Sample Problems - Principles of Corporate Finance Dec 2015(1)

8/16/2019 Sample Problems - Principles of Corporate Finance Dec 2015(1)

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Principles of Corporate FinanceQuestions and Answers

In this document you will find some sample questions about the topics included in the finalexam. Answers are provided. The questions are usually in order of topic but not necessarilyin order of difficulty.

Ch 5: Techniques of project valuation: !"# I$$# etc

Ch 5

8. Payback Consider the following projects:

a. If the opportunity c ost of capital is 1 0%, which projects h ave a positive NPV?

b. Calculate the payback p eriod for eac h project.

c. Which project(s) would a rm using the p ayback rule a ccept if the c utoff periodwere three years?

d. Calculate the discounted payback period for ea ch project.

e. Which project(s) would a rm using the discounted payback rule accept if the cutoffperiod were three years?

A8) %. a.

&'(.').)(*+)

&)((()(((!" A −=+−= $

&,#()(*+).

&)(((+).)(*&)(((

+).)(*&,(((

+).)(*&)(((

+).)(*&)(((/(((!" 5,/0 +=+++++−= $

& '.,-)(*+).

&)(((.)(*+)

&)(((+).)(*&)(((

+).)(*&)((((((!" 5,/C +=++++−= $

!rojects 0 and C have positive !"s.

b. !aybac1 A 2 one year !aybac1 B 2 two years!aybac1 C 2 four years

c. A and 0

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d.

&'('.('.)(*+)

&)(((!" ) A ==

The present value of the cash inflows for !roject A never recovers the initialoutlay for the project# which is always the case for a ne9ative !" project.

The present values of the cash inflows for !roject 0 are shown in the thirdrow of the table below# and the cumulative net present values are shown inthe fourth row:

C ( C ) C / C C ,

7/#(((.(( )#(((.(( )#(((.(( ,#(((.(( )#(((.(( )7/#(((.(( '('.(' %/8.,5 #((5./8 8% .()

7)#('(.') 7/8,.,8 /#-,(.%( #,/ .%) ,

;ince the cumulative !" turns positive between year / and year # thediscounted paybac1 period is:

years/.('#((5./8/8,.,8/ =+

The present values of the cash inflows for !roject C are shown in the third row of the tablebelow# and the cumulative net present values are shown in the fourth row:

C ( C ) C / C C ,

7 #(((.(( )#(((.(( )#(((.(( (.(( )#(((.((7 #(((.(( '('.(' %/8.,5 (.(( 8% .()

7/#('(.') 7)#/8,.,8 7)#/8,.,8 75%).,5

;ince the cumulative !" turns positive between year , and year 5# thediscounted paybac1 period is:

years,.',8/(.'/5%).,5, =+

e.


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The opportunity co st of capital is 9 %. Mr. Clops i s t empted to take B, which has t he higherIRR.

a. Explain to Mr. Clops w hy this i s n ot the correct procedure.

b. Show him how to adapt the IRR rule to choose t he best project.

c. Show him that this p roject also has t he higher NPV.

)/. a. 0ecause !roject A requires a lar9er capital outlay# it is possiblethat !roject A has both a lower I$$ and a hi9her !" than !roject 0. +In fact#

!" A is 9reater than !" B for all discount rates less than )(=.* 0ecause the9oal is to maximi>e shareholder wealth# !" is the correct criterion.

d. To use the I$$ criterion for mutually exclusive projects# calculate the I$$for the incremental cash flows:

C( C) C / I$$ A 7 B ?/(( ))( )/) )(=0ecause the I$$ for the incremental cash flows exceeds the cost of capital#the additional investment in A is worthwhile.

c.

%).%8&+).('*

(().('/5(,((!" / A =++−=

&-'.)(+).('*

)-').('),(/((!" /0 =++−=

Answer:1. IRR A = discount rate ( r ), which is the solution to the following equation:

000,30$)(1

11$ 1,000

=+×−× r r r ⇒ r 2 I$$ A 2 /5.8'=

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16. NPV/IRR. Consider projects A and B:

Cash Flows (dollars)

Project C 0 C 1 C 2 NPV at 10%

A !30,000 1,000 1,000 "$#, #

% !&0,000 33,000 33,000 " ', '3

Calculate IRRs for A and B. Which project does the IRR rule suggest is b est? Whichproject is really best? ( LO8-3 )


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I$$ 0 2 discount rate + r *# which is the solution to the followin9 equation:

000,&0$)(1

11$33,000 =+×+× r r r

⇒ r 2 I$$ 0 2 /(.8'=

The IRR of project A is 25.69%, and that of B is 20.69%. However, project B has thehigher NPV and therefore is preferred. The incremental cash flows of B over A are−$20,000 at time 0 and +$12,000 at times 1 and 2. The NPV of the incremental cashflows (discounted at 10%) is $826.45, which is positive and equal to the difference inthe respective project NPVs.

