Fabozzi Frank, Peterson Pamela. Financial Management and Analysis Workbook

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330 SOLUTIONS

7. right, buy, sell; not, stock, exchange, traded; buy, call; buy, exercise,

strike, expiration; sell, put

8. convertible, stock, investor; straight, without, stock; Callable, issuer,

buy, investor, price, call, prior, convertible, callable

SHORT ANSWER QUESTIONS

Answers

1. If a bond’s present value is greater than its maturity value, it sells at a

premium because investors will pay more for a bond if it pays more

than the going rate for bonds of similar risk. If the bond’s present value

is equal to its maturity value, then the bond sells at par. If the bond sells

below its maturity value, it is trading at a discount because investors

are not going to pay the maturity value for a bond that pays less than

the going rate.

2. All three types of securities are valued by the present value of all

future cash ﬂows expected to be received. With shares of common

stock, the value is equal to the present value of all dividends expected

to be received from that share. As mentioned previously, common

stock has no maturity so the value is the present value of an inﬁnite

stream of dividends. One catch is that the dividends are neither ﬁxed

nor guaranteed. Thus, the value of preferred stock is likewise the

present value of all future dividends and the dividends are guaran-

teed. The value of a debt security is the present value of the sum of

the present value of the interest payments and the present value of the

maturity value.

3. The factors that affect the time value of an option are the value of the

underlying asset, the exercise price, the time value of money, the

expected volatility in the value of the underlying asset, and the time

to maturity.

4. The Dividend Valuation Model is a formula that values a share of

stock that either pays a constant dividend or that pays dividends that

grow at a constant rate. The model states that the value of a share of

stock is equal to the ratio of next period’s dividend to the difference

between the required rate of return and the growth rate of dividends.

SolCh9 Page 330 Tuesday, December 16, 2003 9:27 AM

Valuation of Securities and Options 331

It is useful and ﬂexible, especially for dividends that have changing

rates over time. Its meaning is intuitive—as the current dividend

increases, the value of the stock increases, and in turn, if uncertainty

increases, then the discount rate increases, which decreases the value

of the stock.

5. The yield-to-maturity differs from the yield-to-call in that the number

of periods for which the cash ﬂows are discounted back is the number

of periods to the expected call date and the call price of the bond is

discounted back instead of the face value of the bond.

PROBLEMS

Answers

1. The price of the bond will increase because the cash ﬂows (coupon pay-

ments) are discounted at a lower rate. This increases the present value

which is evident in the increased price of the bond.

2. Yes. According to the option, the investor has one month to decide to

purchase 1,000 shares of XYZ Company for $30 per share plus the

option cost, which translates into $1.50 more per share. Therefore

the cost to the investor is $31.50 per share. Because the current price

is $1 higher than the option price, the investor could exercise this

option and then sell the shares in the open market for a proﬁt of $1

per share. The investor can exercise the option at any time up until

and including the expiration date. Therefore if the price of the stock

falls, the option will not be exercised and the investor will lose his

$1,500. If the investor thinks the stock will rise and wants more than

$1 per share proﬁt, he should exercise the option immediately and

hold the stock until it rises to what he considers an acceptable level.

3. ABC preferred stock

→

Because the return on this investment is less than the required 10%,

the investment would not be made.

dividend

price

----------------------

$3.45

$35

-------------- -

9.86%===

SolCh9 Page 331 Tuesday, December 16, 2003 9:27 AM

332 SOLUTIONS

This investment should only be taken if the investors required rate of

return is less than 8%. The current price is $130, which is greater

than the price at which it will be called, $127.58, so the investor will

not receive the 8% annual return on the investment.

5. The cash ﬂows are as follows:

Since the third year begins the perpetuity:

Therefore, the price per share for the stock that has this particular

cash ﬂow of dividends is:

6. The bond pays $60 every six months for ten periods. It will pay

$1,000 at maturity. The effective annual yield is 14% so the appro-

priate semiannual rate to discount the cash ﬂows is 7%.

= D

(1 + 0.02) = 2.25(1.02) = $2.30

= D

(1 + 0.02) = 2.30(1.02) = $2.35

= D

(1 + 0.02) = 2.35(1.02) = $2.39

= $2.39

Price $11

1.08()

------------------

t 1=

∑

$125

1.08()

-------------------







$28.35 $99.23+ $127.58==

Price

$2.39

0.16

-------------- -

$14.94==

Price

$2.30

1.16

-------------- -

$2.35

1.16()

-------------------

$2.39

1.16()

-------------------

$14.94

1.16()

-------------------

+++ $17.25==

Price $60

1.07()

------------------

t 1=

∑

$1,000

1.07()

---------------------

$456.53 $508.40+ $964.93==

SolCh9 Page 332 Tuesday, December 16, 2003 9:27 AM

Valuation of Securities and Options 333

Because the investor is holding the bond to maturity, the average

annual yield is the yield to maturity on the bond, which is 14%.

