing co"pounded interest over the 9 years. he total interest earned is $&%0)9.1*. he interest earned on the original invest"ent is $)' per year for 9 years% or $)%*'). he interest earned on the interest is the difference of $1%&&.1* 4= $&%0)9.1* 6 $)%*')5. What is the present value of a $#*0 pay"ent in one year ,hen the discount rate is percent? (Round your answer to 2 decimal places.)
$
7resent value
##$.*# 12
Explanation:
PV = FV 8(1+ 8(1+i PV = $#*0 8 (1 + 0.0
= $#*0 8 1.0 = $##.*# en en years ago% ailey invested $1%*00 and loced in a ' percent annual interest rate for )0 years (end #0 years fro" no,. idan can "ae a #0:year invest"ent today and loc in a 9 percent interest rate. o, "uch "oney should he invest no, in order to have the sa"e a"ount of "oney in #0 years as ailey?(Do not round intermediate calculations and round your final answer to 2 decimal places.) 7resent value
$ #%&1).$' 0.12
Explanation:
First% deter"ine ho, "uch ailey ,ill have #0 years fro" no,/ FV 20 × (1 + i 30 20 = PV -10 × FV 20 = $1%*00 × (1 + 0.0')0 20 = = $1%*00 × 10.0# = $1*%0'.# ;o% idan ,ill have to deposit/ PV = FV 20 / (1 (1 + i N 20 / PV = = $1*%0'.# 8 (1 + 0.09#0 = $1*%0'.# 8 &.0**1 = $#%&1).'
!o"pute the present value of an $1%)&0 pay"ent "ade in 9 years ,hen the discount rate is 11 percent. percent. (Do not round intermediate calculations and round your final answer to 2 decimal places.)
$
7resent value
&#(.(& 12
Explanation:
PV = FV/ (1 (1 + i < PV = $1%)&0 8 (1 + 0.11 0.119
= $1%)&0 8 #.&&'0* = $&#.& !o"pute the present value of $&%100 paid in t,o years using the follo,ing discount rates/ 9 percent in the first year and ' percent in the second year. (Do not round intermediate calculations and round your answer to 2 decimal places.)
$
7resent value
*%))#.)1 0.12
explanation:
PV = FV / 4(1 4(1 + i (1 + j 5 PV = $&%100 8 4(1 4(1 + 0.09 × (1 + 0.0'5
= $&%100 8 41.09 × 1.0'5 = $&%100 8 1.1#0 = $*%))#.)1 Which cash flo, ,ould you rather pay% $*#& today or $&00 in t,o years if interest rates are 10 percent? 7ay $&00 in t,o years
7ay $*#& today
V = PV =
FV 8(1 8(1 + i <
$&00. &00. 8 (1 (1 + >>1 >>1# = $&00 8 1.#1000 = $*1).## he present value of $&00 to -e paid in t,o years at a t 10 percent interest is $*1). his a"ount is lo,er than $*#& paid today. herefore% paying the $&00 in t,o years is cheaper. pproi"ately ho, "any years are needed needed to dou-le a $&00 invest"ent invest"ent ,hen interest interest rates are 1).&0 1).&0 percent per year? (Round your answer to 2 decimal places.) 7eriod
years &.)) 1
Explanation:
< = # 8 1).&0 @ &.)) years pproi"ately ,hat interest rate rate is earned ,hen an invest"ent dou-les over 1#.# years? (Round your answer to 2 decimal places.)
3nterest rate
2 &.90 1
Explanation:
< = # 8 1#.# @ &.90 percent Aeter"ine the interest rate earned on a $)%#00 deposit ,hen $)%'00 is paid -ac in one year. (Round your answer to 2 decimal places.)
3nterest rate
2 1'.(& 12
Explanation:
$)%#00 × (1 + i = $)%'00B ;olving for i yields 1'.&2 Cou invested $)%000 in the stoc "aret one year ago. oday% the invest"ent is valued at $)%0. What return did you earn? 2
Deturn earned
## 12
What return ,ould you suffer net year for your invest"ent to -e valued at the original $)%000? (Negative answer should be indicated by a minus sign. Do not round intermediate calculations calculation s and round your final answer to 2 decimal places.)
Deturn earned
2 :1'.0) 12
Explanation:
FV N = PV × × (1 + i N N =
$)%0 = $)%000 × (1 + i 1 (1 + i = $)%0 8 $)%000 i = = 1.## E 1 = 0.## or ##.002 (first year return is positive FV N = PV × × (1 + i N N =
$)%000 = $)%0 × (1 + i 1 (1 + i = $)%000 8 $)%0 i = = 0.'19 E 1 = E0.1'0) E 0.1'0) or E1'.0)2 (second year return is negative What annual rate of return is earned on a $&%000 invest"ent ,hen it gro,s to $9%#&0 in si years? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
nnual rate rate of return
2 10.'0 12
Explanation:
FV N = PV × × (1 + i N N =
$9%#&0 = $&%000 × (1 + i (1 + i = $9%#&0 8 $&%000 (1 + i = 1.'& i = = (1.'&(18 : 1 = 0.10'0 or 10.'02 o, long ,ill it tae $#%000 to reach $%000 ,hen it gro,s at 10 percent per year? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
years
7eriod
1).1* 1
Explanation:
FV N = PV × × (1 + i N N =
$%000 = $#%000 × (1 + 0.10 < (1.10< = $%000 8 $#%000 (the thousands cancel ln (1.10< = ln ).& < × ln 1.10 = ln ).& < = ln ).& 8 ln 1.10 = 1.#&# 8 0.09&)1 = 1).1* years = 1) years% 1. "onths !o"pute the future value in year ' of a $)%#00 deposit in year 1 and another $#%00 deposit at the end of year ) using a 10 percent interest rate. (Do not round intermediate calculations and round your final answer to 2 decimal places.)
$
Future value
10%&'*.#( 0.12
Explanation:
F' = $)%#00 × (1 + 0.10 + $#%00 × (1 + 0.10 & = $%#)&.'9 + $*%)*'.)' = $10%&'*.# Given a 10 percent interest rate% co"pute the year future value if deposits of $)%100 and $*%100 are "ade in years # and )% respectively% and a ,ithdra,al of $1%000 is "ade in year &. (Do not round intermediate calculations and round your final answer to 2 decimal places.)
$
Future value
9%('&.)9 0.12
Explanation:
F = $)%100 × (1 + 0.10 & + $*%100 × (1 + 0.10 * E $1%000 × (1 + 0.10 # = $*%99#.&' + $%00#.'1 E $1%#10.00 = $9%'&.)9 Given a ) percent interest rate% co"pute the year future value of deposits "ade in years 1% #% )% and * of $1%0&0% $1%)&0% $1%)&0% and $1%*&0. (Do not round intermediate calculations and round your final answer to 2 decimal places.)
$
Future value
&%(&0.1$ 0.12
Explanation:
F = $1%0&0 × (1 + 0.0) & + $1%)&0 × (1 + 0.0) * + $1%)&0 × (1 + 0.0) ) + $1%*&0 × (1 + 0.0) # F = $1%#1.#* + $1%&19.** + $1%*&.1' + $1%&)'.)1 = $&%&0.1 What is the future future value of a $'&0 annuity annuity pay"ent over five years if interest rates are 9 percent? percent? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
Future value
$ &%0'(.00 0.12
Explanation:
ssu"e that you contri-ute $#10 per "onth to a retire"ent plan for 1& years. hen you are a-le to increase the contri-ution to $*10 per "onth for the net #& years. Given an ' percent interest rate. What is the value of your retire"ent plan after the *0 years? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
$
Future value of "ultiple annuities
9#)%)1$.9# 0.012
Explanation:
Hrea the annuity strea"s into a level strea" of pay"ents of $#10 for *0 years and another level strea" of pay"ents of $#00 for the last #& years.
!o"pute the present value of a $#%#00 deposit in year ) and another $1%00 deposit at the end of year & if interest rates are ' percent. (Do not round intermediate calculations and round your final answer to 2 decimal places.)
7resent value
$ #%90).*# 0.12
Explanation:
7 = $#%#00 I (1 + 0.0' ) + $1%00 I (1 + 0.0' & = $1%*.*) + $1%1&.99 = $#%90).*# Cou are looing to -uy a car. Cou can afford $#0 in "onthly pay"ents for five years. 3n addition to the loan% you can "ae a $'#0 do,n pay"ent. 3f interest rates are 9.& percent 7D% ,hat price of car can you afford? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
7resent value
$ )*%90*.0$ 0.12
Explanation:
WhatJs the present value of a $'0 annuity pay"ent over four years if interest rates are ' percent? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
7resent value
$ #%''1.&& 0.12
Explanation:
perpetuity pays $1'0 per year and interest rates are '.) percent. o, "uch ,ould its value change if interest rates increased to 9.' percent? (Round your answer to 2 decimal places.) !hange in value
$ ))1.9* 12
Aid the value increase or decrease? Aecrease Explanation:
he difference -et,een these perpetuities is $))1.9*. he value of the perpetuity decreased ,ith an increase in the interest rate. loan is offered ,ith "onthly pay"ents and a 9.& percent 7D. WhatKs the loanKs effective annual rate (LD? (Do not round intermediate calculations and round your final answer to 2 decimal places.) Lffective annual rate
Explanation:
2 10.#0 12
WhatKs the interest rate of a ':year% annual $)%&00 annuity ,ith present value of $#0%000? (Round your answer to 2 decimal places.)