Q22: Protability Index v ersus N PV. Consider projects A and B with the following cashows: ( LO8-3 )

C 0 C 1 C 2 C 3

A !$3# "$ 0 "$ 0 "$ 0

% ! &0 " & " & " &

a. Which p roject has the higher NPV if the discount rate is 10 %?

b. Which has t he higher protability index?

c. Which project is m ost attractive to a rm that can raise anunlimited amount of funds to pay for its i nvestment projects?

Which project is m ost attractive to a rm that is l imited in thefunds i t can raise?

a. * A = !$3# " +$ 0 × annuit factor (10-, 3 eriods)/

2 3& 8

'.13$)10.1(10.0

110.01

0$ 3 =×−×

!" 0 2 3&5( @&/5× annuity factor +)(=# periods*

2 3&5(

1'.1$)10.1(10.0

110.01

&$ 3 =×−×

Thus !roject A has the hi9her !" if the discount rate is )(=.

b. !roject A has the hi9her profitability index# as shown in the table below:

!roject !" of Cash Blow Investment !"!rofitability

Index A &,'.-, & 8 &) .-, (. %

0 &8/.)- &5( &)/.)- (./,

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c. A firm with a limited amount of funds available should choose !roject Asince it has a hi9her profitability index of (. %# i.e.# a hi9her ban9 for thebuc1.D ote that A also has a hi9her !" as well.

Bor a firm with unlimited funds# the possibilities are:

+i* If the projects are independent projects# then the firm should chooseboth projects.+ii* Eowever# if the projects are mutually exclusive# then !roject A should be

selected. It has the hi9her !".

Ch 6

Q11. Real and nominal ows CSC is e valuating a n ew project to produce encapsulators.The initial investment in plant and equipment is $ 500,000. Sales o f encapsulators i nyear 1 are forecasted at $200,000 and costs a t $100,000. Both are expected toincrease by 1 0% a year in line with ination. Prots a re taxed at 35%. Working capitalin each year consists o f inventories o f raw materials a nd is f orecasted at 20% of sales

in the following year.

The project will last ve years a nd the equipment at the end of this p eriod will have nofurther value. For tax p urposes t he equipment can be depreciated straight-line overthese ve years. If the nominal discount rate is 1 5%, show that the net present value ofthe project is t he same whether cal culated using real cash ows o r nominal ows.

Answer ))*

Revenues 200,000

220,00

0

242,00

0

266,20

0

292,82

0

Costs 100,000110,00

0121,00

0133,10

0146,41

0

Depreciation 100,000100,00

0100,00

0100,00

0100,00

0Pretax Proft 0 10,000 21,000 33,100 46,410

Taxes at 35 0 3,500 !,350 11,585 16,244Proft a"ter Tax 0 6,500 13,650 21,515 30,16!

Depreciation 100,000 100,000

100,000

100,000

100,000

Cas# $%o& "ro'

(perations 100,000

106,50

0

113,65

0

121,51

5

130,16

!C#an)e in *or+in) 40,000 4,000 4,400 4,840 5,324 58,564

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Capita%Capita% -nvest'ent 500,000

.et Cas# $%o&s 540,000 96,000102,10

0108,81

0116,19

1188,!3

1Discount $actor / 15 1 000 0 8!0 0 !56 0 658 0 5!2 0 49!

Present a%ue 540,000 83,4!8 !!,202 !1,544 66,433 93,832 .P 14!,510

;ince the nominal rate is )5= and the expected inflation rate is )(=# the real rate is 9iven bythe followin9:

+) r nominal* 2 +) r real* × +) inflation rate*).)5 2 +) r real* × +).)(*

r real 2 (.(,5,5 2 ,.5,5=

Adjustin9 the cash flows to real dollars and usin9 this real rate 9ives us the same result for!" +with a sli9ht roundin9 error*.

R 0 1 2 3 4 5.et Cas# $%o&s no'ina% 540,000 96,000 102,100 108,810 116,191 188,!31

7 ust'ent $actor "orRea% C$ 1 0 909 0 826 0 !51 0 683 0 621.et Cas# $%o&s rea% 540,000 8!,2!3 84,380 81,!51 !9,360 11!,18!

