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Page 1: Finance_questions and answers 220

./

.""'~..

Fundamentals of~inance

Chapters Review Problems and

--; ",

Answers " .

.., "'

Page 2: Finance_questions and answers 220

FtJNt>AMENTALS OF FINANCE

Problems on Chapter 1

I. Which of the following stateIilents is most correct?

a. One of the advantages of the corporate fonn of organization is that there is no double taxation.

b. The partnership fonn of organization has easy transferability of ownership.@ One of the disadvantages of the sole proprietorship form of organization is that

there is unlimited liability. d. Statements b and c are correct. e. None of the statements above is correct.

2. Which of the following could explain why a business might choose to organize as a corporation rather than as a sole proprietorship or a partnership?

a. Corporations generally face fewer regulations. b. Corporations generally face lower taxes.

@ Corporations generally find it easier to raise capital. d. Corporations enjo)' unlimited liability. e. Statements cO and d' are correct.

3. The primary goal ofa publicly-owned firm interested in serving its stockholders should be to

a. Maximize expected total corporate profit. b. Maximize expected EPS. c. Minintize the chances of losses. @) Maxjrn!ze the stock price per share. e. Maxinllze expected net mcome.

4. Which of the following statements is mOst correct?

a. Compensating managers with stock can reduce the agency problem between stockholders and managers.

b. Restrictions are included in credit agreements to protect bondholders from the agenay problem that exists between bondholders and stockholders.

c. The threat of a takeover can reduce the agency problem betweeli bondholders and stOckholders. .

\Sf) StateIilents a and b are correct. ---.e. All ofthe statements above are correct.

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5. Which of the following mechanisms is used to motivate managers to act in the interest ofshareholders?

a. Bond covenants. b. The threat ofa takeover. c. Pressute from the board of directors. d. Statements a and b are correct.

@ Statements b and c are correct.

6. Which of the following statements is most correct?

V One advantage oHarming a corporation is that you have limited liability. b. Corporations fuce fewer regulations than sole proprietorships. c. One disadvantage of being a sole proprietor is that you have to pay corporate

taxes, even though you don't realize the benefits of being a corporation. d. Statements b and c are correct. e. None of the statements above is correct

7. Which of the following actions are likely to reduce agency conflicts between stockholders and managers?

a. Paying managers a large fixed salary. @ Increasing the threat of corporate takeover. c. Placing restrictive covenants in debt agreements. d. All of the statements above are correct. e. Statements b and c are correct.

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·'

FUNDAMENTALS OF FmANCE

Pr.oblems on Chaptet3. . .

Company X has the following balance sheet and income statement (in thousands). Use this infonnation to answer question#1 only:

Balance Sheet:

Cash $ 100 Notes payable $ 100 Inventories 300 Accounts payable 200 Accounts receivable 400 Accruals 100 Total current assets $ 800 Total current liabilities $ 400 Net fixed assets 1,200 Long-term bonds 600

Total debt $1,000 Total common equity 1000

Total assets Total liabilities and equity $2000

Income Statement:

Sales $3,000 Operating costs 1,400 Depreciation 200 Operating income (EBIT) $1,400 Interest 400 Taxable income (EBT) $1,000 Taxes (40%) 400 Net income $ 600

Assume: 365 days per year Stock Market price = $21 Number of outstanding shareS = 250,000 shares

I. Calculate the following ratios:

a. Current: CA ==- 2S'oo :::: 2. CL ItCD

b. Fixed assets turnover: S/.eS ==- '3c::eP = ~L S \2-CONet- FA

c. Times-interest-.eamed: ~IT = l4-oo := 3.5C=~-:---

\>'l~.st e..xf' lfoo

d. Price/Cash flow: Pri ce per 5ho...<e, ==- .;;LI =. b_ S b3 Cr per shoJe (6co+200)/ZSo

e. MarketIBook: R-.= pee 5no-..t-e. 21 5.25 EcoK Vo.\vJ2.. f"U .sh~ , DCO/'2S0

==­

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2. Russell Securities has $109 million in total assets and its corporate tax rate is 40 percent The company recently reported that its basic earning power (BEP) ratio was 17 percent and its return on assets (ROA) was 9 percent What was the company's interest .expense?

RoA-:::: 9 1­TA=~I=

~f'= E.B1T = _LT-,> EBIT --;.1:£,11 -== Ft IA \00

ROA = NT = .09 .....-7.0'1 =.b1L-"" N!= "'I ~ ee,T =: 0];..)TA \00

to> EBT = 1'3 =I> EBIT - In+en:.s\- e.xp :::: ee,l 1-=1- - IfTt· e..;<p = IS

1In\-· e..1<f'. = "2yY1 \

3. You are given the following information: Stockholders' equity = $1,250; shares outstanding = 25; and market/book ratio = 1.5. Calculate the market price of a share of the company's stock.

\.5 -=l/ 1-5 - f?,i~E =IZ5D e'tW+:JI '!tOt sYv;v-eS

1_ 5 -= Pric.e.. -l15OA.-S

\ f'r;ce-:s-sJ

4. A firm has a profit margin of 15 percent on sales of $20,000. If the firm has total liabilities debt of $7,500 and total equities of 15,000, what is the firm's ROA?

R. 0 A- = '3ceD-:f-'300 i"itJooo

PM:::= 151­

RoA=~ TA

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.,

FUNDAMENTALS OF FINANCE

Problems on Chapter 4

I. Which of the following statements is most correct?

o The yield on a -ye ._!p<:>[ate bond will always exceed the yield on a 2-year Treasury bond.

b. The yield on ll! 3-year corp rate bond will always exceed the yield on a 2-year corporate bond'.

c. The yield on a 3-year Trea ury bond will always exceed the yield on a 2-year Treasury bond.

d. All ofthe statements above e correct, e. Statements a and c are correc .

2. Which of the following statements is ost correct? ";..... ~r> '\'%

a. The maturity premiums emb'e ded in the interest rates on US. Treasury securities are due primarily to the fact at the probability of defaul~ is higher on long-term bonds than on short-term bo as. '" ,.}... v- "­

C!). Reinvestment rate risk is 10 er other things held constant, on long-term than on short-term bonds.,/ '

c. The expectations theory ofihe term structure of interest rates states that borrowers generally prefer to borrow'on along-term basis while savers generally prefer to lend on a short-term basis, and that as a result, the yield curve is normally upward sloping.

d. Ifthe maturity risk premium were zero and interest rates were expected to decrease in the future, then the yield curve for US. Treasury securities would, either things

,held constant, have an upward slope. e. None of the statements above IS correct.

3. Which of the following statements is most correct, assuming that the expectations theory is correct? '

a. If the yield curve is upward sloping, the yield on a 2-year corporate bond must be /11. less than the yield on a 5-year Treasury bond. uy If the yield curve is upward sloping, the yield on a 2-year Treasury bond must be

less than the yield on a 5-year corporate bond. C9 Ifthe yield curve is downward sloping, the yield on a IO-yearTreasury bond must be less thari the yield on an B-year corporate bond.

d. All ofthe statements above are correct. G Statements b and c are correct.

4. The real risk-free rate of interest is·3 percent. Inflation is expected to be 4 percent this coming year, jump to 5 percent next year, and increase to 6 percent the year after (Year 3). According to the expectations theory, what should be the interest rate on 3-year, risk-free

securities today? K:"= 3 -/_ \~ =- Lj- Of. \~ ~ 5 y. \P3 '" b (.. a. 18% b. 12% ke.r=::: i- +-'3+-9 =- \go/./c. 6%

Q) 8% 3 e. 10%

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.,

5.

6. ~

7.

9.

Assume that the expectations theory holds, and that liquidity and maturity risk premiums are zero. If the annual rate ofinterest on a 2-year Treasury bond is 10.5 percent and the rate on a I-year Treasury bond is 12 percent, what rate ofinterest should you expect on a I-year Treasury bond one year from now?