2
nnuity interest rate
'.1&
Explanation:
or M calculator/ < = '% 7 = E#0%000% 7M = )%&00% F = 0% !7 3 = '.1&2 Cou ,ish to -uy a $#*%000 car. he dealer offers you a *:year loan ,ith a 10 percent 7D. What are the "onthly pay"ents? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
$
7ay"ent
per "onth $0'.(0 0.12
o, ,ould the pay"ent differ if you paid interest only? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
7ay"ent
$
per "onth #00.00 0.12
Explanation:
3f you only paid interest over the length of the loan and your principal -alance ,as repaid at the end of the *' "onths% your pay"ent ,ould -e $#00.00 per "onth (= $#*%000 × 0.10 I 1# for interest only and you ,ould o,e $#*%000 at the end of the *' "onths% too. Noey realiOes that he has charged too "uch on his credit card and has raced up $*%)00 in de-t. 3f he can pay $1#& each "onth and the card charges 1' percent 7D (co"pounded "onthly% ho, long ,ill it tae hi" to pay off the de-t? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
i"e to pay off the de-t Explanation:
"onths *'.(* 12
or M calculator/ 7 = *%)00% 7M = E1#&% F = 0% 3 = 1.&00B !7 < = *'.* "onths Dachel purchased a $#0%000 car three years ago using a 9 percent% &:year loan. ;he has decided that she ,ould sell the car no,% if she could get a price that ,ould pay off the -alance of her loan. What is the "ini"u" price Dachel ,ould need to receive for her car? (Round the loan payment to the nearest cent but do not round any other interim calculations. Round your final answer to 2 decimal places.)
$
he "ini"u" price
9%0'(.(# 0.12
Explanation:
First calculate the "onthly pay"ent that she has -een paying/
his is the "ini"u" price the car needs to -e sold for and it represents her -rea even price Cou are considering an invest"ent in )0:year -onds issued -y Moore !orporation. he -onds have no special covenants. The all !t"eet #o$"nal reports that 1:year :-ills are currently earning 1.'0 percent. Cour -roer has deter"ined the follo,ing infor"ation a-out econo"ic activity and Moore !orporation -onds/ Deal interest rate = 0.&2 Aefault ris pre"iu" = 1.02 PiQuidity ris pre"iu" = 1.0&2 Maturity ris pre"iu" = #.)02 a. What is the inflation pre"iu"? (Round your answer to 2 decimal places.) Lpected %P
2 1.0&
-. What is the fair interest rate on Moore !orporation )0:year -onds? (Round your answer to 2 decimal places.)
Fair interest rate
2 $.'&
Explanation:
a. Lpected %P = i & '%' = 1.'02 E 0.&2 = 1.0&2 -. i RS = 1.0&2 + 0.&2 + 1.02 + 1.0&2 + #.)02 = .'&2 Tne:year reasury -ills currently earn ).9& percent. Cou epect that one year fro" no,% 1:year reasury
-ill rates ,ill increase to *.1& percent. he liQuidity pre"iu" on #:year securities is 0.0& percent. 3f the liQuidity theory is correct% ,hat should the current rate -e on #:year reasury securities? (Round your answer to 2 decimal places.)
!urrent rate
2 *.0( 0.01
Explanation:
D# = 4(1 + 0.0)9&(1 + 0.0*1& + 0.000&5 18# E 1 = *.02
1
Tn March 11% #0UU% the eisting or current (spot 1:% #:% ):% and *:year Oero coupon reasury security rates ,ere as follo,s/ 1' 1 = 0.'&2%(0.*& 1' # = 1.*&2%(1.10 1' ) = 1.'&2% (1.&0 1' * = #.002(1.& Vsing the un-iased epectations theory% calculate the 1:year for,ard rates on Oero coupon reasury -onds for years #% )% and * as of March 11% #0UU. (Do not round intermediate calculations and round your answers to 2 decimal places.)
years
For,ard rates 2
#
#.0& 0.01
)
#.$& 0.01
*
#.*& 0.01
2 2
Explanation:
f = 4(1 + 1D## 8 (1 + 1D15 E 1 = 4(1 + 0.01*& # 8 (1 + 0.00'&5 E 1 = #.0&2 ) # ) # )f 1 = 4(1 + 1D) 8 (1 + 1D# 5 E 1 = 4(1 + 0.01'& 8 (1 + 0.01*& 5 E 1 = #.&2 * ) * ) *f 1 = 4(1 + 1D* 8 (1 + 1D) 5 E 1 = 4(1 + 0.0#00 8 (1 + 0.01'& 5 E 1 = #.*&2 # 1
7ri"ary "aret financial instru"ents include stoc issues fro" fir"s allo,ing their eQuity shares to -e pu-licly traded on stoc "aret for the first ti"e. We usually refer to these first:ti"e issues as ,hich of the follo,ing? initial pu-lic offerings
direct transfers "oney "aret transfers over:the:counter stocs Which of the follo,ing state"ents is correct? n 37T is an ea"ple of a pri"ary "aret transaction.
Money "arets are su-Rect to ,ider price fluctuations and are therefore "ore risy than capital "aret instru"ents. direct transfer of funds is "ore efficient than utiliOing financial institutions. he "aret seg"entation theory argues that the different investors have different ris preferences ,hich deter"ine the shape of the yield curve. Which of these does
co""ercial -ans secondary "arets
insurance co"panies "utual funds ll of the follo,ing are types of financial institutions ecept . 3nsurance co"panies 7ension funds hrifts Federal Deserve Han Unbiased Epectations !heory ;uppose that the current one:year rate (one:year spot rate and epected one:year :-ill rates over the follo,ing three years (i.e.% years #% )% and *% respectively are as follo,s/
Vsing the un-iased epectations theory% ,hat is the current (long:ter" rate for four:year:"aturity reasury securities? .002
.))2 .&2 .002 D* = 4(1 + .0&(1 + .0&&(1 + .0&(1 + .0518* : 1 = 2 "i#uidity $remium %ypothesis Hased on econo"istsJ forecasts and analysis% one:year reasury -ill rates and liQuidity pre"iu"s for the net four years are epected to -e as follo,s/ 1
Vsing the liQuidity pre"iu" hypothesis% ,hat is the current rate on a four:year reasury security? .)2
.002 .)'2
'.*002 D* = 4(1 + .0&(1 + .0& + .0010(1 + .0'& + .00#0(1 + .0'1& + .00#&518* : 1 = .)&*' Tne:year reasury -ills currently earn *.& percent. Cou epect that one year fro" no,% one:year reasury -ill rates ,ill increase to .& percent. he liQuidity pre"iu" on t,o:year securities is 0.0& percent. 3f the liQuidity theory is correct% ,hat should the current rate -e on t,o:year reasury securities? 1
&.#*2 &.&92
&.&2 &.9&2 D# = 4(1 + .0*&(1 + .0& + .000&5.& : 1 = &.&92
1
ll of the follo,ing are -enefits that financial institutions provide to our econo"y ecept . 3ncreased liQuidity 3ncreased "onitoring 3ncreased dollar a"ount of funds flo,ing fro" suppliers to fund users 3ncreased price ris &nterest rates particular securityJs default ris pre"iu" is ) percent. For all securities% the inflation ris pre"iu" is # percent and the real interest rate is #.#& percent. he securityJs liQuidity ris pre"iu" is 0.& percent and "aturity ris pre"iu" is 0.90 percent. he security has no special covenants. What is the securityJs eQuili-riu" rate of return?
1.'2 ).9&2 '.902
1.'2 i j = #.002 + #.#&2 + ).002 + 0.&2 + 0.902 = '.902
Aeter"ine the interest pay"ent for the follo,ing three -onds (ssu"e a $1%000 par value. ("eave no cells blan' be certain to enter * wherever re#uired. Round your answers to 2 decimal places) /
).)& percent coupon corporate -ond (paid se"iannually *.10 percent coupon reasury note !orporate Oero coupon -ond "aturing in ten years
$ 1$.(&
$ #0.&0
$ 0
Explanation:
).)& percent coupon corporate -ond (paid se"iannually/ X × 0.0))& × $1%000 = $1.& *.10 percent coupon reasury note/ X × 0.0*10 × $1%000 = $#0.&0 !orporate Oero coupon -ond "aturing in ten years/ 0.00 × $1%000 = $0 -ond issued -y Ford on May 1&% 199 is scheduled to "ature on May 1&% #09. 3f today is
years and '0
"onths $
Explanation:
May 1&% #09 "inus
$
7ar value
1%1)(.0& .012
$
3nterest pay"ent
#1.)# 12
Explanation:
7ar value = #09.9 8 1'*. × $1%000 = $1%1).0& 3nterest pay"ent = X × 0.0)&0 × $1%1).0& = $#1.)# !onsider a #.&& percent 37; ,ith an issue !73 reference of 19).'. he -ond is purchased at the -eginning of the year (after the interest pay"ent% ,hen the !73 ,as #0).. For the interest pay"ent in the "iddle of the year% the !73 ,as #0..