Discount $actor /4 545 1 000 0 95! 0 915 0 8!5 0 83! 0 801Present a%ue 540,000 83,4!9 !!,203 !1,545 66,434 93,834 .P 14!,505

15. Project NPV After spending $ 3 m illion o n research, Better Mousetraps h as d evelopeda new trap. The project requires a n initial investment in plant and equipment of $6million. This i nvestment will be depreciated straight-line over ve years t o a value of zero,

but, when the project comes t o an end in ve ye ars, the e quipment can in fact be sold for$500,000. The rm believes t hat working capital at each date must be maintained at 10%of next year's f orecasted sales. Production costs a re estimated at $1.50 per trap and thetraps w ill be sold for $4 each. (There are no marketing expenses.) Sales f orecasts a regiven in the following table. The rm pays tax a t 35% and the required return on theproject is 1 2%. What is t he NPV?

4)5

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!"+purchase* 2

&)# (,#%%().)5

. 5*(+)/((#(((*+&/)(

)tt −=

−××− ∑=

!"+ma1e* 2 ∑=−××−−−

)(

)t t).)5

. 5*(+)/((#(((*+&).5((#((()5(#((( $$

[ ] ++++××+ ,/) ).)5(.)/,'

).)5(.)-,'

).)5(./,,'

).)5(.),/')5(#((((. 5 $

&)#))%# /%).)5

& (#((().)5

(.(,,5).)5

(.(%').)5

(.(%').)5

(.(%')(%-85 −=++++

Thus# the wid9et manufacturer should ma1e the lids.

Q20. Project NPV Marsha Jones h as b ought a u sed Mercedes h orse t ransporter for herConnecticut estate. It cost $35,000. The object is t o save on horse transporter rentals.

Marsha had been renting a t ransporter every other week for $200 per day plus $1.00per mile. Most of the trips a re 80 or 100 miles i n total. Marsha usually g ives t he driver a$40 tip. With the new transporter she will only h ave to pay for diesel fuel andmaintenance, at about $.45 p er mile. Insurance costs for Marsha's t ransporter are$1,200 per year.

The transporter will probably b e worth $15,000 (in real terms) after eight years, whenMarsha's h orse Nike will be ready to retire. Is t he transporter a positive-NPVinvestment? Assume a nominal discount rate of 9% and a 3% forecasted ination rate.Marsha's t ransporter is a personal outlay, not a business or nancial investment, sotaxes ca n be ignored.

A/(. The table below shows the real cash flows. The !" is computed usin9 the real rate#which is computed as follows:

+) r nominal * 2 +) r real* × +) inflation rate*).(' 2 +) r real* × +).( *

r real 2 (.(5% 2 5.% =t 2 ( t 2 ) t 2 / t 2 t 2 , t 2 5 t 2 8 t 2 - t 2 %

Investment 7 5#(((.( )5#(((.(;avin9s %#5%(.( %#5%(.( %#5%(.( %#5%(.( %#5%(.( %#5%(.( %#5%(.( %#5%(.(Insurance 7)#/((.( 7)#/((.( 7)#/((.( 7)#/((.( 7)#/((.( 7)#/((.( 7)#/((.( 7)#/((.(Buel )#(5 .( )#(5 .( )#(5 .( )#(5 .( )#(5 .( )#(5 .( )#(5 .( )#(5 .(

et Cash Blow 7 5#(((.( 8# /-.( 8# /-.( 8# /-.( 8# /-.( 8# /-.( 8# /-.( 8# /-.( /)# /-.(!" +at 5.% =* 2 &),#(%-.'

Q24. Equivalent annual cash ows As a result of improvements i n product engineering,

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United Automation is a ble to sell one of its t wo milling machines. Both machinesperform the same function but differ in age. The newer machine could be sold today for$50,000. Its o perating costs a re $20,000 a year, but in ve years t he machine willrequire a $20,000 overhaul. Thereafter operating costs w ill be $30,000 until themachine is nally so ld in year 10 for $5,000.

The older machine could be sold today for $25,000. If it is k ept, it will need animmediate $20,000 overhaul. Thereafter operating costs w ill be $30,000 a year until themachine is nally so ld in year 5 for $5,000.

Both m achines a re fully depreciated for tax purposes. The company pays t ax at 35%.Cash ows h ave been forecasted in real terms. The real cost of capital is 1 2%. Whichmachine should United Automation sell? Explain the assumptions u nderlying your

answer.