12 loS -= )Z.-r-K (a:J. 9.0% 1-1..:._ _-+_><:_--1 L b 95% - ........---------' 21 =/l.+X

c. 10.0% d. 10.5% 10.5 )( ool9 y.je. 11.0%

One-year Treasury securities yield 5 percent, 2-year Treasury securities yield 5.5 percent, and 3-year Treasury securities yield 6 percent. Assume that the expectations theory holds. What does the market expect will be the yield on I-year Treasury securities two years from

now? ~\ ~ X- ~ ==I>b",[Z.(56)+X]/3 a. 6.0%' 5~ \Ii" b. 6.5% I • Y- ~ 1'6 = X

~ ~:~~ 6/: X =\ -=r-/-] e. 8.0%

The real risk-free rate ofinterest, k*, is 4 percent, and it is expected to remain constant over time. Inflation is expecte4,tp_be 2 percent per year fOf the next three years, after which time inflation is expected to r~n at a constant rate 0(5_11ercent p~!ye¥. The maturity risk premium is equal to 0.1 (t - 1)%, where t = the bond's maturity. What is the yield on a..l.Q:­year Treasury bond?

,,,""= Lf'!- \P'Z...= 2<;.{£rx "3 ~f0 IPi."" '3 ;..J

a. 8.1% b. 8.9% MRP .0,\ (t-I) -/.-:::1+-+'-+ ,/+ 0·9

@ 9.0% :: '1'1_ d. 9.1% kk?F -= k -*'+ \r-t\--IR..P--~==----~e. 9.9% 4-"1- + t2- X2. 'l- -r-'::f XS''l.).-\- 0 ,\ LiD -I) io

Given the following data, find the expected rate ofinflation during the next year.

• k* = real risk-free rate = 3%. • Maturity risk premium on 10-year T-bonds = 2%. It is zero on I-year bonds, and a

linear relationship exists. . • Default risk premium on 10-year, A-rated bonds = 1.5%. • Liquidity premium = 0%. • Going interest rate on l-yearT-bonds = 8.5%.

k 12-1= = l':s 'j. k"t = 3 ;;::a. 3.5% b. 4.5% 1S.'5=3-t-IP\<0 5.5% d. 6.5% ~P\ =SS -J.]e. 7.5%

The real risk-free rate, k*, is 3 percent. Inflation is expected to average 2 percent a year for the next three years, after which time inflation is expected to average 3.5 percent a year. Assume that there is no maturity risk premium. A 7-year corporate bond has a yield of 7.6 percent. Assume that the liquidity premium on the corporate bond is 0.4 percent. What is the default risk premium on the corporate bond?

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v¥- = 3 l Po, 2- 3 =- 2- I. IPy ,_ -=- 3. '5 7."'- I I I ..J, f

., \<Cj-='T.b'l. iLlep=o LP=o.'fi.

a. 0.70% k = K-'f- + IP -+ Ht:.P +Oe..P -T LP ® 1.34% '3 -I- 7.:><'3 -\-4 X3 ,.;- -\- () + Def' -+ (),L.I

c. 1.45% d. 2.01% D€.f =\ L:,Lf~1 e. 2.20%

10. You observe the following yields on Treasury securities ofvariaus maturities:

a. Maturity Yield b. I year 6.0% c. 3 years 6.4 d. 6 years 65 e. 9 years 6.8 f 12 years 7.0 g. 15 years 7.2

Using the expectations theory, fore.cast the interest rate on 9·year Treasuries, six years fromn?j' (That is, what_v1ll beJ!J~Yie)d._an.9fyell!::rreasuries issued in 6 years' time?)

b. 6.50% ~ b .s-/. ~~~ ---=t> 1·2 ::::: 6.5 ;< b -t- 1\ 'j. I c. 6.65% I 5 d. 6.80% "l. ..., ·f \

~ 7.67% ex =-=t.bn 1­,,<-.f·

f 8.00% _

dY. The'r~lil risk-free rate of interest is 2 percent. The market expects that inflation will be 3 percent each year for the next five years, and then will average 5 percent a year thereafter. The maturity risk premium is estimated to be MRPt = O.I%(t - I). In other words, the maturity risk premium on a 2-year security is 0.1 percent or 0.001. A 10-year corporate bond yields 8.6 percent. What is the yield on an 8-year corporate bond that has the same default risk and liquidity as the 10-year bond? __ 5 '( H r..f> _ 0 I (c- \)

1<"=:2."'1- IP,,'L.s=3Y- IPb .. -· -, L

a. 6.45% ;;; 10 • c::-. (j'b. 7.90% ~ )( I ( '6. b ~z. + 5 x3 t· + 5 't. J 7. 'i-O, I IO--i,

(C:) 8.15%''''''''-- P \D +De.P-HP([ 8.42% 15' ,b .=t>\?lR -'eLl" =0

e. 8.60% . =P I<.'il -='2..-r 5 ,/:;-(.-+5t5"/.+0"O-l)+I.'f ­e c=.\"i:i\15 -I]

~ Assume tha~ the current interest rate on a I-year bond is 8 percent, 0e current rate on a 2- . year bond IS 10 percent, and the current rate on a 3·year bond IS 12 percent. If the expectations theory is correct, what is the I-year interest rate expected during Year 3?

KI = 'D'/- \<'2. -=cla'f, . \.(3 = \"2. /, a. 12.0% C )

@ 16.0% """1-' ~ x. I ~ 12. =2. 10-;. +X c. 13 .5% \; I -;:;: J 3 d. 10.5% , \1:,1. ~ J e. 14.0%' 121. Lx: =16'/ ­

13. Assume that a 3-yearTreasury note has no maturity risk premium, and that the real risk-free rate ofinterest is 3 percent. Ifthe T-note carries a yield to maturity of 13 percent, and ifthe ·expected average inflation rate over the next 2 years is II percent, what is the implied expected inflation rate during Year 3?

\-\R.f'=D k.*-=3;. KR.S=13j.,a. 7%& 8% 18,1'=\\'(- -KR.F=1<1f+iPc. 9%

d. 17% 0 \ '2. 3 13 3 -t- (/ T If-/- Xe. 18% ,\-l-------t/---f-l---+i [ X 6·(.J

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FUNDAMENTALS OF FINANCE

Problems on Chapter 5

a. TrueIFalse questions:

I I. Risk refers to the chance that some unfavorable event will occur. F 2. A probability distribution is completely described by a listing of the likelihood of

unfavorable events only. F 3. Portfolio diversification reduces the variability of returns on an individual stock. T 4. The SML relates required returns to firms' market risk. The slope and intercept of

this line' cannot be controlled by the financial manager. f" 5. If the market risk premium increases by I percentage point, then the required

return on all stocks will rise by I percentage point. F 6. A two-stock portfolio will always have a lower standard deviation than a one­

stock portfolio. T 7. Ifyou randomly add additional stocks to your portfolio, the company-specifIc risk

of your portfolio will usually decline, but the market risk will tend to remain the same.

\" 8...Adding more stocks to your portfolio increases the portfolio's expected return. T 9. Two securities with the same stand-alone risk can have different betas. -1- 10. Higher beta stocks have a higher required return.' F II. The slope of the security market line is measured by beta. T 12. Company-specific risk can be diversified away. T 13. A security's beta measures its nondiversifiable (systematic, or market) risk

relative to that ofan average stock. F 14. Market participants are able to eliminate virtually all market risk if they hold a

large diversified portfolio of stocks. T IS. Inflation, recession, and high interest rates are economic events that are

characterized as market risk. F 16. Ifa stock has a negative beta, its expected return must be negative.

T 17. The market risk"premium will increase if, on average, market participants become more risk averse.

b. Answer each of the following questions. Show all your work. There will be no credit for final answers only.

1. The risk-free rate is 5 percent. Stock A has a beta= 1.0 and StockB has a beta = 1.4. Stock A has a required return ofll percent. What is Stock B's required return?