otal return
$ $#.0# 0.12
What is the total return of the 37; in percentage? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
otal return
Explanation:
2 &.90 0.01
Gain = Lnd of year value E Heginning of year value = #10.* 8 19).' × $1%000 E #0). 8 19).' × $1%000 = $1%0'&. E $1%0&1.0' = $)*.&' he "id:year interest pay"ent ,as/ X × 0.0#&& × #0. 8 19).' × $1%000 = $1).0 he end:of:year interest pay"ent ,as/ X × 0.0#&& × #10.* 8 19).' × $1%000 = $1).'* otal dollar return = $)*.&' + $1).0 + $1).'* = $#.0# s a percentage% the return ,as = $#.0# 8 $1%0&1.0' = &.902 !onsider a ).0& percent 37; ,ith an issue !73 reference of 1'*.9. t the -eginning of this year% the !73 ,as 191. and ,as at #01.& at the end of the year. What ,as the capital gain of the 37; in dollars? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
!apital gain
$ &).&* 0.01
What ,as the capital gain of the 37; in percentage? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
!apital gain
2 &.1( 0.01
Explanation:
Gain = Lnd of year value E Heginning of year value = #01.& 8 1'*.9 × $1%000 E 191. 8 1'*.9 × $1%000 = $1%0'9.' E $1%0).#* = $&).&* s a percentage% the gain ,as = $&).&* 8 $1%0).#* = &.12 !onsider the follo,ing three -ond Quotes/ a reasury note Quoted at 99/1&% a corporate -ond Quoted at 10).)0% and a "unicipal -ond Quoted at 101.9&. 3f the reasury and corporate -onds have a par value of $1%000 and the "unicipal -ond has a par value of $&%000% ,hat is the price of these three -onds in dollars? (Do not round intermediate calculations and round your final answers to 2 decimal places.)
$
reasury note !orporate -ond Municipal -ond
99*.$9 0.01
$ 1%0)).00 0.01
$ &%09(.&0 0.01
Explanation:
reasury note at 99/1&/ (99 + 1&8)#2 × $1%000 = 0.99*'& × $1%000 = $99*.9 !orporate -ond at 10).)0/ 10).)02 × $1%000 = 1.0))0 × $1%000 = $1%0)).00 Municipal -ond at 101.9&/ 101.9&2 × $&%000 = 1.019& × $&%000 = $&%09.&0 !o"pute the price of a &. percent coupon -ond ,ith 10 years left to "aturity and a "aret interest rate of 9.0 percent. (ssu"e interest pay"ents are se"iannual. (Do not round intermediate calculations and round your final answer to 2 decimal places.)
Hond price
$ (('.'( 12
3s this a discount or pre"iu" -ond? Aiscount -ond Explanation:
or M calculator/ < = #0% 3 = *.&% 7M = #'.00% F = 1%000B !7 7 = E'.' ;ince the -ondKs price is less than $1%000% it is a discount -ond. .*& percent coupon -ond ,ith fifteen years left to "aturity is priced to offer a .9 percent yield to "aturity. Cou -elieve that in one year% the yield to "aturity ,ill -e percent. What is the change in price the -ond ,ill eperience in dollars? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
!hange in -ond price
$
Explanation:
!alculation of current -ond price/
((.&& 12
'.) percent coupon -ond ,ith 1 years left to "aturity is priced to offer a .& percent yield to "aturity. Cou -elieve that in one year% the yield to "aturity ,ill -e .* percent. What ,ould -e the total return of the -ond in dollars? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
otal return
$ #.(# 12
What ,ould -e the total return of the -ond in percentage? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
otal return
2 0.#) 0.01
Explanation:
!alculation of the current -ond price/
WhatKs the current yield of a *.#0 percent coupon corporate -ond Quoted at a price of 101.'? (Round your answer to 2 decimal places.)
!urrent yield
2 *.1) 0.01
Explanation:
*.#02 8 101.'2 = 0.0*1) = *.1)2 WhatJs the taa-le eQuivalent yield on a "unicipal -ond ,ith a yield to "aturity of &.# percent for an investor in the )) percent "arginal ta -racet? (Round your answer to 2 decimal places.) aa-le eQuivalent yield
2 (.($ 0.01
Explanation:
&.*0 percent coupon -ond ,ith 1 years left to "aturity is offered for sale at $9&&.#. What yield to "aturity is the -ond offering? (ssu"e interest pay"ents are se"iannual. (Round your answer to 2 decimal places.)
Cield to "aturity
2 &.'1 0.01
Explanation:
M calculator/ < = )*% 7 = E9&&.#% 7M = #.0% F = 1%000B !7 3 = #.902 CM = #.902 × # = &.'12 client in the #& percent "arginal ta -racet is co"paring a "unicipal -ond that offers a &.0 percent yield to "aturity and a si"ilar:ris corporate -ond that offers a .0 percent yield. Aeter"ine the eQuivalent taa-le yield. (Round your answer to 2 decimal places.) 2
LQuivalent taa-le yield
$.$( 0.01
Which -ond ,ill give the client "ore profit after taes? !orporate -ond Explanation:
First deter"ine the LC/
;ince . percent is less than .0 percent% the client should tae the corporate -ond. *.*& percent coupon "unicipal -ond has 1# years left to "aturity and has a price Quote of 10.0. he -ond can -e called in eight years. he call pre"iu" is one year of coupon pay"ents. (ssu"e interest pay"ents are se"iannual and a par value of $&%000. !o"pute the -ondKs current yield. (Round your answer to 2 decimal places.) !urrent yield
2 *.1( 0.01
!o"pute the yield to "aturity. (Round your answer to 2 decimal places.) Cield to "aturity
2 ).(& 0.01
!o"pute the taa-le eQuivalent yield (for an investor in the ) percent "arginal ta -racet. (Round your answer to 2 decimal places.)
2
LQuivalent taa-le yield
&.'$ 0.01
!o"pute the yield to call. (Round your answer to 2 decimal places.) Cield to call
2 ).9* 0.01
Explanation:
!urrent yield = (0.0**& × $&%000 8 (1.00 × $&%000 = *.*&2 8 10.02 = *.12 M calculator/ < = #*% 7 = E&%))&% 7M = 111.#&% F = &%000B !7 3 = 1.'&2 CM = 1.'&2 × # = ).&2
M calculator/ < = 1% 7 = E&%))&% 7M = 111.#&% F = &%###.&0B !7 3 = 1.9#2 C! = 1.9#2 × # = ).9*2 he current yield is lo,er than the coupon rate -ecause this is currently a pre"iu" -ond. his is also sho,n -y the CM % ,hich is lo,er than the coupon rate. he C! is co"paratively high% -ut it is currently unliely that the -ond ,ill -e called early since interest rates are only a little lo,er than the coupon rate and the call pre"iu" ,ould have to -e paid. ssu"e on a given day in Tcto-er% the Ao, Nones 3ndustrial verage set a ne, high at a close of ##%)*.&)% ,hich ,as up 1*&.)0 that day. What ,as the return (in percent of the stoc "aret that day? (Round your answer to 2 decimal places.)
Deturn of stoc "aret
2 0.$& 0.01
Explanation:
F = 7 × (1 + i ##%)*.&) = (##%)*.&) E 1*&.)0 × (1 + i i = (##%)*.&) 8 ##%*'9.#) E 1 = 0.&2 Cour discount -roerage fir" charges $'.0 per stoc trade. o, "uch "oney do you need to -uy 10 shares of 7fiOer% 3nc. (7FL% ,hich trades at $*0.*#? (Round your answer to 2 decimal places.)
$
"ount needed
$%*(&.90
Explanation:
($*0.*#8share × 10 shares + $'.0 = $%*&.90 Cour full:service -roerage fir" charges $1'0 per stoc trade. o, "uch "oney do you receive after selling #10 shares of
"ount received
*%'*).#0
Explanation:
($#).9#8share × #10 shares E $1'0 = $*%'*).#0 preferred stoc fro" AuQuesne Pight !o"pany (AZV7D pays $).10 in annual dividends. 3f the reQuired return on the preferred stoc is .00 percent% ,hatKs the value of the stoc? (Round your answer to 2 decimal places.)