/,. In order to solve this problem# we calculate the equivalent annual cost for each of the twoalternatives. +All cash flows are in thousands.*

Alternative 1—Sell the new machine : If we sell the new machine# we receive the cashflow from the sale# pay taxes on the 9ain# and pay the costs associated with 1eepin9the old machine. The present value of this alternative is:

5,/) ).)/(

).)/(

).)/(

).)/(

).)/(/((*. 5+5(@(5(!" −−−−−−−−=

&' .%().)/

(*+5(. 5).)/

555 −=−−+

The equivalent annual cost for the five7year period is computed as follows:

!" ) 2 GAC ) × @annuity factor# 5 time periods# )/=

3' .%( 2 GAC ) × @ .8(5

GAC) 2 3/8.(/# or an equivalent annual cost of &/8#(/( Alternative 2—Sell the old machine : If we sell the old machine# we receive the cashflow from the sale# pay taxes on the 9ain# and pay the costs associated with 1eepin9the new machine. The present value of this alternative is:

5,// ).)//(

).)//(

).)//(

).)//(

).)//(

(*@(. 5+/5/5!" −−−−−−−=

)('%-85 ).)/(

).)/(

).)/(

).)/(

).)/(

).)//( −−−−−−

&)/-.5)).)/

(*+5. 5( ).)/

5)()( −=−−+

The equivalent annual cost for the )(7year period is computed as follows:

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!" / 2 GAC / × @annuity factor# )( time periods# )/=

3)/-.5) 2 GAC / × @5.85(

A Normal Project:

Valuing a n ew Computer system

Obsolete Technologies is co nsidering the purchase of a new computer system to help handle

its w arehouse inventories. The system costs $ 50,000, is e xpected to last 4 years, and should

reduce the cost of managing inventories b y $ 22,000 a year. The opportunity c ost of capital is

10%. Should Obsolete go ahead?

Answer:

The net present value is

The project has a positive NPV of $19,738. Undertaking it would increase the value of therm by that amount.

Investment Timing ProblemObsolete Te chnologies i s con templating the p urchase o f a n ew computer system. The

proposed investment has a net present value of almost $20,000, so it appears t hat the cost

savings w ould easily justify t he expense of the system. However, the nancial manager is not

persuaded. She reasons that the price of computers is continually falling and therefore

suggests p ostponing the purchase, arguing that the NPV of the system will be even higher if

the rm waits u ntil the following year. Unfortunately, she has been making the same

argument for 10 years, and the company is st eadily losing business t o competitors w ith more

efficient systems. Is t here a aw in h er reasoning?

Answer:

TABLE Obsolete Tec hnologies: The g ain from purchase of a co mputer isrising, but the NPV today is highest if the computer i s purchased in year 3(dollar values in thousands).

Year ofPurchase Cost ofComputer PVSavings NPV at Year ofPurchase ( r = 1 0%) NPVToday

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0 $50 $70 $20 $20.0

1 45 70 25 22.7

2 40 70 30 24.8

3 36 70 34 25.5 ←optimalpurchase date

4 33 70 37 25.3

5 31 70 39 24.2

Long- and Short Lived Equipment --- Equivalent Annual Cost Concept

Low-energy l ightbulbs t ypically c ost $3.50, have a life of 9 years, and use about $1.60 ofelectricity a year. Conventional lightbulbs are cheaper to buy, for they cost only $.50. On theother hand, they last only a bout a year and use about $6.60 of energy. If the discount rate is5%, which product is ch eaper to use?

To answer this q uestion, you need rst to convert the initial cost of each bulb to an annualgure and then to add in the annual energy co st. The following table sets o ut the calculations:

Low-Energy

!l"

Con#ent$onal

!l"

1. Initial cost, $ 3.&0 0.&0

. sti ated life, ears 2 1

3. Annuit factor at &- '.10' .2&

. qui4alent annual annuit , $,=(1)5(3)

. 2 .&

&. Annual energ cost, $ 1.#0 #.#0

#. 6otal annual cost, $, = ( ) " (&) .02 '.1

Assumption: nerg costs are incurred at the end of each ear.

It seems t hat a low-energy bulb provides an annual saving of about $7.12 – $2.09 = $5.03.

When to Replace an O ld Machine

Our earlier comparison of machines I and J t ook the life of each machine as xe d. Inpractice, the point at which equipment is r eplaced reects e conomics, not physical collapse.