\\ Q..F =- 5 oj_ \=J!\ = \ \2'& = I ' '+ k A -= \ \ oj.12.4% 13.4% \< e. I< H -r- Ct:: '" - Ke"J 138=0

c. 14.4% d. 15.4% 'S; () te \ \ = ':5 'J,-\- Ck: r>1 - 5) I e. 16.4% =D f, -=0 \<m- 5 =I> k = II "j,

={:> \:::B =5-t (11- 5 ) \ ,y =

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2. You hold a diversified portfolio consisting ofa $10,000 investment in each of20 different common stocks (that is, your total investment is $200,000).!The portfolio beta is equal to 1.2. You have decided to sell one ofyour stocks that has a beta equal to 0.7 for $10,000. You plan to use the proceeds to purchase another stock that has a beta equal to lA. What will be the beta of the new portfolio? 0- va. t" tt,(

\ L = \ + l\ q '\ b""""" J Iq a. 1165 • LD Co;=t) W)

f,!]) 1.235 ~, c. 1.250

d. 1.284 e. 1.333

3. An investor is forming a portfolio by investing $50,000 in stock A that has a beta of 1.50, and $25,000 in stock B that has a beta of0.90. The return on the market is equal t~~6~percent and Treasury bonds have a yield of '!...PercentCWhat IS the reguued -rate o~etUrn on the mvestor's portfo!W?

o (50,=0 )1.5 -r(ZS,COO)o.c; .1.3Gl 6.6% "tSDOO I.: 1'5,0:::0 b. 6.8%' \ J c. 5.8% Lt -/ --I- (fd. - Y. -;:) 1- :3 = b 'b I d. 7.0% ­e. 7.5%

4. Assume a new law is passed that restricts investors to holding only one asset. A risk-averse investor is considering two possible assets as the asset to be held in isolation. The assets' possible returns and related probabilities (that is, the probability , distributions) are as follows: k;< =: () . 10 (-3 'j.) +0, \D (Lf-) +a,De ~'/.

Asset X Assety-rO'LS('6-(,)t-o,~(:,C\O-r)=[6 ,15' J ..l..k. ..l--.k ~ r l 0.10 -3% 0.05 -3% I<y =,,;,,--\5-/.

0.10 2 0.10 2 )2. (' b IS'/ 0.25 5 0.30 5 (j'" =O.IO(-3y-b.6-j. -+0,10 2.1,- , ~ 0.25 8 030 8 1- -\-D:Z5(5:1. - b.\Si)'--ra:2.'SC-1>--;'-b,lS~ 0.30 10 0.2510 -\--o:z,a(lo l.-{,,\'5yJ'-=15.13J:.

Which asset should be preferred? 0", = 3.9't /. =t> CV x = 3.'1~ Y. 4-0-.bY--=-.

b. IS /'.

~. ~:::~~: :~~~::~: ~:~~:~dr~~~b~ \so:~er. c 1/~ f 0 ,5 \0\ c. Either one, since the expected returns are the same. d. Asset x, since its standard deviation is lower.

@ Asset Y, since its coefficient of variation is lower and its expected return is higher.

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Pold = ~)Q,'iH- (~') (I ,a) -{~ )lo '<~)fOI9qC1

ko1d -;::; \(e.f' + l tr'vl- KeF") b 5. A portfolio manager is holding the following investments:

= 5'l- + l5SI-)(0,C\I-t2Q"

Stock Amount Invested Beta =- ~ \0 . \1,5"1- ~J. J ./ X $10 million 1.4 Y 20 million 1.0 Z 40 million 0.8

The manager plans to sell his holdings of Stock Y. The money from the sale will be used to purchase another $15 million of Stock X and another $5 million of StockZ. The risk-free rate is 5 percent and the market risk premium is 5.5 percent. How many percentage points higher will the required return 'on the portfolio be after he completes this transaction? ,jLJ-S:,\

bn == (~)(j,'f) -t(~ )CI,O) ,,-~(o,~) a. 007% bNO.J) = \. 01 q 3 b. 0 18% l<~ = 5:;/. + (55-}.)(,\,0143):= ~ \O.s 1-25 b -f. ]

@ 0.39% l d'. 0.67% ID. Si'Z,£ I - 10. 1'251- y- =1 O.3C12C\ /. e. 1.34%

6. The following probability distributions ofretums for two stocks have been estimated:

Returns Probability Stock A StockB

0.3 12% 5% 0.4 8 4 0.3 6 3

What is the coefficient ofvariation forthe stock that is less risky, assuming you use the coefficient ofvariation to rank riskiness?

a -3.62 Ex:pe.c.:\-ed ~-tum 1D' sh::cK A=0.3(12j.j-tOH-(iS,7-)+ b. 0.28 O,?:J(6'/) -::: l ?? (0 {.~ c. 0.19

~. ~:~~ Expe(.-+ed re-lvsn fb( sitr.lc e:, -" D,5(5·/.}--r-b,Lf(Lj.·t"}-t­

D3[3-1-) =\47]"'- ,2S-t-eu.dilid teJ. fti s-t~ f\=C?:~ClL';':-'6,b/~+o.Lt(3-:i-8. b "/'j"1

o.3(biC - 2.ed)'] 'h _{2.·~1-q91.]

Smru:lD.rcl D <':-\1. fa'.stceY. £::, = O· T1- Lj b 1. . eVA =' 2-Tj-L\9~/. =\o.28j C\J\)=O;1--.:r4"'~/.:",[9,\cU

~.b~ q~

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., -r I

r T

I

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I

FUNDAMENTALS OF FINANCE

Problems on Chapter 6 a . TrueIFalse questions: L If an Investment pays 10 percent interest compounded annually, its effective rate will

also be 10 percent. . 2. The future value ofan annuity due will exceed the future value ofan ordinary annuity

(assuming all else equal). 3. The present value of an annuity due will exceed the present value of an ordinary

annuity (assuming all else equal). 4. The nominal interest rate will always be greater than or equal to the effective annual

interest rate. 5. If a loan has a nominal rate of 10 percent, then the effective rate can never be less

than 10 percent 6. If there is annual compounding, then the effective, periodic, and nominal rates of

interest are all the same. 7. The proportion of the payment of a fully amortized loan that goes toward interest

• de~over timel:---:" ../;; ­8. The value of a perpetuity will allProach infinity as the interest rate used to evaluate

the perpetuity approaches zero.

b. Answer each of the following questions. Show all your work. There will be no credit for final answers only.

'1. -what is the future value of a 5-yeal\:ordinary annu~th annual payments of $200, evaluated at a.15 percent mterest rate!\) I "-- 2> '+ 5

a. $ 670.44 I I I III ZtOZCO ;>mZWZD::>b$ 9.842.1 ~~l

c. $1,169.56 =5 d. $1,522.64 ----.o,?F" 7 (~ $1,348.48 .

2. You have the opportunity to buy a perpetuity that pays \$1)iOOI~ually. Your required rate of return on this investment is@ercent. You should be essenRally indifferent to buying or not buying the investment if it were offered at a price of

a. $5,000.00 p \J CrY..>" e---n.ul-u'\ =::: Pm t 1000 b. $6,000.00 ,-·r·y -'-':-.­

0.\5I.'C\. $6,666.67 I '[( $7,500.00

e. $8,728.50 3. A real estate investment has the following expected cash flows:

Cash Flows $10,000

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Page 13: Finance_questions and answers 220

2 25,000 3 50,000 4 35,000

The discount rate is 8 percent. What is the investment's present value? o 1?,y: I Z 3 '-1,

a. $103,799 (' 0 10 -d; JO 35 (]V $96,110 j J

c. $ 95,353 I d. $120,000 I'\f''! ~ J-----~ e. $ 77,592 __

"----5i';/------ ­

4. If$1 00 is .pI;;"~ an account that earns a nominal 4 percent, compounded quarterly, what will it be worth in 5 years? D \ L 3 't 5

(i) $12202 'i \ \ \

b. $10510 Ie'!( ---I> F'V ? c. $135.41 Fv" == PV (l +- i r'OM)ml<f\ d, $12090 "" . ltx.5 r "\ e. $117.48 rVS = loo (I + 0Z;) "\122.02 J