$
alue of stoc
&1.$( 0.01
Explanation:
he gro,th rate g eQuals Oero/
fir" is epected to pay a dividend of $1.1& net year and $1.)0 the follo,ing year. Financial analysts -elieve the stoc ,ill -e at their price target of $)0 in t,o years. !o"pute the value of this stoc ,ith a reQuired return of 11.1 percent. (Round your answer to 2 decimal places.)
alue of stoc
Explanation:
$ #$.)9 0.12
fir" recently paid a $0.0 annual dividend. he dividend is epected to increase -y 1# percent in each of the net four years. 3n the fourth year% the stoc price is epected to -e $*#. 3f the reQuired return for this stoc is 1*.&0 percent% ,hat is its current value? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
$
!urrent value
#$.(1 12
1#01# Explanation:
Find the dividends in the net four years/ A1 = $0.0 × (1 + 0.1# = $0.# A# = $0.# × (1 + 0.1# = $0.&# A) = $0.&# × (1 + 0.1# = $0.'*)0 A* = $0.'*)0 × (1 + 0.1# = $0.9**1
= $0.# 8 1.1*& + $0.&# 8 1.1*& # + $0.'*)0 8 1.1*& ) + ($0.9**1 + $*# 8 1.1*&0 * = $#.1
nnual dividends of General Llectric (GL gre, fro" $0.') in #001 to $1.#0 in #00. What ,as the annual gro,th rate? (Round your answer to 2 decimal places.) nnual gro,th rate
2 (.$& 0.01
Explanation:
Financial analysts forecast Pi"ited Hrands (PA gro,th rate for the future to -e '.& percent. PAKs recent dividend ,as $0.*0. What is the value of Pi"ited Hrands stoc ,hen the reQuired return is 10.& percent? (Round your answer to 2 decimal places.)
alue of stoc
$ #1.(0 0.12
Explanation:
7ayche 3nc. (7CU recently paid an $0.'# dividend. he dividend is epected to gro, at a 1& percent rate. he current stoc price is $0.&1. What is the return shareholders are epecting? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
2
;hareholders return
1$.&$ 12
Explanation:
First convert A0 to A1/ $0.'# × (1 + 0.1&0 = $0.9*).
fir" does not pay a dividend. 3t is epected to pay its first dividend of $0.)0 per share in t,o years. his dividend ,ill gro, at 1* percent indefinitely. Vse a 1&.& percent discount rate. !o"pute the value of this stoc. (Round your answer to 2 decimal places.) ;toc alue
$ 1(.)# 12
Explanation:
;toc price ;toc price ,ith ne, 78L
Explanation:
$ *1.*# 0.01
$ &1.&0 0.01
Vltra 7etroleu" (V7P has earnings per share of $1.9 and a 78L ratio of )).#0. WhatKs the stoc price? (Round your answer to 2 decimal places.) ;toc price
Explanation:
$ &$.11 0.01
FedL !orp stoc ended the previous year at $10'.19 per share. 3t paid a $0.&0 per share dividend last year. 3t ended last year at $111.*9. 3f you o,ned )*0 shares of FedL% ,hat ,as your dollar return and percent return? (Round your percent return answer to 2 decimal places.)
$
Aollar return
1%#9# ).&1 0.01
7ercent return
2
Explanation:
Aollar Deturn = (Lnding alue E Heginning alue + 3nco"e = $111.*9 × )*0 E $10'.19 × )*0 + $0.&0 × )*0 = $1%#9# #'.*9S&90:)#.9S&90+#.S&90 7ercentage Deturn = $1%#9# 8 ($10'.19 × )*0 = ).&12 corporate -ond that you o,n at the -eginning of the year is ,orth $'90. Auring the year% it pays $*' in interest pay"ents and ends the year valued at $''0. What ,as your dollar return and percent return? (Round your $ercent return to 2 decimal places.) $
Aollar return
)' *.#( 0.01
7ercent return
2
Explanation:
Aollar Deturn = !apital gain + 3nco"e = $''0 6 $'90 + $*' = $)' 10)0
:10#0 +)#=
7ercent return = $)' 8 $'90 = *.#2 Dan the follo,ing three stocs -y their ris:return relationship% -est to ,orst. Dail aul has an average return of 9 percent and standard deviation of )# percent. he average return and standard deviation of 3dol ;taff are 1# percent and )0 percentB and of 7oer:D:Vs are percent and )9 percent. Dan 1 # )
;toc 3dol staff Dail aul 7oer:D:Vs
Explanation:
Dan -y coefficient of variation/ Dail aul !o = )# 8 9 = ).&% 7oer:D:Vs !o = )9 8 = .&0% and 3dol ;taff !o = )0 8 1# = #.&0.
n investor o,ns $10%000 of do-e ;yste"s stoc% $11%000 of Ao, !he"ical% and $11%000 of Tffice Aepot. What are the portfolio ,eights of each stoc? (Round your answers to decimal places.) 7ortfolio ,eights do-e ;yste"
0.)1#& 0.001
Ao, !he"ical
0.)*)' 0.001
Tffice Aepot
0.)*)' 0.001
Explanation:
otal portfolio = $10%000 + $11%000 + $11%000 = $)#%000 do-e ;yste" ,eight = $10%000 8 $)#%000 = 0.)1#& Ao, !he"ical ,eight = $11%000 8 $)#%000 = 0.)*)' Tffice Aepot ,eight = $11%000 8 $)#%000 = 0.)*)' Cear:to:date% Tracle had earned a 61.** percent return. Auring the sa"e ti"e period% alero Lnergy earned .'0 percent and McAonaldJs earned 0.&# percent. 3f you have a portfolio "ade up of #& percent Tracle% #0 percent alero Lnergy% and && percent McAonaldJs% ,hat is your portfolio return? (Round your answer to 2 decimal places.) 7ortfolio return
2 1.*9 0.01
Explanation:
7ortfolio Deturn = (0.#& × 61.**2 + (0.#0 × .'02 + (0.&& × 0. = 1.*92 he past five "onthly returns for Yohls are ).9# percent% *.& percent% 6#.0 percent% 9.** percent% and 6#.9* percent. What is the average "onthly return? (Round your answer to + decimal places.) verage return
2 #.&'$ 0.001
Explanation:
verage Deturn = ().9#2 + *.&2 6 #.02 + 9.**2 6 #.9*2 8 & = #.&'2 he past five "onthly returns for YohlKs are ).'' percent% *.* percent% 6#.0# percent% 9.*# percent% and 6#.90 percent. !o"pute the standard deviation of YohlsK "onthly returns. (Do not round intermediate calculations and round your final answer to 2 decimal places.)
;tandard deviation
2 &.0' 12
Explanation:
verage Deturn = ().''2 + *.*2 6 #.0#2 + 9.*#2 6 #.902 8 & = #.&02
a-le 9.# verage Deturns for Honds 19&0 to 19&9 190 to 199 190 to 199 19'0 to 19'9 1990 to 1999 #000 to #009
verage verage verage verage verage verage
Honds 0.02 1.& &.& 1). 9. '.1
a-le 9.* nnual ;tandard Aeviation for Honds 19&0 to 19&9 190 to 199 190 to 199 19'0 to 19'9 1990 to 1999 #000 to #009
Honds *.'2 .) . 1&.' 1#.& 10.9
!alculate the coefficient of variation of the ris:return relationship of the -ond "aret (Vse the a-ove a-les during each decade since 19&0. (Round your answers to 2 decimal places.) Aecade 19&0s
!o
190s
*.#0
190s
1.#0
19'0s
1.1&
1990s
1.#9
#000s
1.)&
Explanation:
he lo,er the coefficient of variation% the -etter the ris:return relationship. he early t,o decades% 19&0s and 190s% have a poor ris:return relationship for -onds. he 19&0s coefficient of variation is not
defined -ecause the average return is Oero. he poor relationship in the 190s is caused -y the very lo, return in that decade. he three full decades since 190 have had a good ris:return relationship. 3f you o,n '00 shares of lasa ir at $&0.0'% '&0 shares of Hest Huy at $&'.&#% and 00 shares of Ford Motor at $'.'1% ,hat are the portfolio ,eights of each stoc? (Round your answers to + decimal places.)
7ortfolio ,eights lasa ir
0.*#1 0.001
Hest Huy
0.&#) 0.001
Ford Motor
0.0&$ 0.001
Explanation:
otal portfolio = ('00 × $&0.0' + ('&0 × $&'.&# + (00 × $'.'1 = $9&%09#.00 lasa ir ,eight = ('00 × $&0.0' 8 $9&%09#.00 = 0.*#1 Hest Huy ,eight = ('&0 × $&'.&# 8 $9&%09#.00 = 0.&#) Ford Motor ,eight = (00 × $'.'1 8 $9&%09#.00 = 0.0& Cou have $1'%000 to invest. Cou ,ant to purchase shares of lasa ir at $*).)% Hest Huy at $&#.##% and Ford Motor at $'.9. o, "any shares of each co"pany should you purchase so that your portfolio consists of #0 percent lasa ir% )0 percent Hest Huy% and &0 percent Ford Motor? (Do not round intermediate calculations and round your final answers to the nearest whole number.)
lasa air Hest -uy Ford "otor
shares ') 12
shares 10) 12
shares 1%00* 12
Explanation:
lasa ir/ 0.#0 × $1'%000 8 $*).) = ') shares Hest Huy/ 0.)0 × $1'%000 8 $&#.## = 10) shares Ford Motor/ 0.&0 × $1'%000 8 $'.9 = 1%00* shares Hecause of rounding the nu"-er of shares and to allo, for any co""ission or trading costs% you "ay have to purchase a share or t,o less of a stoc. he ta-le -elo, sho,s your stoc positions at the -eginning of the year% the dividends that each stoc paid during the year% and the stoc prices at the end of the year. Heginning of Aividend 7er !o"pany ;hares Cear 7rice ;hare Lnd of Cear 7rice Nohnson !ontrols 00 $*.#1 $1.*) $ '.&
Medtronic Airect Zualco""
00 900 00
&'.' #.#* **.)'
0.
&*.'1 #&.9 *0.##
0.&#
What is your portfolio dollar return and percentage return? (Round your answers to 2 decimal places.) 7ortfolio Deturn $ Aollar return )%###.00 12 2
7ercentage return
#.)( 12
Explanation:
!onsider the follo,ing annual returns of Molson !oors and 3nternational 7aper/
Cear 1 Cear # Cear ) Cear * Cear &
Molson !oors 3nternational 7aper 19.'2 &.#2 6 9.1 61'.# *0.0 6 0.9 6 '.) #.) 1.9 611.'