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We usually decide when to replace. For example, we usually replace a car not when it nallybreaks down but when it becomes m ore exp ensive an d troublesome to kee p up than areplacement.

replacement problem:

You are operating an old machine that will last 2 more years b efore it gives u p the ghost. Itcosts $ 12,000 per year to operate. You can replace it now with a new machine that costs$25,000 but is m uch more efficient (only $8,000 per year in operating costs) and will last for 5years. Should you replace the machine now or stick w ith it for a while longer? Theopportunity cost of capital is 6%.

Costs (tho!sands o dollars)

&ear' 0 1 2 3 PV at*%

ew achine & $& .'0

qui4alent annualannuit

13.23 13.23 13.23

13.23 13.23 & .'0

The cash ows of the new machine are equivalent to an annuity of $13,930 per year. So wecan equally well ask w hether you would want to replace your old machine, which costs$12,000 a year to run, with a new one costing $13,930 a year.

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CAsh Blow Gstimation# Capital 0ud9etin9 Hecisions

Idea: Use the incremental cash ows o nly.Self-TestA rm is co nsidering an investment in a n ew manufacturing plant. The s ite a lready isowned by the co mpany, but existing buildings would need to be d emolished. Which ofthe following should be t reated as incremental cash ows?

a. +he ,ar et #al!e o the s$te.

7. +he ,ar et #al!e o the e/$st$ng "!$ld$ngs.

c. e,ol$t$on costs and s$te clearance.

d. +he cost o a new access road !t $n last year.

e. Lost cash lows on other rojects d!e to e/ec!t$#e t$,e s ent on the new ac$l$ty.

f. F!t!re de rec$at$on o the new lant.

Answer: a,7. 6he site and 7uildings could ha4e 7een sold or ut to another use.

6heir 4alues are o ortunit costs, which should 7e treated asincre ental cash outflows.

c. 8e olition costs are incre ental cash outflows.d. 6he cost of the access road is sun9 and not incre ental.

e. ost cash flows fro other ro;ects are incre ental cash outflows.

f. 8e reciation is not a cash e< ense and should not 7e included,e


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Suppose you nance a project partly with debt. How should you treat the proceeds f rom the

debt issue and the interest and principal payments o n the debt? The probably s urprising

answer: Regardless of the actual nancing, you should view the project as i f it were all-

equity-nanced, treating all cash outows r equired for the project as c oming from

stockholders a nd all cash inows a s g oing to them

Project Cash Flows

It is h elpful to think o f a project's ca sh ow as co mposed of three elements:

Hiscussion points: Chan9e in wor1in9 capital# salva9e value# etc

An Example:

As the n ewly appointed nancial manager of Blooper Industries, you a re a bout to a nalyse a

proposal for mining and selling a small deposit of high-grade magnesium ore. 6 You a re giventhe forecasts sh own in the spreadsheet.

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Financial projections f or Blooper's m agnesium mine (dollar values in thousands)

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We can now see how Blooper arrives a t its forecast of working capital:

0 1 2 3 *

1. Recei4a7les ( 51 re4enues)

$0 $ ,&00

$ ,# & $ ,'&#

$ , 2 $3,032 0

. In4entories (.1& following ear>s e< enses)

1,&00 1,&'& 1,#& 1,'3# 1, 3 0 0

3. ?or9ing ca ital (1 " ) 1,&00 ,0'& , '2 , 23 ,'1' 3,032 0

Note: Columns may not sum due to rounding.

Project Evaluation.

PC Shopping Network may up grade its m odem pool. It last upgraded 2 yea rs ag o, when itspent $115 million on equipment with an assumed life of 5 ye ars a nd an assumed salvagevalue of $15 million for tax p urposes. The rm uses st raight-line depreciation. The oldequipment can be sold today for $80 million. A new modem pool can be installed today for$150 million. This w ill have a 3-year life and will be depreciated to zero using straight-linedepreciation. The new equipment will enable the rm to increase sales b y $ 25 million peryear and decrease operating costs b y $10 million per year. At the end of 3 years, the newequipment will be worthless. Assume the rm's t ax rate is 3 5% and the discount rate forprojects of this sort is 10%. ( LO9-2 )

a. Page 294What is t he net cash ow at time 0 if the old equipment is r eplaced?

b. What are the incremental cash ows in years 1, 2, and 3?

c. What are the NPV and IRR of the replacement project?

Answer:. a. Annual de reciation is ($11& − $1&)5& = $ 0 illion.

0oo1 value at the time of sale is &))5 − +/ × &/(* 2 &-5 million.