5. Gomez Electronics needs to arrange financing for its expansion program. Bank A offers to lend Gomez the required funds on a loan in which interest must be paid monthly, and the quoted rate is 8 percent Bank"B will charge 9 percent, with interest due at the end of the year. What is the difference in the effective annual rates charged by the two banks? EAR = E:fF = (I + i 00""")"'1 _ I

a. 025% rv;

b. 0:50% (l-+ Cb.CW.J'2L - l ~ ,?:?~ 0 "I. @ 0.70% Vf)(XJJroe& \'2..

d. 1.00% LDanv\""",-\\.tj II ] e. 1.25% cARr, = 9-;. 9 '(. - ~ .y!- ~(j olD '/­

6. An investment pays you 9 percent interest compounded semiannually. A second investment of equal risk pays interest compounded quarterly. What nominal rate of interest would y'ou have to recelve on the second· investment in order to make you indifferent between the two investments? C 0 0 9 )2. Ci1 2.D'2 -/

a. 8.71%' "lsI- ~. E.f'lR == I +- ~ - I = . CJ /0

(E) 8.90% 2nd : Cj .LD3 -I. = [I + loOM)'t - \ c. 9.00% <,t

~: ~:;~~ Vnorn =:: go gOI 7; )

7. Your bank account pays a' nominal interest rate of 6 percent, but interest is compounded daily (on a 365-day basis). Your plan is to deposit $500 in the account today. You also plan to deposit $1,000 in the account at the end of each of the next three years. How much will you have in the account at the end of three years, after making your final depo~it?

r:.v

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() 6 :;:; ( .3 1 I

a. $2,591 FV b. $3,164 c. $3,500 d. $3,779

0 $3,788

8. You are contributing money to an investment account so that you can purchase a house in five years. You plan to contribute six payments of $3,000 a year. The first payment will be made today (t = 0) and the final payment will be made five years from now (t = 5). Ifyou earn 11 percent in your investment account, how much money will you have in the account five years from now (at t = 5)?

a. $19,412 0 WI. 12 3 4 5 b $20856 1-. I I . I . I ... r

! c: $21:683 2i:xo .30= 30m 3a:o 3= 3t'co @ $23,739

FV=?= 231-38. be. $26,350

9. You just put $1,000 in a bank account that pays 6 percent nominal annual interest. compounded monthly. How much will you have in your account after 3 years?

a. $1,006.00 'f' b Yo II I" I b. $1,056.45 .--\ 000 p-.J ? c. $1,180.32 \2:)1..3 1l d $119100 Fv= loCO (\--t- O,Ob:,\ = I9.f,.bi)

@ $1:196:68 '- \ 2.. :; fJ

10. Steven just deposited $10,000 in a bank account that has a 12 percent nominal ,,~

interest Tate, and the interest is compounded monthly. Steven also plans to contribut<Y"') ­another $10,000 to the account one year (12 months) from now and another $20,000 to the account two years from now. How much will be in the account three years (36

0 .. I .2. 0,?month)frs om now.! ,z.y. \ J I a. $57,231 \0 _ (0 - = _ F\l? b $48993 I J J • ( ,\"Z.X2. c: $50:971 0J = 10 ,0= Cl + 0,12. )2.,>(3 --t- IOp::::o \ --r 0,12) -t-

Gl\ ( 12. 0'7..:><1 1~ ~ $49,542 2D t:CO \ + 00\2. -lUQ 5/f1 5 e. $49,130 1 ,2. - n J •

11. Erika opened a savings account today and she immediately put $10,000 into it. She plans to contribute another $20,000 one year from now, and $50,000 bYo years fr~m now. The savings account pays a 6 percent annual interest rate. Ifshe makes no other eposits~ or withdrawals, how much will she have in the account 10 years from today?

a. $ 8,246.00 I bY. I[ t· - - - - 'i b. $116,937.04 101_ 2f) _ '30­

(£) $131,390.46 I I . \ 10 d. $164,592.62 FV :::= [01000 C1+ 0 ,Db.J e. $190,297.04 T 2.0 a:D CI + 0,06) 9

1

+ ~,COO (I +O,Db;&' {13I J 390.LJi]

Page 3 0/3

Page 15: Finance_questions and answers 220

FUNDAMENTALS OF FINANCE

Problems on Chapter 7

a. TruelFalse questions:

T I. All else equal, long-tenn bonds have more interest rate risk than short-tenn bonds. T 2. All else equal, high-coupon bonds have more reinvestment rate risk than low­

coupon bonds. I 3. All else equal, short-tenn bonds have more reinvestment rate risk than do long­

tenn bonds. F 4. If interest rates increase, all bond prices. will increase, but the increase will be

greatest for bonds that have less interest rate risk. T 5. All else equal, if a bond's yield to maturity increases, its price will fall. F 6. All else equal, if a bond's yield to maturity increases, its current yield will fall. F 7. If a bond's yield to maturity exceeds the coupon rate, the bond will sell at a

premIUm over par. T 8. Ifa coupon bond is selling at par, its current yield equals its yield to maturity. T 9. Long-tenn bonds have more interest rate price risk, but less reinvestment rate risk

than short-tenn bonds. F· 10. Bonds with higber coupons have more interest rate price risk, but less

reinvestment rate risk than bonds with lower coupons. F ~ If interest rates remain constant for the next five years, the price of a discount bond

will remain the same for the next five years. T· 12. Ifa bond is selling at a discount to par, its current yield will be less than its yield

,,!lto.maturity. . I \8ISinking fund provisions sometimes work to the detriment of bondholders-­

../.7particularly if interest rates have declined over time. I (0i If interest rates have increased since the time a company issues bonds with a

sinking fund provision, the company is more likely to retire the bonds by buying them back in the open market, as opposed to calling them in at the sinking fund

.f) call price. F= c:J Under a sinking fund, bonds will be purchased on the open.market by·the issuer

when the bonds are selling at a premium and bonds will be called in for redemption when the bonds are selling at a discount.

T 16. The sinking fund provision makes a debt issue less risky to the investor. F 17. Junk bonds typically have a lower yield to maturity relative to investment grade

bonds. . F (!§! A debenture is a secured bond that is backed by Same or all of the finn's fixed

assets. F· 19. Subordinated debt has less default risk than senior debt. -I~ ®J. Rising inflation makes the actual yield. to maturity on a bond greater than the

/71 quoted yield to maturity, which is based on market prices. T ~I The yield to maturity for a coupon bond that sells at its par value consists entirely

ofan interest yield; it has a zero expected capital gai·ns yield.F 22. Other things held constant, a callable bond would have a lower required rate of

return than a noncallable bond. T ~The total yield on a bond is derived from interest payments and changes in the

Page 1 af3

Page 16: Finance_questions and answers 220

price of the bond. -1- 24. The price of a discount bond will increase over time, assuming that the bond's

yield to maturity remains constant over time. . F' 25. When large firms are in financial distress, they are almost always liquidated. T tJ!l Debentures generally have a higher yield to maturity relative to mortgage bonds. i'G.?, All else equal, senior debt will generally have a lower yield to maturity than

subordinated debt. . F n,g. An indenture is a bond that is less risky than a subordinated debenture. F {j;j If a company increase.s its debt ratio, this is likely to reduce the default premium

on its existing bonds. T 30. All else equal, senior debt has less default risk than subordinated debt. F 31. When companies enter Chapter II, their assets are immediately liquidated and the

firm no longer continues to operate.

b. Answer each of the following questions. Show all your work. There will be no credit for final answers only.

I. An annual coupon bond with a ujio'G:face value matures i.u.l.xears. The bond currently sells for<$974.6..8i' and has a:J;percent yield to maturity. What is the bond's annual coupon rate?

2. You i~~d to purchase £3;gear, $1,OUe value bond that pay~~erest of$filJ. everj.Qftlonths. Ifyour nominal annual required rate of return is ~rcent with semiannual compounding, how much should yon he wjJlingto pay for this bond?

3. A bond that matures i@Ms has ~percent semiannual coupon (i.e., the bond pays a $iihoupon every six months) and a face value of$ I)!QQ.. The bond has a nominal yield to uiaturity o~ercent. What is the price ofthe bond today?

