Introduction to FinanceBUSFIN 1030
Professor Schlingemann
Problem Set 3SOLUTIONS
Problem 1:
You are deciding among three cars to use as a company car. The garage offers you a leasedeal and two different options for purchasing the car. You are completely indifferentamong these cars except for their costs. Once you have decided which car to take, youwill always take the same car again at the end of its useful life. The pretax residual valuesalvage value! for the car at the end of its useful life is e ual to #$$ %
n
! & of the purchase price, where
n
is e ual to the lifetime of the car. 'll cars are fully depreciatedaccording to its lifetime on a straightline (asis with no halfyear convention. Thediscount rate is )& and the tax rate is *$&. 'ssume that you pay the price of the car upfront, and the annual costs at the end of the year. The costs of leasing occur at the end of each period.
For example, if you purchase Car B, you pay $18,000 in year 0 and $1,000in year 1, year 2, etc. If you lease car A, you pay $,! 0 in year1, year 2, etc.
! +oteconsider all relevant cash flows for this pro(lem.
Lease A Purchase B Purchase
Purchase price #,$$$/0,$$$Total annual costs
1
/,20$3$$ 4ifetime of the car 5 years 0 years # years1 6ncludes all aftertax costs like fuel, wear and tear, maintenance, etc.7sing the 8 uivalent 'nnual 9ost 8'9! method, which of the cars should you decide todrive always:
ANS! #:
;irst find the relevant cash flows associated with each purchase optionPurchase < =epreciation tax shield > *$& ? 5,2$$ > )*$'ftertax salvage value > 5,2$$ @ *$& ? 5,2$$ > *,$PA
<
> #,$$$ B
=−−−
00
$).#$,*$).###$).$)*$3$$
#2,2/.2/
6ntro to ;inance  Pro(lem Set 5  C Schlingemann *$$$#
#AC
B
⇒
=−
0
$).###$).$
B
#AC
#2,2/.2/
⇒
#AC
B
/,$23.*5Purchase 9 =epreciation tax shield > *$& ? *,0$$ > 0$$'ftertax salvage value > *,0$$ @ *$& ? *,0$$ > *,$$$PA
9
> /0,$$$ B
=−−−
##
$).#$$$,*$).###$).$0$$
53,5).)5
#AC
C
⇒
=−
#
$).###$).$
B
#AC
53,5).)5
⇒
#AC
C
5,3#/.)/Purchase 9 has the lowest cost per year note that the lease is already in per year!.
Problem $:
You are thinking a(out investing your money in the stock market. You have the followingtwo stocks in mind stock ' and stock <. You know that the economy can either go inrecession or it will (oom. <eing an optimistic investor, you (elieve the likelihood of o(serving an economic (oom is two times as high as o(serving an economic depression.You also know the following a(out your two stocks
State o% the conom&
Probabilit&#
A
#
B
<oom#$&@*&Decession2&/$&a!9alculate the expected return for stock ' and stock < (!9alculate the total risk variance and standard deviation! for stock ' and for stock <c!9alculate the expected return on a portfolio consisting of e ual proportions in (othstocks.d!9alculate the expected return on a portfolio consisting of #$& invested in stock ' andthe remainder in stock <.e!9alculate the covariance (etween stock ' and stock <.f!9alculate the correlation coefficient (etween stock ' and stock <.g!9alculate the variance of the portfolio with e ual proportions in (oth stocks using thecovariance from answer e.h!9alculate the variance of the portfolio with e ual proportions in (oth stocks using the portfolio returns and expected portfolio returns from answer c.
ANS! #
6ntro to ;inance  Pro(lem Set 5  C Schlingemann *$$$*
a!p(oom! > *%5 and precession!>#%5 +ote that pro(a(ilities always add up to #!8D
'
! > *%5 ? $.#$ B #%5 ? $.$2 > $.$2) .2)&!8D
<
! > *%5 ? $.$* B #%5 ? $./$ > $.#* #*&! (! S=D
'
! > E*%5 ? $.#$$.$2)!
*
B #%5 ? $.$2$.$2)!
*
F
$.0
> $.$#02 #.2&!S=D
<
! > E*%5 ? $.$*$.#*!
*
B #%5 ? $./$$.#*!