!o"pute each stocKs average return% standard deviation% and coefficient of variation. (Round your answers to 2 decimal places.)
verage return
Molson !oors 2
;tandard deviation !oefficient of variation
11.'$ 12
3nternational 7aper 2 0.)# 12
2 #0.(( 12
1.(& 12
2 1(.$) 12
&&.09 12
Which stoc appears -etter? Molson !oors Explanation:
Molson !oors has eperienced a "uch higher average return than 3nternational 7aper ,ith slightly "ore ris (standard deviation. hus% it is not a surprise that Molson !oors has a significantly -etter (lo,er coefficient of variation. Molson !oors is superior on a ris:return -asis.
t the -eginning of the "onth% you o,ned $&%000 of General Ayna"ics% $9%000 of ;tar-ucs% and $%000 of
7ortfolio return
2 .(( 12
Explanation:
otal portfolio = $&%000 + $9%000 + $%000 = $#0%000 General Ayna"ics ,eight = $&%000 8 $#0%000 = 0.#&00 ;tar-ucs ,eight = $9%000 8 $#0%000 = 0.*&00
!o"pute the epected return given these three econo"ic states% their lielihoods% and the potential returns/ (Round your answer to 2 decimal places.) Lcono"ic ;tate Fast gro,th ;lo, gro,th Decession
Lpected return
7ro-a-ility Deturn 0.11 &9 2 0.&# #& 0.) E# 2 9.&0 0.01
Explanation:
Lpected return = (0.11 × &92 + (0.&# × #&2 + (0.) × E#2 = 9.&02 Follo,ing are three econo"ic states% their lielihoods% and the potential returns/ Lcono"ic ;tate Fast gro,th ;lo, gro,th Decession
7ro-a-ility Deturn 0.#* )0 2 0.) 0.*0 E19
Aeter"ine the standard deviation of the epected return. (Do not round intermediate calculations and round your answer to 2 decimal places.)
;tandard deviation
2 19.)) 0.12
Explanation:
Lpected return = (0.#* × )02 + (0.) × 2 + (0.*0 × 6192 = #.1#2 http/88,,,.Oen,ealth.co"8-usinessfinanceonline8DD8LD!alculator.ht"l
Follo,ing are four econo"ic states% their lielihoods% and the potential returns/ Lcono"ic ;tate Fast gro,th ;lo, gro,th Decession Aepression
7ro-a-ilit Deturn y 0.#& 9 2 0.0 1 0.1) E1 0.0# E*'
!o"pute the epected return and standard deviation. (Do not round intermediate calculations and round your answers to 2 decimal places.)
Lpected return
#$.91 12
2
;tandard deviation
)).00 12
2
Explanation:
Lpected return = (0.#& × 92 + (0.0 × 12 + (0.1) × 612 + (0.0# × 6*'2 = #.912
he average annual return on an 3nde fro" 19' to 199& ,as 10.0& percent. he average annual :-ill yield during the sa"e period ,as ).#& percent. What ,as the "aret ris pre"iu" during these ten years? (Round your answer to 2 decimal place.) 2
verage "aret ris pre"iu"
$.'0
Explanation:
verage "aret ris pre"iu" = 10.0&2 E ).#&2 = .'02 3f the ris:free rate is ).0 percent and the ris pre"iu" is 1. percent% ,hat is the reQuired return? (Round your answer to / decimal places.)
DeQuired return
2 &.#
Explanation:
DeQuired return = ).02 + 1.2 = &.#2 Cou have a portfolio ,ith a -eta of 1.'1. What ,ill -e the ne, portfolio -eta if you eep '' percent of your "oney in the old portfolio and 1# percent in a stoc ,ith a -eta of 0.9#? (Do not round intermediate calculation and round your answer to 2 decimal places.)
1.(0 0.01
Explanation:
What is the -eta of your portfolio? (Do not round intermediate calculation and round your answer to 2 decimal places.)
7ortfolio -eta
1.*9 12
Explanation:
First deter"ine the total value of the portfolio and the ,eights of each stoc in the portfolio/ otal value = $1#%)& + $1%'#0 + $19%)0& = $*9%&00 Tly"pic ;teel ,eight = $1#%)& 8 $*9%&00 = #&2 Dent:a:!enter ,eight = $1%'#0 8 $*9%&00 = )2 Pincoln Lducational ,eight = $19%)0& 8 $*9%&00 = )92
DeQuired return
1*.$0
Aeter"ine ,hether the "anager is saying the fir" is undervalued or overvalued. Vndervalued Explanation:
Vse !7M to deter"ine the fir"Ks reQuired return/ *.02 + 1.& × (10.02 6 *.02 = 1*.02 ;ince the return reQuired for the level of ris is 1*.02 and the "anager -elieves a 1.&02 return ,ill -e achieved% the "anager is saying the fir" is undervalued. astings Lntertain"ent has a -eta of 0.9. 3f the "aret return is epected to -e 1#.10 percent and the ris:free rate is &.10 percent% ,hat is astingsK reQuired return? (Round your answer to 2 decimal places.)
2
astingsK reQuired return
9.9) 0.01
Explanation:
astingsK reQuired return = &.102 + 0.9 × (1#.102 E &.102 = 9.9)2 ;uppose 7accarKs current stoc price is $.#& and it is liely to pay a $#.1 dividend net year. ;ince analysts esti"ate 7accar ,ill have an &.0 percent gro,th rate% ,hat is its reQuired return? (Round your answer to 2 decimal places.)
DeQuired return
2 '.&1 0.01
Explanation:
Aiddy !orp. stoc has a -eta of 1.1% the current ris:free rate is & percent% and the epected return on the "aret is 1&.00 percent. What is AiddyKs cost of eQuity? (Round your answer to 2 decimal places.) !ost of eQuity
2 1$.00
Explanation:
iL = if + [L 4 L(iM E if 5 = 0.0& + 1.1 40.1&0 E 0.0&5 = 0.100% or 1.002 T-eron% 3nc.% has a $1& "illion (face value 10:year -ond issue selling for 99 percent of par that pays an annual coupon of '.)& percent. What ,ould -e T-eronKs -efore:ta co"ponent cost of de-t? (Round your answer to 2 decimal places.)
!ost of de-t
2 '.&0 0.01
Explanation:
Cields iA = 0.0'&0#*% or '.&02 ;uppose that PilyMac 7hotography epects LH3 to -e approi"ately $#10%000 per year for the foreseea-le future% and that it has 1%000 10:year% 9 percent annual coupon -onds outstanding. (Vse a-le 11.1 What ,ould the appropriate ta rate -e for use in the calculation of the de-t co"ponent of PilyMacKs W!!? a rate
2 )9
Explanation:
he interest pay"ents on the -onds ,ould total 1%000 × $1%000 × 0.09 = $90%000% resulting in LH of $#10%000 E $90%000 = $1#0%000. ;ince% as taa-le inco"e falls fro" $#10%000 to $1#0%000 the fir" is entirely in the )9 percent ta -racet fro" a-le 11.1% the average applica-le ta rate ,ould also -e eQual to )9 percent. 3PY has preferred stoc selling for 9' percent of par that pays a percent annual coupon. What ,ould -e 3PYKs co"ponent cost of preferred stoc? (Round your answer to 2 decimal places.) 2
!ost of preferred stoc
$.1# 0.01
Explanation:
A1 i 7
$
=
0.01# =% or .1#2
= 70
$9'
Far!ry 3ndustries% a "aer of teleco""unications eQuip"ent% has & "illion shares of co""on stoc outstanding% # "illion shares of preferred stoc outstanding% and #0%000 -onds. ;uppose the co""on shares are selling for $# per share% the preferred shares are selling for $1*.&0 per share% and the -onds are selling for 9' percent of par. What ,ould -e the ,eight used for eQuity in the co"putation of Far!ryKs W!!? (Round your answer to 2 decimal places.)
2
Weight used
().&) 0.01
Explanation:
L
&" × $# =
L+7+A
&" × $# + #" × $1*.&0 + #0%000 × 0.9' × $1%000 $1)&"
=
= 0.)&)% or ).&)2 $1')."
;uppose that NH !os. has a capital structure of ' percent eQuity% ## percent de-t% and that its -efore:ta cost of de-t is 1# percent ,hile its cost of eQuity is 1 percent. ssu"e the appropriate ,eighted: average ta rate is #& percent. What ,ill -e NHKs W!!? (Round your answer to 2 decimal places.) W!!
2 1*.*$ 0.01
Explanation:
L
7
W!!=
A
i L+ L+7+A
(1 E iA×!
i 7+ L+7+A
L+7+A
=0.' × 12 + 0 × 02 + 0.## × 1#2 × (1 E 0.#& = 1*.*2 Hetter7ie 3ndustries has "illion shares of co""on stoc outstanding% * "illion shares of preferred stoc outstanding% and #0%000 -onds. ssu"e the co""on shares are selling for $*& per share% the preferred shares are selling for $##.&0 per share% and the -onds are selling for 9' percent of par. What ,ould -e the ,eights used in the calculation of Hetter7ieKs W!!? (Do not round intermediate calculations and round your answers to 2 decimal places.)