4. A $1,000 par value bond pays interest o@each quarter and will mature inG' yeats. ITyour nominal annual required rate of return i@ercentwith quarterly compounding, how much should you be willing to pay for this bond?

5. . corporate bond matures in <:Eyears. The bond has an 8 percent semiannual coupon and a par value of $1,000. The bond is callable in two years at a call price of $1,050. The price of the bond today is $1,075. What are the bond's yield to maturity and yield to call?

6. Consider a $1·,000 par value bond with Q~rcent annual coupon. The bond pays interest annually. There.arayears rem~ning until maturity. Whay,s the current yield on the bond assummg that the reqUired return on the bond IS Qll.1:>ercent?

7. A bond with a face value of$l,OOO matures in 4 years. The bond has an 8 percent annual coupon and a yidd to maturity of 10 percent. IT market interest rates remain at 10 percent, what will be the price ofthe bond tWo years from today?

_.----_...- ...--_.­8. A 3-year bond with a.9,yercent semiannual.cQ!!Q()'!! is currently selling at par. A

3·year bond with a 9 pe2C;:iiiiriiiinual coupon has !h~.s8-!T!e risk, and therefore, the same effective annual return as the' semiiil;nualb"and. ITthe annual coupon bond

Page 20/3

Page 17: Finance_questions and answers 220

has a face val\.l."'. QU1,QOO, what will be its price? - ... -" .,

9. A 3-yearbond with a 10 percent semiannual coupon and a $1,000 face value has a nominal yield to maturity of7.5 percent. The bond, which may be called ·after 2 years, has a nominal yield to call of 5.54 percent. What is the bond's call price?

10. Meade Corporation bonds mature in 3 years and have a yield to maturity of12, percent. The par value of the bonds is $1,000. The bonds have a.lQ..percent coupon rate and pay interest on a Sl<xIJMi!m;m aJ basis. What are the current yield and capital gains yield on the bonds for this year? (Assume that interest rates do not change over the course ofthe year.)

11. Cold Boxes Ltd. has 100 bonds outstanding (maturity value = $1,000). The nominal required rate ofreturn on these bonds is currently 10 percent, and interest is paid semiannually. The bonds mature in 3 years, and their current market value is $768 per bond. What is the annual.coupon interest rate?

Page 3 aJ3

Page 18: Finance_questions and answers 220

, .0 qrteshQrI W c-~'- c.~-/ cr-~( ~ -'---;- .

. ,/ \J eo, ==- '371t,b2,7- , YTI'1 =-Kd.:o 51- 1 ? f l'n-;:;::< ," ,

/' '.' ·,°t-\---~\~.---_+t ~1 FX, /p.:, == ~ hf- -+ (Y\ ')7-'tb<rl- ht h\ ~L

, fd (l-t.(d)t. C\-\-~d)~

,J 'J7't.b87=Il'\t [ (l.~~l +

Coupon ra.te. =' I" \ . . ~ = 2> {. . . ' PdY \Jo.\Ul: _ \000

-, 4- ,"- S'"I S·/· 1 \, ), I, !, I•<c ~o 60 <0 60'c \0 0 0

Vfj -==- W [ -+ _I_ -+ ~_\~ -\- \ -'r \ --'r \ .'1-\- lo~? (l·oS) (loS)' (\.05)' (\o~)' (I.OS)' (\05)6 (1.05)'

::~~:~

.===~======:=====:=====:==~===

0V 't5 [ \ \ \ + \ \ +) ,. \00

~ = (\.6'-'-) -t (\"''')~ + ().o")' + -(-6 J -+ ,'\ v, ~ J (\.0'1')4- (1.0,+)5 I.D"r) (I· a"')

= \,Olb.J.\l '1 i

21'+S to 1­ 8 \ ! I \ I I \

(

35 \CO~

L ho[ I \ ... ' .. + \ ') \ \000Ve,= --'.!J +- -+ _. J-r (10:') (.0:')' (\ .o:,)~ (I. M)&

Cl- S; c: \ I \ i , ,

4-<:> 'to '\~~0\,10,50

Page 19: Finance_questions and answers 220

.... ~

·0 2\o-f.

\ \ I I

~

-. I.'] .; 1000

(1':I)':I· r ; c (\. \)J'. .

'n~ ."')c) 't C y= 70 _ 0_0-;>'::>6::= 7. 5(,!­

'32 s, 3~'t

. -_. .:

@vr:,.-;

.

I ,

2­\ \

80

3 I I

ao ,

l>o \aoQ

z I,

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3

\ 'TS

4

'-'5

, \

,,>D

\ ~6

tfi,t\~

z. .3 5 ,;, Il , ", I I So So 50 5°s" \ 0 0(1

v~-= SoC I +. \ . -\- +\ ]-\-- loco.", \,0:'3.":1':)8 .. -; (\.0'125) (\.04-25)'" ll.o4-2Sf _ (\. ,,'tIS),

; i C'::'l=A =0.0')6)S='3.b1.')'j

00,'3' . ' -_:'~:~-: j 'SiY\(c YTfYI =-C Y+C G ="'> 3,<:;' ='3.625-\-(6 = GG=A· \25/t~\t~

<:,O£ 1. I .J '+ 5Z..~:-:<J;'''-It[ I . \ I 1-\")J->i/bO- h ---+ __ + ... +~ \ \ \ \, \, \ \ :! \ .r+i (1.05) (I·DS)" (,-oS]< ~2 "I"+ 10"'0 ~ooot." \- -:;r~-r- - ­

(\ .6;;:J', ,

I Y\HSemia IIY1Uo. \ '> = 4-3 bS') .8 f.j';

ttnYlv..o.\ (0\1,\)0'0 to.\e. = In-\-~ 2 1000

p",~ V~\u{i

. -;;;;J

{~

,,\',

.-J

Page 20: Finance_questions and answers 220

" ~

FUNDA1vffiNTALS OF Fll-lANCE 210

Fall 2005

Problems on Chapter 8

a. TruelFalse questions:

VI. The constant growth model takes into consideration the capital gains earned on a stock. y.. 2. It is appropriate to use the constant growth model to estimate stock value even if the

growth nite never becomes constant. -;( 3. Two firms with the same dividend and growth rate must also have the same stock price.

\./"4. The stock valuation model, Po = Dr/(k:, - g), can be used for firms which have negative growth rates.

>< 5. H a stock has a required rate of return k, = 12 percent, and its dividend grows at a constant rate of 5 percent, this implies that the stock's dividend yield is 5 percent.

'/.. 6. The price of a stock is the present value of all expected future dividends, discounted at the dividend growth rate.

'/- 7. H a market is strong-form efficient this implies that the returns on bonds and stocks should be identical.

)< 8. H a market is weak-form efficient this implies that all public information is rapidly incorporated into market prices..

·X 9. Hyour uncle earns a return higher than the overall stock market, this means the stock market is mefficient.

XIO. H the .st, ed, market is ,vt-' '.:-f<li"TD efficient, then information aboul recent trende ," "Cocl: prices would be very useful when it comes to selecting stocks:

X II. Semistrong-fonir market efficiency implies that all private and public information is rapidly incorporated into stock prices.

·X 12. An individual who has information about past stock prices should be able to profit from this information in a weak-form efficient market.

X. 13. An. individual who has inside information about a publicly traded company should be able to profit from this information in a strong-form efficient market.

X. 14. H.a market is weak-form efficient, this means that you can expect to beat the market by using technical analysis that relies on the charting ofpast prices

t/j5. Preferred stockholders have priority over common stockholders. ~. Preferred stock provides steadier and more reliable income to investors than common stock.

b. Answer ·each of the following ouestions. Show all your work. There will be no credit for final answers only.