*
F
$.0
> $.#3)33 #3.)33&!c!Portfolio weights G
'
>$.0 and G
<
>$.0 8D
P
! > $.0 ? $.$2) B $.0 ? $.#* > $.#$550 #$.550&!d!Portfolio weights G
'
>$.# and G
<
>$.3 8D
P
! > $.# ? $.$2) B $.3 ? $.#* > $.##22) ##.22)&!e!9OA D
'
,D
<
! > *%5 ? $.#$$.$2)! ? $.$*$.#*! B #%5 ? $.$2$.$2)! ? $./$$.#*! > @$.$$5)555f!9ODDD
'
,D
<
! > @$.$$5)555 % $.$#02 ? $.#3)33! > @# DoundingH Demem(er thecorrelation coefficient cannot (e less than @#!g!A'DD
P
! > $.0
*
? $.$#02
*
B $.0
*
? $.#3)33
*
B * ? $.0 ? $.0 ? @$.$$5)555 > @$.$$$**S=D
P
! > .30)&h!8D
P
I<oom! > $.0 ? $.#$ B $.0 ? $.$* > $.$/ /&!8D
P
IDecession! > $.0 ? $.$2 B $.0 ? $./$ > $.*5 *5&! Jence, 8D
P
! > *%5 ? $.$/ B #%5 ? $.*5 > $.#$550 #$.550&!'nd, S=D
P
! > E*%5 ? $.$/$.#$550!
*
B #%5 ? $.*5$.#$550!
*
F
$.0
> $.$30) .30)&!
Problem 3:
You are thinking a(out a portfolio where you put half your money in stock ' see pro(lem *! and half your money in the risk free asset like a Treasury (ill!. The risk freeasset has a return of 0&.a.Ghat is the variance and standard deviation of the risk free asset: (.Ghat is the covariance (etween stock ' and the risk free asset:c.Ghat is the expected return on your portfolio:d.Ghat is the variance on your portfolio:e.Ghat is the standard deviation on your portfolio:
ANS! #
6ntro to ;inance  Pro(lem Set 5  C Schlingemann *$$$5
a!<y definition they are (oth Kero $!. (!'gain, (y definition the answer is Kero $!c!Portfolio weights G
'
>$.0 and G
;
>$.0 8D
P
! > $.0 ? $.$2) B $.0 ? $.$0 > $.$250 2.50&!d!A'DD
P
! > $.0
*
? $.$#02
*
> $.$$$$3e!S=D
P
! > $.$$$$3
$.0
> $.$$3/* $.3/*&!
Problem ':
Fro%en Fruitca&es International Inc
. is considering the following proLect. They want tointroduce a new line of pastries and desserts. The sales for this division are expected to (e0$$,$$$ per year for each of the next 5 years. ;or this expansion you are a(le to usesome of your existing machines that are currently not (eing used. ;our years ago you paid *0$,$$$ for these machines and the current market value of the machines is##$,$$$. You have (een using a 0year straightline full depreciation on these machines.There is no need to (uy any additional e uipment. Aaria(le costs for the division are proLected at 20& of sales. ;ixed costs are #$$,$$$ per year. Total net working capitalre uirements are )0,$$$ at the start, #$$,$$$ in year #, and 0$,$$$ in year *. +etworking capital will (e recovered at the end of three years. The tax rate is 5/&. a.Ghat is the cash flow from assets for this proLect in each year: (.Ghat is the +PA of this proLect if the discount rate is #$&:c.6f
Fro%en Fruitca&es International Inc
. is expected to pay a dividend of #./0 nexttime, and the dividends are expected to grow at /.0& forever, what is the cost of e uity or re uired rate of return on e uity! for
Fro%en Fruitca&es International Inc
. if the current stock price is *3.
'int( you do not need any information from part a. or the pre)ious pa*e for ans+erin* this uestion
!.d.6f
Fro%en Fruitca&es International Inc
. has #$& de(t in its capital structure, with aYTM of 2&, what is the weighed cost of capital,

ACC
, for
Fro%en Fruitca&es International Inc
.:e.Ghat is the +PA of the new proLect if it has the same risk as
Fro%en Fruitca&es International Inc
. as a whole: 7se the information in
c
. and
d
.!f.'ssuming the dividendgrowth model you used in part
c
. is correct, and the return onthe market portfolio is #5& and the riskfree rate of return is *&, what
must
(e the (eta of this proLect:
'int( use the CA/ or
!
ANS! #
a.9ash ;low > Operating 9ash ;low  +et 9apital Spending  'dditions to +etGorking 9apitalOperating 9ash ;lows for each year are 8<6TB =epreciation  Tax. Niven that thefirm does not purchase any new e uipment, there are no incremental depreciationexpenses from operating activities8<6T > 0$$,$$$  5*0,$$$  #$$,$$$ > )0,$$$
6ntro to ;inance  Pro(lem Set 5  C Schlingemann *$$$/