2
LQuity ,eight
(*.19 12
7referred stoc ,eight
#1.#0 12
2 2
Ae-t ,eight
*.$# 12
Explanation:
L
" × $*& = " × $*& + *" × $##.&0 + #0%000 × 0.9' × $1%000
L+7+A
$)1&" = $*#*.0" = 0.*19% or *.192 7
*" × $##.&0 = " × $*& + *" × $##.&0 + #0%000 × 0.9' × $1%000
L+7+A
$90" = $*#*.0" = 0.#1#0% or #1.#02 A
#0%000 × 0.9' × $1%000 =
" × $*& + *" × $##.&0 + #0%000 × 0.9' × $1%000
L+7+A
$19." = $*#*.0"
= 0.0*#% or *.#2 ;uppose that Hro,n:MurphiesK co""on shares sell for $1.&0 per share% that the fir" is epected to set their net annual dividend at $0.*) per share% and that all future dividends are epected to gro, -y percent per year% indefinitely. ssu"e Hro,n:Murphies faces a flotation cost of 10 percent on ne, eQuity issues. What ,ill -e the flotation:adRusted cost of eQuity? (Round your answer to 2 decimal places.) 2
!ost of eQuity
'.() 0.01
Explanation:
A1 iL =
+g 70 E F $0.*) =
+ 0.0 $1.&0 E (0.10 × $1.&0
= 0.0')% or '.)2 ;uppose your fir" has decided to use a divisional W!! approach to analyOe proRects. he fir" currently has four divisions% through A% ,ith average -etas for each division of 0.&% 1.0% 1.#% and 1.&% respectively. ssu"e all current and future proRects ,ill -e financed ,ith 0.0 de-t and 0.*0 eQuity% the current cost of eQuity (-ased on an average fir" -eta of 1.0 and a current ris:free rate of * percent is 1# percent and the after:ta yield on the co"panyKs -onds is 9 percent. What ,ill the W!!s -e for each division? (Round your answers to 2 decimal places.) W!!s 2
Aivision
'.$0 0.01
Aivision H
10.#0 0.01
Aivision !
10.'* 0.01
Aivision A
11.'0 0.01
2 2 2
rev/ 11)0#01)Z!*1*&)
Explanation:
We can solve for the epected rate of return on the "aret/ iL = if + [L 4L(iM E if 5
1#2 = *2 + 1.0 4L(iM E *25 '2 = 4L(iM E *25 L(iM = 1#2 We can solve for the divisional costs of eQuity using the average divisional -etas/ For Aivision / i L = if + [L 4L(iM E if 5 = *2 + 0.& × 41#2 E *25 = '.02 For Aivision H/ i L = if + [L 4L(iM E if 5 = *2 + 1.0 × 41#2 E *25 = 1#.02 For Aivision !/ i L = if + [L 4L(iM E if 5 = *2 + 1.# × 41#2 E *25 = 1).2 For Aivision A/ i L = if + [L 4L(iM E if 5 = *2 + 1.& × 41#2 E *25 = 1.02 Finally% ,e can solve for the divisional W!!s For Aivision / W!!= L iL + A iA × (1E! = 0.* × '.02 + 0. × 92 = '.02 L+7+A L+7+A L For Aivision H/ W!!
A
=
For Aivision !/ W!!
iL + L+7+A
L+7+A
L
A
=
For Aivision A/ W!!
(1E! = 0.* × 1#.02 + 0. × 92 = iA×10.#02
(1E! = 0.* × 1).2 + 0. × 92 = iA×10.'*2
iL + L+7+A
L+7+A
L
A
=
(1E! = 0.* × 1.02 + 0. × 92 = iA×11.'02
iL + L+7+A
L+7+A
;uppose that M<3
2
W!!
9.(9 0.01
Explanation:
L W!!=
7 i L+
L+7+A
A (1 E iA×!
i 7+ L+7+A
L+7+A
=0.) × 11.02 + 0.0' × 9.&02 + 0.#9 × 9.002 × (1 E 0.)*
= 9.92 n all:eQuity fir" is considering the proRects sho,n -elo,. he :-ill rate is & percent and the "aret ris pre"iu" is ' percent. 7DTNL! LU7L!LA DLVD< HL '2 0.) H #0 1.1 ! 1* 1.) A 1' 1.&
!alculate the proRect:specific -ench"ars for each proRect. (Round your answers to 2 decimal places.)
2
7roRect
(.*0
7roRect H
1).'0
7roRect !
1&.*0
7roRect A
1(.00
2 2 2
3f the fir" uses its current W!! of 1) percent to evaluate these proRects% ,hich proRect% ,ill -e incorrectly reRected? 7roRect Explanation:
Vsing the fir"Js W!! of 1) percent as the 3DD -ench"ar% proRect ,ould -e reRected. Vsing eQuation 11:#% the proRect:specific -ench"ars for each proRect should -e/ For 7roRect / i L
= if + [L 4L (iM E if 5 = &2 + 0.) × 4'25 = .*02
For 7roRect H/ i L = if + [L 4L (iM E if 5 = &2 + 1.1 × 4'25 = 1).'02 For 7roRect !/ i L = if + [L 4L (iM E if 5 = &2 + 1.) × 4'25 = 1&.*02
For 7roRect A/ i L = if + [L 4L (iM E if 5 = &2 + 1.& × 4'25 = 1.002 3f 7roRect Js epected return of ' percent had -een co"pared to the proRect:specific reQuired return of .*0 percent% it ,ould have -een accepted. herefore% 7roRect ,ould have -een incorrectly reRected if the fir":,ide W!! had -een used as its -ench"ar.
;uppose you sell a fied asset for $9#%000 ,hen itJs -oo value is $11*%000. 3f your co"panyJs "arginal ta rate is ))2% ,hat ,ill -e the effect on cash flo,s of this sale (i.e.% ,hat ,ill -e the after:ta cash flo, of this sale?
\
$99%#0
$1%*0
$11*%000 $##%000 !F = $11*%000 + ($9#%000 6 $11*%000 (1 6 .)) = $99%#0 Cour !o"pany is considering a ne, proRect that ,ill reQuire $#0%000 of ne, eQuip"ent at the start of the proRect. he eQuip"ent ,ill have a deprecia-le life of years and ,ill -e depreciated to a -oo value of $#0%000 using straight:line depreciation. he cost of capital is 1)2% and the fir"Js ta rate is *02. Lsti"ate the present value of the ta -enefits fro" depreciation.
\
$1%90*
$100%000 $0%000 $*0%000 Aepreciation = ($#0%000 6 $#0%0008 = $100%000 $100%000 .*0= $*0%000 ta savings each period. cross the entire proRect% these savings ,ill constitute a period annuit y. 7"t = *0%000% F = 0% 3 = 1)% < = % 7 = 1%90* Cour !o"pany is considering a ne, proRect that ,ill reQuire $1'%000 of ne, eQuip"ent at the start of the proRect. he eQuip"ent ,ill have a deprecia-le life of & years and ,ill -e depreciated to a -oo value of $)%000 using straight:line depreciation. he cost of capital is 92% and the fir"Js ta rate is )02. Lsti"ate the present value of the ta -enefits fro" depreciation. $#%100 $900
\
$)%&01
$)%000 Aepreciation = ($1'%000 6 $)%0008& = $)%000 $)%000 .)0= $900 ta savings each period. cross the entire proRect% these savings ,ill constitute a & period annuit y. 7"t = 900% F = 0% 3 = 9% < = &% 7 = )%&01
YA;% 3nc.% has spent $)*0%000 on research to develop a ne, co"puter ga"e. he fir" is planning to spend $1*0%000 on a "achine to produce the ne, ga"e. ;hipping and installation costs of the "achine ,ill -e capitaliOed and depreciatedB they total $**%000. he "achine has an epected life of three years%
a $9%000 esti"ated resale value% and falls under the M!D; :year class life. Devenue fro" the ne, ga"e is epected to -e $&*0%000 per year% ,ith costs of $190%000 per year. he fir" has a ta rate of *0 percent% an opportunity cost of capital of 11 percent% and it epects net ,oring capital to increase -y $0%000 at the -eginning of the proRect.
What ,ill the cash flo,s for this proRect -e? (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)
Cear
0
1
$ F!F
#
$
$ ##0%&1(.** 0.12
:#&*%000.00 0.12
$ ##'%0#*.$* 0.12
Explanation:
Cear
0
1 &*0%000. 00
&*0%000. 00
0.00
Fied Ecosts
0.00
190%000. 00
190%000. 00
190%000. 00
Aepre Eciation
0.00
#%#9). 0
*&%01. 0
)#%1'1. 0
LH3
$
0.00
E
]
0.00
Aepre +ciation
0.00
T!F
$
0.00
$
1#9%*'#. &
0.00
$
)#)%0. *0
$
19*%##). '*
##0%&1. **
$
1#1%9&. )
$
#%#9). 0
$
)0*%9)'. *0
$
&*0%000. 00
$
$
$
)
;ales
aes
$
#
1'#%9). 0* *&%01. 0
$
##'%0#*. *
)1%'1'. *0 1#%1#. )
$
190%91. 0* )#%1'1. 0
$
)
###%'#. *
)$$%*&(.9
^
0%000.0 0
0.00
0.00
E 0%000.0 0
^F E
1'*%000. 00
0.00
0.00
E )%&'&.# '
F!F
E$
#&*%000. 00
$
##0%&1. **
$
##'%0#*. *
$
)%*&. 9#
Cou are evaluating a proRect for he iff:any golf clu-% guaranteed to correct that nasty slice. Cou esti"ate the sales price of he iff:any to -e $*10 per unit and sales volu"e to -e 1%000 units in year 1B 1%&00 units in year #B and 1%)#& units in year ). he proRect has a ):year life. aria-le costs a"ount to $#)0 per unit and fied costs are $100%000 per year. he proRect reQuires an initial invest"ent of $1'%000 in assets% ,hich ,ill -e depreciated straight:line to Oero over the ):year proRect life. he actual "aret value of these assets at the end of year ) is epected to -e $)%000.