I. Jolmst9n Corporation is growing at a constfu"1t rate of6 percent per yea. It has both COIT.:.iTIOn

stock and non-participating preferred stock outstanding. The~f preferred stock (kJ is 8 percent. ple p~lue ~f the ,Preferred s;o,c..'<: is ~pO, fu""1G t~e stoc!< r.23 a stated dividendof ]0

percem or pru-. 'Yv'1mI is tne.':rlar~~:z Jotnt p;,e;~;l).. (f -r.. ,.'-A~"'? ~ 1. 0

a. $125 'I')b. $120 I. f .: i u (. ",c:. ,,"'. c. $175.-... ICC_..- X<&.; $150 lee e. $200

Page I of 4

,...... ..... c

Page 21: Finance_questions and answers 220

r··· " p, Dl \<:.-()

2. A share of preferred stock a La uarter1 dividend of $2.50. If the price of this preferred stock is currently $5 , what is ominal annual r~:Frfuim:7

Dp(~) =:: d5 / \Ji",,- SO a. 12% b. 18% ~) 20% d. 23% e. 28%

3. Womack Toy Company's stock is currently trading at $25 per share. The stock's dividend is projected to increase at~L!::lte of7 pe:cent per year The required rat:. ofretum on;\lJe, :L ~ '-J stock, 1<" IS 10 percent:~!Dbe expected pnce ofthe stocl:;.'l.Lears.fr.om1odaj? /:' i . I I -\ -.--1

, D\ -.:2 S 0 ~ t'j, , j<:. S -= \0 J - ?'\ ~ ~ 0_ :;, ~ - c - -:J' ..........

P, "po C'41a. $36.60 \'1

b. $34.15 ":;:. t>s oR p 0, )lj c. $28.39 ILj -= l.\ = t-b ( \+ 9

@) $3277 l<-9 P J. S (i •-r,o:)) it0;

e. $30.63 li = 3 ~ _=t-=f

4. Allegheny Publishing's stock is expected to pay a year-end .dividend, Db of $4.00. The dividend is expected to grow at a constant rate of 8 percent per year, and the stock's required rate of return is 12 percent. Given this inf~rrnation,(wlJat IS ~e expected pnce of the stock, ei~ years fiOIllIlowl ) 0, -:: Lj I CI" \$ 1- ;. 1(:'0'-" \21. f) _") __ ", r"'€, - ,

,~ $200.00 t'",.=. D;. ,. q _ \DO ~ $18509\O.;;,.':j 01-;2- - ,of,'

c. $171.38 'a g, . d.$24760 ~ "" ~~ , .. ':1) .= iOa ( 'l-t ,<:>'6) =c. \ gS, oC, e. $136.86 ...

5. Waters Corporation has a stock price of $20 a share. The stock's year-end dividend is expected to be $2 a share (01 = $2.00). The stock's required rate of return i@percent and the stock~s. dividend is expected to grow a't the same constant rate forever. What is the expected price ofthe stock seven years from now? ~_

p~ .=. :l.c; I U t .::. .J-.

G) $28 ~ ,.., " )'" b. $531' \ c " \-t~ J

c. $27 ..... 1.. C:> C. \+."'2>?" d. $23 ­e. $39

6. Thames Inc's most recent dividend was $2.40 per share (Do = $2.40). The dividend is expected to grow at a rate of 6 percent per year. The risk-free rate is 5 percent w.""1G the r~tl.lJ.ll on the: :J.1s.rket is 9 ?e~cen:t. if the comp8..L""1is beta is 1.3) 'ivhat is the p~c~ of u'1e

stock today?' \~ '" =- .-:. .-i <2i ~ 6 r ;--..., i-'......-_._-\ ~ , ­'~ --' a. $72.14

i__.... . .b. $57.14 c. $40.00 d. , $68.06

Page 2 of 4

Page 22: Finance_questions and answers 220

M

V'" -- ~0_.'- _ --t- .\':; >-- _L,' "'\0 ;;;-... ~". '=v 'i.... i..) ~ ~ '" . __ ':>.. '" ­..)v (t-j'~) C;-+ ~c:T ( \--0 t-:oj .L Y s·· ,:) ,\ 2. _ , \

/ ~ . / p.. \, b'? ...... I .\<:>;2.'; ~c:.63 "-C \ ( \ ../e:-, $605.. 7. ' +- ~ ' .. 0 0 ( ­-eo­

L7 \,\:;1. (\,\'.1-)'- 0.11-)2 =60'{,3 /I 7. The last dividend paid by Klein Company was $1.00. Klein's growth rate is expected to be aI constant 5 percent foi:<Z years, after which dividends are expected to grow at a rate ofl0 percent

forever. Klein' uired rate ofretum on equity (k,) is 12 percent. ewnat is the current price of

\ em s common stock. \\,:::.i . g -::: S "I. t:0Y" t-".~a 'i-EO.fS

\ '- a. $2100 s= \<::J{. \="~:L ----1/ = ) j<;..s~i')..!· . )'$\r/ 1t b. $3333 , ) (j j;-.. $4225 '~~~ @)$5016 ~ J e. $58.75

. 8. An analyst estimating the intrinsic value of the Rein Corporation stock estimates that its free cash flow at the end of the year (t = I) will be $300 million. The analyst estimates that the firm's free cash flow will grow at a constant rate of 7 percent a year; and that the company's weighted ~ge cost?f capital is II percent. The company currently has debt and preferred stock totaling

($500 million) There are 150 milJion outstanding shares of common stock What is the intrinsic ville @Tshare20fthe cQIllPilI1Y'U!otkP .

c;.()" Sao -i1,,\\leC\..- J="C F "" SOD I g =- r /' V-.l ","CC ::: \ \ t·

""cl ~ 10=''''1' ba \'-'1 \! pI'" re:rEC\ ~ 'Sec " ......$16 67 c\'''-bl- + H \1$2500 1--\ \] e.q....~ 'r'f c $33 33 -# e~ c;hof~S '" \S 0 ,'-"--' =~~ s~,o"'s @ $46 67 -=/000 ..e~..$50 00 -J c~,po '" "f'C"",_ '" ",,-"">0 _ - c-bO {Y""'.,

1 i;d ;;: L) 6 , 6:"'Zi ) -v',; Ace. - , , d - ,0T - ..- ­

~ A stock that currently trades for $40 per share is expected to pay a year-end dividend of $2 per share. The dividend is expected to grow at a constant rate over time. The stock has a beta ~, the risk-free rate is (5 ;percent, and the market risk premium i{3}percent. What is the stock;s

expected price seven years fr~m~otab? ',. D; '" ;)

.n-s·

~o. Mack Industries just paid a dividend of $1.00 per share (Do = $100). Aiialysts expect th~ company's dividend to grow 20 percent this year (D l = $1.20) and 15 percent next year. After two years the divid~nd ;s expected to grow at a const&"lt rate of 5 uercent. The reo";T~d rate of return on the company's stock is 12 percent. What shoulQ be the company's current stock price?

!O ~ \. .'1.;:-' ..~ '< .)<:0-.;: -.' a. $12.33 ., .

. .-. -. ., ' ~. -:" .... ' ~- ',- --!, ".,'i-, $1665 c. $1691ev $1867 e. $19.67

~.Page30f4 I -:' ~.

Page 23: Finance_questions and answers 220

40 _ .2 \ i-9

-::t;> Ljo (. II-g) =.)

! \-9 =­ 2­~c.

-\\-9 == '3 =::

,d'S'

,-<:)6 -=i7 -6 '(­"I

l?t= ~(H-9) -:4(:) (1 7­

j-.O(,)

~ bO, ,<-;'S

:­,_

G L: : .C:::" I .J

Page 24: Finance_questions and answers 220

.... r"

ll. Stewart Industries expects to pay a $3.00 per share dividend on its common stock at the end of the year (DI = $3.00). The dividend is expected to grow 25 percent a year until t = 3, after which time the dividend is expected to grow at a constant rate of 5 percent a year (D, -,---jA 6875 and D4 = $4.?l21875). The stock's beta is 1.2, the risk-free rate of interest is 6 percent; and the market rate ofreturn is 11 percent. What is the company's current stock price?