;ales price 2 &%( million# so net7of7tax proceeds from the sale are:

&%(− +(. 5 × &5* 2 &-%./5 million

Therefore# the net cash outlay at time ( is &)5( − &-%./5 2 &-).-5 million.

b. The project saves &)( million in operatin9 costs and increases sales by &/5million. Hepreciation expense for the new machine would be &5( million

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per year. Therefore# includin9 the depreciation tax shield# operatin9 cashflow increases by:

+&/5 &)(* × +) − (. 5* +&5( × (. 5* 2 &,(./5 million per year

c. !" 2 −&-).-5 @&,(./5 × annuity factor +)(=# years*

2 3

,3&.$(1.10)0.101

0.101

$ 0. &$'1.'& 3 =×−×+ or &/%. 5 million

To find the internal rate of return# set the !" of the annuity to &-).-5 andsolve for the discount rate + r *:

-33.31IRR '&.'1$)(1

11$ 0. & 3 ==⇒=+×−×

r

r r r

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Ch 10Sensitivity Analysis

Sensitivity Analysis. Emperor's C lothes F ashions ca n invest $5 million in a n ew plant for

producing invisible makeup. The plant has a n expected life of 5 years, and expected salesare 6 million jars of makeup a year. Fixed costs a re $2 million a year, and variable costs a re$1 per jar. The product will be priced at $2 per jar. The plant will be depreciated straight-lineover 5 years t o a salvage value of zero. The opportunity c ost of capital is 1 0%, and the taxrate is 4 0%. ( LO10-2 )

a. What is project NPV under these ba se-case assum ptions?

b. What is N PV if variable costs t urn out to be $1.20 per jar?

c. What is N PV if xed costs t urn out to be $1.5 million per year?

d. At what price per jar would project NPV equal zero?

3. Re4enue = rice × quantit = $ × # illion = $1 illionGxpense 2 variable cost fixed cost 2 +&) × 8 million* &/ million 2 &% million

Hepreciation expense 2 &5 million 5 years 2 &) million per year

Cash flow 2 +) − T *× +revenue 3 expenses* + T × depreciation*

2 @(.8( × +&)/ million 3 &% million* +(.,× &) million* 2 &/.% million

a. !" 2 3&5 million @&/.% million × annuity factor +)(=# 5 years*

2 3&5 million &/.% million

#1.&$(1.10)0.101

0.101

& =×−×

million

b. If variable cost 2 &)./(# then expenses increase to:

+&)./( × 8 million* &/ million 2 &'./ million

CB 2 @(.8( × +&)/ million 3 &'./ million* +(., × &) million* 2 &/.(% million

!" 2 3&5 million @&/.(% million × annuity factor +)(=# 5 years*

2 3&5 million &/.(% million

.$(1.10)0.101

0.101

& =×−×

million

c. If fixed costs 2 &).5 million# expenses fall to:+&)× 8 million* &).5 million 2 &-.5 million

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Cash flow 2 @(.8( × +&)/ million 3 &-.5 million* +(., × &) million* 2 & .) million

!" 2 3&5 million @& .) million × annuity factor +)(=# 5 years*

2 3&5 million & .) million

'&.#$(1.10)0.10

1

0.10

1& =

×−×

million

d. Call P the price per jar. Then:

$evenue 2 P × 8 million

Gxpense 2 +&) × 8 million* &/ million 2 &% million

Cash flow 2 @+) 3 (.,(* × +8P 3 %* +(.,( × )* 2 .8 P 3 ,.,

!" 2 35 @+ .8 P 3 ,.,* × annuity factor +)(=# 5 years*

2 35 @+ .8P 3 ,.,*×

−× &(1.10)0.101

0.101

2 35 @+ .8P 3 ,.,* × .-'(% 2 3/).8-'5 ) .8,8' P 2 ( ⇒ P 2 &).5' per jar

Scenario Analysis.

The most likely o utcomes for a particular project are estimated as f ollows:

• Unit price: $50

• Variable cost: $30

• Fixed cost: $300,000

• Expected sales: 30,000 units p er year

However, you recognize that some of these estimates a re subject to error. Suppose that eachvariable may turn out to be either 10% higher or 10% lower than the initial estimate. Theproject will last for 10 years and requires an initial investment of $1 million, which will bedepreciated straight-line over the project life to a nal value of zero. The rm's tax rate is35%, and the required rate of return is 1 2%. ( LO10-2 )

a.What is p roject NPV in the best-case scenario, that is, assuming all variables t ake on thebest possible value?

b.What about the worst-case scenario?