3ncrease
&1%#&0
Explanation:
;ales ,ill go fro" $*10%000 to $1&%000 -et,een years 1 and #% so
Cear ;ales aria-le E costs
# $
0%000
)%&00
E Fied costs Aepreciatio E n
100%000
&9%000
LH3 E aes
$
1))%&00 *%#&
$
'%&
&9%000
T!F
$
1*&%&
;uppose you sell a fied asset for $119%000 ,hen its -oo value is $1)9%000. 3f your co"panyKs "arginal ta rate is )& percent% ,hat ,ill -e the effect on cash flo,s of this sale (i.e.% ,hat ,ill -e the after:ta cash flo, of this sale? $ !F 1#$%000 explanation:
he after:ta cash inflo, fro" the sale of the asset ,ill -e/ !F = Hoo value + (Maret value E Hoo value × (1 E T ) = $1)9%000 + ($119%000 E $1)9%000 × (1 E 0.)& = $1#%000 Cour fir" needs a co"puteriOed "achine tool lathe ,hich costs $*%000 and reQuires $11%00 in "aintenance for each year of its ):year life. fter three years% this "achine ,ill -e replaced. he "achine falls into the M!D; ):year class life category. ssu"e a ta rate of )* percent and a discount rate of 11 percent.
3f the lathe can -e sold for $*%00 at the end of year )% ,hat is the after:ta salvage value? answer to 2 decimal places.)
$ ;alvage value after ta
*%#'$.1# 0.12
Explanation:
he lathe ,ill have a re"aining -oo value of .*12 × $*%000 = $)%*'#.0. he after:ta cash flo,s fro" the sale of the lathe ,ill -e/
!F = Hoo value + (Maret value E Hoo value × (1 E T ) = $)%*'#.0 + ($*%00 E $)%*'#.0 × (1 E 0.)*
= $*%#'.1#
Cou have -een ased -y the president of your co"pany to evaluate the proposed acQuisition of a ne, special:purpose truc for $&0%000. he truc falls into the M!D; ):year class% and it ,ill -e sold after three years for $19%*00. Vse of the truc ,ill reQuire an increase in
What ,ill the cash flo,s for this proRect -e? (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)
Cear
0
1
$ F!F
#
$ :&1%*00.00 0.12
$ 1$%9&#.10 0.12
1'%'*#.&0 0.12
Explanation:
Cear ;ales
0 $
1 0.00
aria Ele costs
0.00
Fied Ecosts
0.00
Aepre Eciation
0.00
LH3
$
0.00
E
aes
$
$
0.00
Aepre +ciation
0.00
0.00
$
0.00 E
$
0.00
]
#
$
1%100.0 0
) 0.00
$
0.00 E
1%100.0 0
0.00 0.00
E
1%100.0 0
1%&.0 0
##%##&.0 0
%*0&.00
*)&.00
E$ &%1#&.00
$ 9%9&.00
1*.90
E 1%*#.&0
)%#9.)0
#'.10
E$ )%)'#.&0
$ %)9'.0
1%&.0 0
##%##&.0 0
%*0&.00
#9%#$(.*
T!F
$
0.00
$
1%9&#.1 0
$
1'%'*#.& 0
$
1)%'0). 0
^
1%*00.00
0.00
0.00
E 1%*00.00
^F E
&0%000.0 0
0.00
0.00
E
F!F
E$
&1%*00.0 0
$
1%9&#.1 0
$
1'%'*#.& 0
$
1*%0). 0
#9%#.* 0
Cou are trying to pic the least:epensive car for your ne, delivery service. Cou have t,o choices/ the ;cion % ,hich ,ill cost $1%&00 to purchase and ,hich ,ill have T!F of E$1%00 annually throughout the vehicleKs epected life of three years as a delivery vehicleB and the oyota 7rius% ,hich ,ill cost $#*%000 to purchase and ,hich ,ill have T!F of E$900 annually throughout that vehicleKs epected *: year life. Hoth cars ,ill -e ,orthless at the end of their life. Cou intend to replace ,hichever type of car you choose ,ith the sa"e thing ,hen its life runs out% again and again out into the foreseea-le future. 3f the -usiness has a cost of capital of 1) percent% calculate the L!. (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)
;cionJs L! oyotaJs L!
$ :'%$''.11 0.12
$ :'%9$'.$$ 0.12
Which one should you choose? ;cion Explanation:
Tne iteration of each delivery car ,ill consist of the follo,ing cash flo,s/ Cear ;cion !Fs oyota 7rius !Fs
0 1 1%&0 1%0 E$ E$ 0 0 #*%00 E$ E$ 900 0
he <7 of one ;cion ,ill -e/
# E$ 1%00 E$ 900
) 1%0 E$ 0
*
E$ 900
E$ 900
Cou are considering the purchase of one of t,o "achines used in your "anufacturing plant. Machine has a life of t,o years% costs $100 initially% and then $1*& per year in "aintenance costs. Machine H costs $10 initially% has a life of three years% and reQuires $1#0 in annual "aintenance costs. Lither "achine "ust -e replaced at the end of its life ,ith an eQuivalent "achine. he discount rate is 11 percent and the ta rate is Oero. !alculate the L!. (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)
L! Machine Machine H
$ :#0).)9 12
$ :1'9.&( 12
Which one should you choose? Machine H Explanation:
Tne iteration of each "achine ,ill consist of the follo,ing cash flo,s/ Cear Machine !Fs Machine H !Fs
0 E$ 100 E$ 10
he <7 of one Machine ,ill -e/
1 E$ 1*& E$ 1#0
# E$ 1*& E$ 1#0
) E$ 1#0
http/88,,,.investopedia.co"8calculator8netpresentvalue.asp
!o"pute the <7 for 7roRect M if the appropriate cost of capital is percent. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your final answer to 2 decimal places.)
7roRect M i"e/ !ash flo,
<7
0 E$#%000
1 $&&0
# $'0
) $#0
* $'00
& $)00
$ &19.90 12
;hould the proRect -e accepted or reRected? ccepted Explanation:
$&&0 E <7 $#%00 = 0 + $&19. = 90
(1.0
$'0
1
+
(1.0
$#0
#
+
(1.0
)
$'00 +
(1.0
*
$)00 +
(1.0&
!o"pute the <7 for 7roRect Y if the appropriate cost of capital is percent. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your final answer
to 2 decimal places.)
7roRect Y i"e/ !ash flo,
<7
0 1 E$11%)00 $&%&0
# $%&0
) $%&0
* $&%&0
& E$11%)00
$ 1%*(0.(* 0.12
;hould the proRect -e accepted or reRected? ccepted Explanation:
$&%&0 E <7 $11%)0 = 0 + $1%*0. = *
$%&0 +
(1.01
(1.0#
$%&0 +
$&%&0 +
(1.0)
(1.0*
E$11%)00 +
(1.0&
!o"pute the pay-ac statistic for 7roRect if the appropriate cost of capital is 9 percent and the "ai"u" allo,a-le pay-ac period is four years. (Round your answer to 2 decimal places.) 7roRect i"e/ !ash flo,
0 E$#%*00
1 $910
# $900
) $'00
* $&'0
& $)'0
years
7ay-ac
#.(* 0.01
;hould the proRect -e accepted or reRected? ccepted Explanation:
Cear !ash Flo, !u"ulative !ash Flo,
0 E$#%*00 E$#%*00
1 $910 E$1%*90
# $900 E$&90
) $'00 $#10
* $&'0
& $)'0
his proRect ,ill achieve pay-ac at ti"e # + $&908$'00 = #.* years. !o"pute the discounted pay-ac statistic for 7roRect A if the appropriate cost of capital is 11 percent and the "ai"u" allo,a-le discounted pay-ac is four years. (Do not round intermediate calculations and round your final answer to 2 decimal places. &f the pro0ect does not pay bac'1 then enter a * (ero).)
7roRect A i"e/
0
1
#
)
*
&
!ash flo,
E$1#%00 $)%&10 $*%&00 $1%'*0
Aiscounted pay-ac period
$0
$1%)#0
0
;hould the proRect -e accepted or reRected? DeRected Explanation:
Cear !ash Flo,
0 6$1#%00
7resent alue of !ash Flo, !u"ulative !ash Flo,
= 6$1#%00 = 6$1#%00
1 $)%&10 $)%&1081.11 = $)%1#.1 = 6$9%*).'*
# $*%&00 $*%&00 8 (1.11# = $)%&#.)0 = 6$&%'&.&*
) $1%'*0 $1%'*0 8 (1.11) = $1%)*&.)9 = 6$*%**0.1*
he <7 for this proRect is negative% so discounted pay-ac never occurs. !o"pute the 3DD for 7roRect F. he appropriate cost of capital is 1) percent. (Do not round intermediate calculations and round your final answer to 2 decimal places.)