I) = '3 ? g =d5/ t-- 5 a. $29.89 b. $3064 f:.~~:::6 I. 9::: S"/. c. $37.29 d. $53.69 D'--t ~ Lf. q J\:/-,S

(£)$59.05 \::.rn;< II /. <i-----=-------~

12. The Textbook Production Company has been hit hard due to increased competition. The company's analysts predict that earnings (and dividends) will decline at a rate of 5 percent annually forever. Assume that k, = 11 percent and Do = $2.00. What will be the price of the company's stock three years from now? ~ .' .'1.

\<:::.=- \ I I '3 ",-'5/, \.J q"""Q ( H9 J a. $2717 G ('" =' :l -=--,,;l. (1+ ,05)'-;b. $ 6.23 p P ? oK. Del c. $28.50 ,,~ 6 (\+9) =V p_;o - =0 l.b9.q

. .::- 'f'-s ----gCD $1018 e.$20.63 \. (;:LC\_ ::: \6, \ ~

.H-+-' 0-0>

13. Berg Inc. has just paid a dividend omw Its stock is now selling fo~8-j;>er share. The firm is half as risk-j as the market. Th" expected re1J 1m 00 the market i(l1Ppercent, and the yi~ 01lJl--S. Treasury bonds is lJJ?erce!lt. If the market is in equilibrium, what growth rate is_

expected? k",::..i~-i- ~ "'1':'-.' \~ 6"'l \;l, . s:;,.J a. 13% ?::. L'c:o( \.,.<;I,).~ . . ." D. 10% c <-~ -s < ~ ZOO'j =-y c. 4% 4\5 =: :,;cl \."~) I 1 _. ('; i<' -== 8 /.

I'd) 8% .. '\~-S '-J; 1

9- 'I.e J .•

Y -2% 6-'--\8'01::: ~+~

14. Given the following information, calculate the expected capital gains yield for Chicago Bears Inc.: beta = 0.6; kM = 15%; kRF = 8%; D I = $2.00; Po = $25.00. Assume the stock is in equilibrium and exhibits constant growth.

a. 3.8% b. 0% 9~. 8.0%

-"

: ."~~. ~::-::.;JL 4.2% e. 2.5% o'_'''''''-­

~S,. ...:2-c­, \2-L.--<:'-)

~):: . 0 14).. .::=:\7 L.J. ,;L /'

Page 4 of 4

Page 25: Finance_questions and answers 220

3

b+(i\-b)i.~

-=.\,).

o i '- 3 D ;to, ( H3)

::..~ C\ -+ .d.5) "" ~ ,~s 4. C\d\;;R5'

L.j '{,~,"'S + '(.;1- .0'3 ..~i·l~

( l.tV

-::; J, Eo::, g + ;;U=i SCi-t- 3, :?3 +- '=' G ,Cr~

='Sq .0 l.j Y

Page 26: Finance_questions and answers 220

.' ,

FUNDAMENTALS OF FINANCE

Problems on Chapter 9

a. TrueIFalse questions:

1"-\ T(YIf a company's tax rate increases but the yield to maturity of its noncallable bonds remains

the same, the company's marginal cost of debt capital used to calculate its weighted average cost of capital will fall.

F 2. All else equal, an increase in a company's stock price will increase the marginal cost of retained earnings, k,.

F 3. All else equal, an increase in a company's stock price will increase the marginal cost of issuing new common equity, k,.

F 4. Since the money is readily available, the cost of retained earnings is usually a lot cheaper than the cost of debt financing.

r 5. When calculating the cost of preferred stock, a company needs to adjust for taxes, because preferred stock dividends are tax deductible.

I 6. When calculating the cost of debt, a company needs to adjust for taxes, because interest payments are tax deductible.

~I 7. The WACC measures the after-tax cost ofcapitaL ""\ 8. The WACC measures the marginal costof capitaLF 9. There is no cost associated mill usmg retained earnings. F" 0· Ifa company's tax rate increases, then, all else equal, its weighted average cost of capital will

lIlcrease. ...,­\ 11. Flotation costs can increase the weighted average cost of capitaL

""\ 12 An increase in the risk-free rate is likely to increase the marginal costs of both debt and equity financing.

I 13. if the company's beta increases, this will increase the cost of equity financing, even if the company is able to rely on only retained earnings for its equity financing.

F 14. The WACC exceeds the cost ofequity financing. FC' (l~e cost of retained earnlngs exceeds the cost of issuing new Common stock. F ~i~ce debt capital is riskier than equity capital, the cost of debt is always greater than the

F@. BecauseWACC.

of the risk of bankruptcy, the cost of debt capital is always higher than the cost of equity capitaL . .

, 18. If a company assigns the same cost of capital to all of its projects regardless of the project's risk, then it follows that the company will generally reject too many safe projects and accept too many risky projects.

F 19. Higher flotation costs tend to reduce the cost ofequity capital. F 20. The cost of retained earnings is zero because retained earnings are readily available and do

notrequire the payment of flotation costs. F 21. The lower a company's tax rate, the greater the advantage of using debt in terms oflowering its

WACC

Page J 0/4

Page 27: Finance_questions and answers 220

b. Answer each of the following questions. Show aU your work. There will be no credit for final answers only.

I. . The common stock of Anthony Steel has a beta of 1.20. The risk-free rate is 5 percent and the market risk premium (kM .kRF) is 6 percent Assume the firm will be able to use retained earnings to fund the equity portion of its capital budget What is the company's cost of retained earnings, 1<,?

~-'Ia. 7.0% b. 7.2% c~")

11.0% 8"12.2%&:: r\~

e. 12.4% '-::J

2. A company just paid a $2.00 per share dividend on its conunon stock (Do = $2.00). The dividend is expected to grow at a constant rate of 7 percent per year. The stockcurrently sells fur $42 a share. If the company issues additional stock, it must pay its investment banker a flotation cost of $1.00 per share. What is the cost of external eqUity~ .

r V' i:J a 11.76% dV 't / b. 1188%· vP0. ~ I

c. 11.98% S-' I Jf. d. 12.22% "'<j> e. 12.30%

3. A company has determined that its optimal capital structure consists oK40 percent debt ai#6il per«entieqwl¥> Assume the firm will not have enough retained earnings to fund the equity portion of its C;;pital budget Also, assume th~1iI!1!accQ~ts for flotation costs by adjusting the cost of capital. Given the following infonnaticm::-calculate the firm's weighted average ~

o 1<.= 8%. o et incom $40000. o a out rati - 50%, o Tax rate = 40~ o Po = $25. . ~--., O~IO,OOO. • Flotation cost on additional equity = 15%.

cQ 7.60% b. 8.05% c. 11.81% d. 13.69% e. 14.28%

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Page 28: Finance_questions and answers 220

A'::: ~

~

4. Hatch Corporation's target capital structure ~p~Uleb~fiQpercent ~~o~-~t~~~d 10 ,percent preferrea::stOCK.:'-1nfonnation regarding e company's c"st of capital can be summarized as follows:

'1'0. . • The company's bonds hav~nominal yield to rnatur!w~ • The company's preferred stock sel~3" share and pays an annual dividend 6'

share. ~

• The company'S:Common ~c..k sell~'share, and is expected to pay a dividend of ~ share at the end oftlie year (i.e., D1 - $2 0.0),. The dividend is expected t~ at a constant rate Q("'Uercent a year. .

• The finn will be able to use retained earnings to fund the equity portion of its capital budget .r;;;'

• The company's tax rate i~O/1iercent.