Jost Ki1ely 0est Case Forst Case

!rice &5( &55 &,5"ariable cost & ( &/- &

)'a.odabasi 3 4 As 6/ /()57)8


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Bixed cost & ((#((( &/-(#((( & (#(((;ales (#((( units #((( units /-#((( units

Cash flow 2 @+) 3 T *× +revenue 3 cash expenses* + T × depreciation*

Hepreciation expense 2 &) million )( years 2 &)((#((( per year

0est7case CB 2 (.85 × @ #(((× +&55 3 &/-* 3 &/-(#((( +(. 5 × &)((#(((* 2

&,8(#)((

Forst7case CB 2 (.85 × @/-#((( × +&,5 3 & * 3 & (#((( +(. 5× &)((#(((* 2

& )#)((

)/=# )(7year annuity factor 2

#&0.&(1.1 )0.11

0.11

10 =×−

0est7case !" 2 +5.85(// × &,8(#)((* 3 &)#(((#((( 2 &)#5''#888

Forst7case !" 2 +5.85(// × & )#)((* 3 &)#(((#((( 2 3&%/,#/-%

/(a.odabasi 3 4 As 6/ /()57)8


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CH 7 Introducton to is! and eturn

Q5 Diversication In which of the following situations w ould you get the largest reduction in riskby spreading your investment across t wo stocks?

a.The two shares a re p erfectly co rrelated.

b.There is n o correlation.

c.There is m odest negative c orrelation.

d.There is p erfect negative correlation.

5. (d) This strategy does t he most to reduce risks because the stocks move in opposite

directions. When one goes up, the other goes down, and vice versa. This d oes the most to reduce riskin a portfolio.

Q6 Portfolio risk To calculate the variance of a three-stock portfolio, you need to add nine boxes:

Use the same symbols t hat we u sed in this ch apter; for example, x 1 = proportion invested in stock1 and σ 12 = cova riance b etween stocks 1 a nd 2. Now complete the nine boxes.

Q7 Portfolio risk S uppose the standard deviation of the market return is 2 0%.

e.What is t he standard deviation of returns o n a well-diversied portfolio with a beta of1.3?

f.What is t he standard deviation of returns o n a well-diversied portfolio with a beta of0?

g.A well-diversied portfolio has a standard deviation of 15%. What is i ts b eta?

h.A poorly d iversied portfolio has a standard deviation of 20%. What can you say aboutits beta?

-. a. /8=

/)a.odabasi 3 4 As 6/ /()57)8


22/26

b. Leroc. .-5d. Kess than ).( +the portfolioMs ris1 is the same as the

mar1et# but some of this ris1 is unique ris1*

Q8 P ortfolio beta A portfolio contains e qual investments i n 10 stocks. Five have a betaof 1.2; the remainder have a beta of 1.4. What is t he portfolio beta?

i.1.3.

j.Greater than 1.3 because the portfolio is not completel

k.Less t han 1.3 because diversication reduces b eta.

%. a. ). +Hiversification does not affect mar1et ris1.* This can befound by findin9 the avera9e of all of the betas: +5 x ).,* +5 x )./* )( 2 ). .

4) $is1 and diversification Konesome Nulch Jines has a standard deviation of ,/=per year and a beta of .)(. Amal9amated Copper has a standard deviation of )=a year and a beta of .88. Gxplain why Konesome Nulch is the safer investment for adiversified investor.

A) . In the context of a well7diversified portfolio# the only ris1 characteristic of asin9le security that matters is the securityMs contribution to the overall portfolio ris1.This contribution is measured by beta. Konesome Nulch is the safer investment for adiversified investor because its beta + (.)(* is lower than the beta of Amal9amatedCopper + (.88*. Bor a diversified investor# the standard deviations are irrelevant.

CH"CAP#

9. True/false True or false? Explain or qualify a s n ecessary.

a. Investors d emand higher expe cted rates of return on stocks w ith more variablerates of return.

b. The C APM predicts t hat a s ecurity with a beta o f 0 will offer a z ero e xpected return.

c. An investor who puts $ 10,000 in Treasury b ills a nd $20,000 in the market portfoliowill have a beta of 2.0.

d. Investors d emand higher expected rates o f return from stocks with returns t hat are

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23/26

highly exp osed to macroeconomic risks.

e. Investors d emand higher expected rates o f return from stocks with returns t hat arevery s ensitive to uctuations i n the stock market.

A$ '. a. Balse. investors demand hi9her expected rates of return on stoc1s withmore nondiversifiable ris1.

b. Balse. a security with a beta of >ero will offer the ris17free rate of return.

c. Balse. Treasury bills have a beta of ( and the mar1et has a beta of ).Therefore# with ) of the investorMs money in T bills and / of his orher money in the mar1et# the beta will be: +) × (* +/ × )* 2 (.8-.

d. True

e. True

)5. CA!J The Treasury bill rate is ,=# and the expected return on the mar1etportfolio is )/=.