7roRect F i"e/ !ash flo,
0 E$11%00
1 $*%#00
# $&%0)0
) $#%)0
* $)%000
2
3DD
10.*& 12
;hould the proRect -e accepted or reRected? DeRected Explanation:
E$11%00 0=
(1+3DD0
$*%#00 +
(1+3DD1
$&%0)0 +
(1+3DD#
$#%)0 +
(1+3DD)
$)%000 +
(1+3DD*
3DD = 10.*&2 ;ince 3DD _ i% this proRect should -e reRected. !o"pute the M3DD statistic for 7roRect N if the appropriate cost of capital is 10 percent. (Do not round intermediate calculations and round your final answer to 2 decimal places.)
7roRect N i"e/ !ash flo,
0 E$1%)00
1 $**0
# $1%)0
) E$&&0
* $)90
& E$1)0
* $0 $0 8 (1.11 = $0.00 = 6$*%**0.
2
M3DD
1#.&( 12
;hould the proRect -e accepted or reRected? ccepted Explanation:
Cear
0 E $
!ash Flo, 7resent alue (3f
1%)00
1
#
)
*
&
$**0
$1%)0
E$&&0
$)90
E$1)0
E $ 1%)00 E 1%9).9* $
;u" of 7
$**0 × (1.10* = $**.#0
Future alue (3f 7ositive
$1%)0 × (1.10) = $#%19.&)
;u" of F
E$&&0
E$1)0
(1.10) = E$*1).##
(1.10& = E$'0.# $)90 × (1.101 = $*#9.00 $)%#*#.)
E 1%9).9* $
Modified !Fs
$)%#*#.)
With this ne, set of "odified cash flo,s% the M3DD is/ E$1%9).9* 0
=
3DD =
(1+3DD0
$)%#*#.) +
(1+3DD&
1#.&2
;ince our M3DD decision statistic is greater than the ten percent cost of capital% ,e ,ould accept the proRect under the M3DD "ethod. !o"pute the 73 statistic for 7roRect ` if the appropriate cost of capital is percent. (Do not round intermediate calculations and round your final answer to 2 decimal places. &nclude a minus sign for negative answers.)
7roRect ` i"e/ !ash flo,
73
0 E$)%000
1 $0
# $'00 2
:).$9 12
;hould the proRect -e accepted or reRected? DeRected rev/ 110#01#
) $90
* $#0
& $*#0
Explanation:
$0 <7 = E$)%000 + (1.01 = $110.'#
$'00 + (1.0#
$90 + (1.0)
$#0 +
*
(1.0
$*#0 +
(1.0&
73 = $110.'# = :).92 $)%000 ;ince 73 _ 0% the proRect should -e reRected. !o"pute the 73 statistic for 7roRect Z if the appropriate cost of capital is 1) percent. (Do not round intermediate calculations and round your final answer to 2 decimal places.)
7roRect Z i"e/ !ash flo,
0 1 E$1#%*00 $*%0&0
# $*%''0
) $*%''0
* $#%'&0
2
73
1.10 12
;hould the proRect -e accepted or reRected? ccepted Explanation:
$*%0&0 <7 = E$1#%*00 + (1.1)1 = $1)&.'
$*%''0
$*%''0
$#%'&0
+ (1.1)#
+ (1.1))
+ (1.1)*
$1)&.' 73 =
=
1.102
$1#%*00 ;ince 73 0% this proRect should -e accepted. ;uppose your fir" is considering investing in a proRect ,ith the cash flo,s sho,n -elo,% that the reQuired rate of return on proRects of this ris class is 9 percent% and that the "ai"u" allo,a-le pay-ac and discounted pay-ac statistics for the proRect are ).& and *.& years% respectively. i"e/ !ash flo,
0 1 E$&%#00 $1%#&0
# $#%*&0
) $1%&0
* & $1%&0 $1%*&0 $1%#&0
Vse the <7 decision rule to evaluate this proRect. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places.)
$
<7
#%1)9.$* 0.12
;hould it -e accepted or reRected? ccepted Explanation:
E <7 $&%#0 = + 0
$1%#&0 (1.09
1
$#%*&0 +
#
(1.09
$1%&0 +
(1.09
)
$1%&0 +
(1.09
*
$1%*&0 +
$1%#&0 +
&
(1.09
(1.09
= $#%1)9.* he proRect should -e accepted -ecause the <7 is positive. ;uppose your fir" is considering investing in a proRect ,ith the cash flo,s sho,n -elo,% that the reQuired rate of return on proRects of this ris class is ' percent% and that the "ai"u" allo,a-le pay-ac and discounted pay-ac statistics for the proRect are ).& and *.& years% respectively. i"e/ !ash flo,
0 1 E$*%900 $1%#0
# $#%*0
) $1%0
* & $1%0 $1%*0 $1%#0
Vse the 73 decision rule to evaluate this proRect. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your final answer to 2 decimal places.)
2
73
&&.1) 12
;hould it -e accepted or reRected? ccepted Explanation:
$1%#0 <7 = E$*%900 =$#%01.)0
+ (1.0'
1
$#%*0 +
(1.0'
#
$1%0 +
)
(1.0'
$1%0 +
(1.0'
*
$1%*0 +
(1.0'
&
$1%#0 +
(1.0'
$#%01.)0 73 =
=
&&.1)2
$*%900 ;ince 73 0% the proRect should -e accepted. ;uppose your fir" is considering investing in a proRect ,ith the cash flo,s sho,n -elo,% that the reQuired
rate of return on proRects of this ris class is 11 percent% and that the "ai"u" allo,a-le pay-ac and discounted pay-ac statistics for your co"pany are #.& and ).0 years% respectively. i"e/ !ash flo,
0 1 # ) * & E$#)*%000 $&%00 $')%900 $1*0%900 $1#1%900 $'1%100
Vse the discounted pay-ac decision rule to evaluate this proRect. (Do not round intermediate calculations and round your final answer to 2 decimal places.)
years
Aiscounted pay-ac
).0& 12
;hould it -e accepted or reRected? DeRected Explanation:
!u"ulative 7 of cash flo, ,ill s,itch fro" negative and positive -et,een years ) and */ Cear !ash Flo,
0 E #)*%000 $
1
#
)
*
&
$&%00
$')%900
$1*0%900
$1#1%900
$ '1%100
$&%00
$')%900
$1*0%900
$1#1%900
(1.11# = $'%09&.00
(1.11) = $10)%0#&.00
(1.11* = $'0%#99.00
E$10%1&.9
E$)%90.'#
E (1.111 !ash Flo, 7 $ #)*%000 = $&9%1'9.19 E !u". !ash Flo, 7 #)*%000 E$1*%'10.'1 $
$%0'.*'
$)%90.'# ;pecifically%
A7H = ) +
=
).0& years%
,hich is greater than the "ai"u" allo,a-le
$'0%#99.00
discounted pay-ac% so proRect should -e reRected.
;uppose your fir" is considering investing in a proRect ,ith the cash flo,s sho,n -elo,% that the reQuired rate of return on proRects of this ris class is 11 percent% and that the "ai"u" allo,a-le pay-ac and discounted pay-ac statistics for your co"pany are ).0 and ).& years% respectively. i"e/ !ash flo,
0 1 # ) * & E$#)'%000 $%100 $'*%)00 $1*1%)00 $1##%)00 $'1%&00
Vse the 73 decision rule to evaluate this proRect. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your final answer to 2 decimal places.)
73
2 &1.)& 12
;hould it -e accepted or reRected? ccepted Explanation:
$%100 <7 =E$#)'%000 + = $1##%#1&.*
$'*%)00 +
(1.111
$1*1%)00 +
(1.11#
$1##%)00 +
(1.11)
$'1%&00 +
(1.11*
(1.11&
$1##%#1&.* 73 =
=
&1.)&2
$#)'%000 ;ince 73 0% the proRect should -e accepted.
;uppose your fir" is considering investing in a proRect ,ith the cash flo,s sho,n -elo,% that the reQuired rate of return on proRects of this ris class is 1# percent% and that the "ai"u" allo,a-le pay-ac and discounted pay-ac statistics for your co"pany are ) and ).& years% respectively. i"e/ !ash flo,
0 E$)0&%000
1 $&1%'00
# $0%000
) $11)%000
* $10'%000
& $%#00
Vse the M3DD decision rule to evaluate this proRect. (Do not round intermediate calculations and round your final answer to 2 decimal places.)
2
M3DD
10.'# 12
;hould it -e accepted or reRected? DeRected Explanation:
Cear 0 !ash Flo, E$ )0&%000 Future alue (3f 7ositive ;u" of F Modified !Fs E$)0&%000
1 $&1%'00 $&1%'00 × (1.1#* = $'1%&0'.)0
With this ne, set of "odified cash flo,s% the M3DD is/ E$)0&%000 0 =
(1+3DD
0
$&09%0.* +
(1+3DD&
# $0%000 $0%000 × (1.1#) = $9'%)**.9
) $11)%000 $11)%000 × (1.1## = $1*1%*.#0
* $10'%000 $10'%000 ×(1.1#1 = $1#0%90.00