What is the company's weighted average cost ofcapital CNACC)?

a 9.25% (]) 9.70%

c. 10.03% d. 10.59% e. 11.30%

5. Longstreet Corporation has a target capital structure that consists o@ercent deb!,C5b> percent common equity, and®percent preferred stock Th~ate is@ percent The company has projects in which it would like to invest with costs that tal I 500 000 Longstreet will retain $500,000 of net income this year. The last dividend $ the current stock price is @and the ~ ·tate of the company is 10 percent. If the company raises capi through a new equity ::e the flotation costs are W pereebt The cost of referr . ercent and the cost of debt imerc~nt. (Assume debt and preferred stock have no flotation costS.) What is the weighted average cost ofcapital at the finn's optimal capital budget?

a 12.58% b. 18.15% c. 12.18% d. 12.34% e. 11.94%

@Grateway Inc. has a weighted average cost ofcapital of 11.5 percent. Its target capital structure is 55 percent .equity and 45 percent debt. The company has sufficient retained earnings to fund the equity portion of its capital budget. The before-tax cost ofdiobt is 9 percent, and the company's tax rate is 30 percent. Ifthe expected dividend next period (Dl) is $5 and the current stock price is $45, what is the company's growth rate?

a 2.68% b. 3.44% c. 4.64%

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Page 29: Finance_questions and answers 220

· ,

d. 6.75% e. 8.16%

7. Bradshaw Steel has a capital structure with 30 percent debt <all long-term bonds) and 70 percent common equity. The yield to maturity on the company's long-term bonds is 8 percent, and the firm estimates that its overall composite WACC is 10 percent The risk-free rate of interest is 5.5 percent, the market risk premium is 5 percent, and the company's tax rate is@percent. Bradshaw uses the CAPM to determine its cost ofequity. What is the beta on Bradshaw's stock?

a. L07 b. 1.48 c. 1.31 d. 0.10 e. 1.35

(Thefollowing information applie< to the next two problems.)

8. Becker Glass Corporation expects to have earnings before interest and taxes during the corning year~ 000, and it expects ~~d dividends to .wow indefinitely at a constant annual rate - .5 percent The firm haS=$5,Qilll,OilO-Of.debt outstandmg BBll@g a coupen mterest rate o.C8 percent,',and it has 100,000 shares of common stock outstanding. HistOrically, Becker has paid 50 percent of net earnings to common shareholders in the fonn of dividends. The current price of Becker's common stock is $40, but it would incur a 10 percent flotation cost if it were to sell new stock. The firm's tax rate is 40 percent

8.1. What is the fim€ost of@tained earnings] J)

a 15.0% b. 15.5% c. 16.0% d. 16.5% e. 17.0%

8.2. What is Becker's cost ofnewly issued stock?

a. 16.0% b. 16.5% c. 170% d. 17.5% e. 180%

Page 4014

Page 30: Finance_questions and answers 220

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Page 31: Finance_questions and answers 220

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Page 32: Finance_questions and answers 220

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Page 33: Finance_questions and answers 220

FUNDAMENTALS OF FINANCE

Problems on Chapter 10

a. TrueIFalse questions:

I I. The NPV method assumes that cash flows will be reinvested at the cost of capital, while the IRR method assumes reinvestment at the IRR.

T 2. Ifa project's internal rate ofretum (IRR) exceeds the cost of capital, then the project's net . present value (NPV) must be positive.

F 6J IfProject A has a higherIRR than ProjectB, then Project A must also have a higher NPY. I liD NPV can be uegative ifthe IRR is positive. 1 5. The NPV method is not affected by the multiple IRR problem.I (J5. If a project with uormal cash flows has an IRR that exceeds the cost of capital, then the

project must have a positive NPY. F 7. Ifthe IRR ofProject A exceeds the IRR ofProject B, then Project A must also have a higher

NPY. -1- 8. The:MJRR method uses a more reasonable assumption about reinvestment rates than the IRR

method and overcomes the problems of cash flow timing and project size that lead to criticism ofthe regular IRR method

F 9. Because discounted payback takes accouut of the cost of capital, a project's discounted payback is normally shorter than its regular payback.

F I O.lfthe cost of capital is less than the crossover rate for two mutually exclusive projects' NPV profiles, a NPVIIR.R conflict will not occur.

F II. Ifthe cost ofcapital is relatively high, this will favor larger, longer-term projects over smaller, shorter-term alternatives because it is good to eam high rates on larger amounts over longer periods.

F 12. The Modified Internal Rate of Return (MIRR) compounds cash outflows at the cost of capital.

F 13. The discounted payback method overcomes the problems that the payback method has with cash flows occurring after the payback period.

I 14. For independent projects, the decision to accept orreject will always be the same using either the IRR method or the NPV method.

T 15. One ofthe disadvantages ofchoosing between mutually exclusive projects on the basis ofthe discounted payback method is that you might choose the project with the faster payback period but with the lowertotal return.

F 16. When choosing between mutually exclusive projects, managers should accept all projects with IRRs greater than the weighted average cost ofcapital.

F 17. To find the MJRR, we first compound CFs at the regular IRR to find the TV, and then we discount the TV at the cost ofcapital to find the PY.

Page 1 0/4

Page 34: Finance_questions and answers 220

b. Answer each of the following questions. Show all your work. There shall be no credit for final answers only.

1. The Seattle COIporation has been presented with an investment opportunity that will yield cash flows of$30,000 per year in Years 1 through 4, $35,000 per year in Years 5 through 9, and $40,000 in Year 10. This investment will cost the finn $150,000 today, and the firm's cost of capital is 1°percent. Assume cash flows occur evenly during the year, 1/365th each day. What is the payback period for this investment?

a. 5.23 years b. 4.86 years c. 4.00 years d. 6.12 years e. 4.35 years

2. Project A has a 1°percent cost ofcapital and the following cash flows:

ProjectA Year Cash Flow

-$300 100

2 150 3 200 4 50

°1

What is Project A's discounted payback?

a. 2.25 years b. 2.36 years c. 2.43 years d. 2.50 years e. 2.57 years

3. As the director of capital budgeting for Denver.Corporation; you are. evaluating two mutually exciusive projects with the following net cash flows:

Project X ProjectZ Year Cash Flow Cash Flow

° -$100,000 -$100,000 1 50,000 10,000 2 40,000 30,000 3 30,000 40,000 4 10,000 60,000

IfDenver's cost ofcapital is 15yercent, which project would you choose?

a. Neither project. b. Project X, since it has the higher IRR. c. ProjectZ, since it has the higherNPY.

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Page 35: Finance_questions and answers 220

d. Project X, since it has the higher NPV. e. Project Z, since it has the hig!J.er IRR.

Year o I 2 3 4

The project has a regular payback of 2.25 years. What is the project's internal rate of return (IRR)?

a. 23.1% b. 143.9% c. 17.7% d. 335% e. 41.0%

5. Braun Industries is considering an investment project that has the following cash flows:

Year Cash Flow o -$1,000 I 400 2 300 3 500 4 400

The company's WACC is 10 percent. What is the project's payback, internal rate of return (IRR), and net present value (NPV)?

a. Payback = 2.4, IRR = 1O.OO%,NPV = $600. b. Payback = 2.4, IRR = 21.22%, NPV = $260. c. Payback = 2.6, IRR = 21.22%, NPV = $300. d. Payback = 2.6,IRR =21.22%, NPV = $260. e. Payback = 2.6, IRR = 24.12%, NPV = $300.

Page 3 of4

Page 36: Finance_questions and answers 220

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Page 37: Finance_questions and answers 220

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Page 38: Finance_questions and answers 220

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Page 39: Finance_questions and answers 220

I

.,,

6. Bowyer Robotics is considering two mutually exclusive projects with the following after-tllX operating cash flows'

Project I Project 2 Year CashFlow Cash Flow

;>. 0 -$400 -$500. ! '; 1 175 50 2 100 100

3 250 300 4 175 550

At what cost ofcapital would these two projects have the same net present value (NPV)?

r, a. 10.69%, .

:~~\ b. 16.15%

; .j c. 16.89% d. 20.97%r:'~ .r e. 24.33%

\.'.,. t .,.' .' 7. A company is considering a project with the fullowing cash flows: '.,' ~

Project Year Cash Flow o -$100,000 I 50,000 2 50,000 3 50,000 4 -10,000

The project's weighted average cost of capital is estimated to be Ib percent What is the modified iriternal rate ofreturn (MIRR)?

a. 11.25% b. 11.56% c. 13.28% d. 14.25% e. 20.34%

Page 4 af4

Page 40: Finance_questions and answers 220

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