24/26

r 2 (.(, @).5 × +(.)/ 3 (.(,* 2 (.)8 2 )8.(=

d. Bor any investment# we can find the opportunity cost of capital usin9 thesecurity mar1et line. Fith β 2 (.%# the opportunity cost of capital is:

r 2 r f β+r m 3 r f *r 2 (.(, @(.% × +(.)/ 3 (.(,* 2 (.)(, 2 )(.,=

The opportunity cost of capital is )(.,= and the investment is expectedto earn '.%=. Therefore# the investment has a ne9ative !".

17. Cost of capital Epsilon Corp. is e valuating an expansion of its b usiness. The cash-owforecasts f or the project are as f ollows:

Page 214

The rm's e xisting assets h ave a beta of 1.4. The risk-free interest rate is 4 % and theexpected return on the market portfolio is 1 2%. What is t he project's N PV?

)-. Birst calculate the required rate of return +assumin9 the expansion assets bear the same level of ris1 as historical assets*:

r 2 r f β+r m 3 r f *

r 2 (.(, @)., × +(.)/ 3 (.(,* 2 (.)5/ 2 )5./=

The use this to discount future cash flowsO !" 2 7/5./'

earCas#$%o&

Discount$actor P

0 100 1 100 001 15 0 868 13 022 15 0 !54 11 303 15 0 654 9 814 15 0 568 8 525 15 0 493 ! 396 15 0 428 6 42! 15 0 3!1 5 5!8 15 0 322 4 849 15 0 280 4 20

/,a.odabasi 3 4 As 6/ /()57)8


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10 15 0 243 3 64 .P 25 29

Ch $C%S& %F CAPI&A'Think for a moment what the cost of capital for a project means. It is t he rate of return that

shareholders c ould expect to earn if they invested in equally risky se curities. So one way to

estimate the cost of capital is t o nd securities t hat have the same risk as t he project and

then estimate the expected rate of return on these securities.

11. Cost of capital The total market value of the common stock of the Okefenokee RealEstate Company is $ 6 million, and the total value of its d ebt is $ 4 million. The treasurerestimates t hat the beta of the stock is c urrently 1 .5 and that the expected risk premiumon the market is 6 %. The Treasury b ill rate is 4 %. Assume for simplicity that Okefenokeedebt is r isk-free a nd the c ompany d oes n ot pay t ax.

a. What is t he required return on Okefenokee stock?

b. Estimate the company cost of capital.

c. What is t he discount rate for an e xpansion o f the c ompany's p resent business?

d. Suppose t he company wants to diversify into the manufacture of rose-coloredspectacles. The beta of unleveraged optical manufacturers i s 1 .2. Estimate therequired return on Okefenokee's n ew venture.

)). a. r equity 2 r f β × +r m 3 r f * 2 (.(, +).5 × (.(8* 2 (.) 2 ) =.

b.

×+

×=+= (.)

million&)(million&8(.(,

million&)(million&,r

"Gr

"Hr equitydebtassets

.

r assets 2 (.(', 2 '.,=.

c. The cost of capital depends on the ris1 of the project bein9 evaluated. If the ris1 of theproject is similar to the ris1 of the other assets of the company# then the appropriaterate of return is the company cost of capital. Eere# the appropriate discount rate is'.,=.

d. r equity 2 r f β × +r m 3 r f * 2 (.(, +)./ × (.(8* 2 (.))/ 2 ))./=.

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×+

×=+= (.))/

million&)(million&8(.(,

million&)(million&,r

"Gr

"Hr equitydebtassets

.

r assets 2 (.(% / 2 %. /=.

14. Company cost of capital You are given the following information for Golden FleeceFinancial:

Calculate Golden Fleece's c ompany cost of capital. Ignore taxes.

),. The total mar1et value of outstandin9 debt is & ((#(((. The cost of debt capital is%=. Bor the common stoc1# the outstandin9 mar1et value is:

&5( × )(#((( 2 &5((#(((. The cost of equity capital is )5=. Thus# Nolden BleeceMscompany cost of capital is:

(.)55((#(((((#(((

5((#((((.(%5((#(((((#(((

((#(((r assets ×

++×

+=

r assets 2 (.)/, 2 )/.,=

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Sample Problems - Principles of Corporate Finance Dec 2015(1)

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