Solutions Manual CHAPTER 10 THE TIME VALUE OF MONEY
SUGGESTED ANSWERS TO THE R EVIEW EVIEW QUESTIONS AND PROBLEMS I.
Questions
1. The The futu future re valu valuee repr repres esen ents ts the expe expect cted ed wort worth h of a sing single le amou amount nt,, whereas the present value represents the current worth. FVn = PV (1 + i n - Future Value PV = FVn
1 ! Present Value n (1 + i ". The prese present nt value value of a singl singlee amount amount is the discoun discounted ted value value for for one future pa#ment, whereas the present value of an annuit# represents the discounted value of a series of consecutive pa#ments of e$ual amount. %. &one# has has a time value value 'ecause 'ecause funds funds receiv received ed toda# toda# can 'e reinve reinvested sted to reach a greater greater value in the future. future. person would rather rather receive receive )1 toda# than )1 in ten #ears, 'ecause a peso invested toda#, invested at * percent is worth )1.1 after after ten #ears. -. nfl nflat atio ion n ma/e ma/ess a peso peso toda# toda# worth worth more more than than a peso peso in the futur future. e. 0ecause inflation tends to erode the purchasing power of mone#, funds received toda# will 'e worth more than the same amount received in the future. . The greate greaterr the the num'er num'er of compound compounding ing period periods, s, the larger larger the future future value. The investor should choose dail# compounding over monthl# or $uarterl#. *. 2ifferent 2ifferent finan financial cial appli applicatio cations ns of the the time time value value of mone# mone# are3 are3 a ' c d e II. Problems
4$uipment 4$uipment purchase purchase or new new produ product ct decis decision. ion. Present value of a contract providing providing future pa#ments. pa#ments. Future Future worth worth of an invest investmen ment. t. 5egular 5egular pa#ment pa#ment necess necessar# ar# to to provide provide a future future sum. sum. 5egula 5egularr pa#men pa#mentt necessa necessar# r# to amorti amorti6e 6e a loan. loan.
10-1
Chat!" #$
The Time Value of Money
P"o%l!& # (7se Ta'le "
PV = FVn (PVFi,n a ' c d
) 8,999 )1*,999 )",999 ) 1,999
x x x x
.8 .* .%1 .991
= = = =
)-,-*),9" ),8 )1
P"o%l!& ' (7se Ta'le 1
FVn = PV (FVFi,n a ' c d
)1",999 )1",999 )1",999 )1",999
x x x x
1.91 .-19.8% 11.-*
= = = =
)18,91" )*,*88 )1%9,9"9 )1%,*9- (:, 9 periods
.9 .%1
= =
)*,98)-,"
*.19 1.1
= =
)%%,9 )*8*,%*9
."9 81.8%
= =
)%,*99 )-,*-,*-9
P"o%l!& ( (7se Ta'le " and Ta'le -
PV = FVn (PVFi,n a )1",999 ' )1,999
x x
PV; n = (PVF i,n c ) ,999 d )-9,999
x x
P"o%l!& ) (7se Ta'le %
FV;n = (FVFi,n a '
)8,999 )8,999
x x
P"o%l!& * (7se Ta'le - 10-2
The Time Value of Money
PV; n = (PVF i,n PV; 14 = ()*,99
x
(8."-- = )%,8*
P"o%l!& + ,7se Ta'le "
PV = FVn (PVFi,n = ()%9,999 x (.% = )1,9 P"o%l!& - (7se Ta'le - and Ta'le "
a.
PV; n = (PVF i,n = ()-,999 x (*.1- = )"*,"
'. PV = FVn (PVFi,n = ()"*," x (.8"* = )""8,-19 P"o%l!& (7se Ta'le " and Ta'le %
a.
PV = FVn (PVFi,n = ()"%,* x (.-- = )1%,9%".9*
'. = FV;n < FVFi,n = )"%,* < 11.8 = )",999 P"o%l!& / (7se Ta'le %
FV;n = (FVFi,n = ()1,99 x (1%.181 = )1,1.9
P"o%l!& #$ (7se Ta'le 1 10-3
Chat!" #$
Chat!" #$
The Time Value of Money
f the sum is dou'ling, then the ta'ular value must e$ual to ". n Ta'le 1, loo/ing down the 8: column, we find the factor closest to " (1. on the !#ear row. The factor closest to % (".% is on the 1-!#ear row.
P"o%l!& ## (7se Ta'le "
PV = FVn (PVFi,n
a PV = (),999 (PVF9.9,- = (),999 (9.8"% = )-,11 ' PV = (),999 (PVF9.19,- = (),999 (9.*8% = )%,-1 c PV = (),999 (PVF9.1,- = (),999 (9." = )",8*9
P"o%l!& #' (7se Ta'le "
PV = FVn (PVFi,n
a PV1 = (),999 (PVF9."9,1 = (),999 (9.8%% = ) -,1*.99 ' PV" = ()*,999 (PVF9."9," = ()*,999 (9.*- = ) -,1*-.99 c PV% = (),99 (PVF9."9,% = (),99 (9. = ) -,%-".9 d PV- = (),99 (PVF9."9,- = (),99 (9.-8" = ) %,*1.99 e PV = (),99 (PVF9."9, = (),99 (9.-9" = ) %,81.99 Total Present Value
10-4
= )"9,19.9
The Time Value of Money
Chat!" #$
P"o%l!& #( (7se Ta'le -
5ewrite the 4$uation PV; n = (PVF i,n to solve for the interest rate. 2ividing 'oth sides of the e$uation '# gives a new e$uation3 PVF i,n = PV; n < . ow, solve the new e$uation as follows3 PVF i,6 = )"9,999 < ),1-".1 = %.88 >oo/ up PVF of %.88 for six #ears in Ta'le - and the result is an interest rate of 1- percent.
P"o%l!& #) (7se the 4$uation3 PV of a perpetuit# = < i
a PV of a perpetuit# = )99 < 9.9 = )19,999 ' PV of a perpetuit# = )99 < 9.19 = ) ,999
P"o%l!& #* (7se Ta'le 1
The ending amount of )",8% is divided '# the 'eginning amount of )1,999 to produce a FVF for ten #ears. FVFi,n = FVn < PV FVFi,10 = )",8% < )1,999 = ".8% >oo/ up the value of i for an FVF of ".8% in Ta'le 1 for ten #ears and the result is an annual compound growth rate of 11 percent.
III. Multiple Choice Questions
1. ". %. -. .
? ? ? ? 2
*. . 8. . 19.
0 ? 0 2
11. 1". 1%. 1-. 1.
10-5
2 0