7. Assume the interest is paid at the end of the year, then:

8. The entire yield is the capital yield: $1,000 = $738.75(1 + r)

Solving algebraically for the rate:

9. The round trip transactions cost of $10.99

× 2 must be considered in

the return calculation:

10.

Return

Ending price Beginning price Interest+–

Beginning price

--------------------------------------------------------------------------------------------------------

$1,037.50 1,000 93.75+–

$1,000

---------------------------------------------------------------------

13.125%=

Coupon yield

Interest

Price

-------------------

$93.75

$1,000

------------------

9.375%===

Capital yield

$1,037.50 1,000–

$1,000

-----------------------------------------------

3.75%==

$1,000

$638.75

---------------------

1– 5.76%==

Return

Sell price Buy price–

Buy price

-----------------------------------------------------

1,000 8.625 10.99–×()1,000 5 10.99+×()–

1,000 5 10.99+×()

-----------------------------------------------------------------------------------------------------------------------

$8,614.01 5,010.99–

5,010.99

------------------------------------------------------- -

71.9%=

$1,080

1 r+()

------------------

t 1=

∑

$1,000 100+

1 r+()

----------------------------------

SolCh9 Page 333 Tuesday, December 16, 2003 9:27 AM

334 SOLUTIONS

Using a ﬁnancial calculator: r = 4.82% for six months. To ﬁnd the

effective annual yield to call:

EAR 1 Interest rate per period+()

periods per year

1–=

1.0482()

1–=

9.87%=

SolCh9 Page 334 Tuesday, December 16, 2003 9:27 AM

CHAPTER

335

Risk and Expected Return

FILL IN THE BLANKS

Answers

1. uncertainty, knows, tax, demand, economy, interest; risk, uncertainty;

Uncertainty, knowing; Risk, uncertainty, greater, uncertainty, greater,

risk

2. Cash, sales, operating, ﬁnancial; Sales, uncertainty, units, good, price;

Operating, variable, ﬁxed; Financial, ﬁnancing

3. debt, interest, principal, payments, bondholders, owners; cash, debt,

default, credit; default, debt

4. Reinvestment, reinvesting; yields, reinvest, interest, bond, return;

yield, coupon, longer, more, more, reinvest; yield, time, maturity,

greater, more, value

5. Interest, sensitivity, value, interest; Market, rate, discount, present,

discount

6. Purchasing, price level; borrows, long, coupon, increases, beneﬁts,

increase, creditor, cheaper

7. Currency, domestic, foreign, value, future; Currency, cash, currency

SolCh10 Page 335 Tuesday, December 16, 2003 9:27 AM

336 SOLUTIONS

8. Risk, dislike; averse, avoid; neutral; neutral, compensation, risk; pref-

erence, afﬁnity

9. Diversiﬁcation, vary, same, same; returns, correlated; tendency;

returns, positively, same, negatively, opposite; uncorrelated, no

10. Risk, add, unsystematic, company; Risk, assets, market, systematic

11. William Sharpe, return, risk, assets; capital, pricing, CAPM; CAPM,

return, asset, return, risk-free, risk; return, compensation, value, pre-

mium, compensation, risk; diversiﬁed, risk, assets, nondiversiﬁable,

market, systematic

12. CAPM, risk, return, arbitrage, model, APM, Stephen Ross; APM,

asset, identical, different, identically; returns, compensate, risk, risk,

economic, company; theoretical, pricing, factor

SHORT ANSWER QUESTIONS

Answers

1. The degree of operating leverage (DOL) is the ratio of the percentage

change in operating cash ﬂows to the percentage change in units sold.

The degree of ﬁnancial leverage (DFL) is the ratio of the percentage

change in cash ﬂows to the owners to the percentage change in operat-

ing cash ﬂows. The degree of total leverage (DTL) is the product of

DOL and DFL. DTL measures the sensitivity of the cash ﬂows to own-

ers to changes in unit sales.

The degree of operating leverage measures the sensitivity of oper-

ating cash ﬂows to changes in sales and the degree of ﬁnancial lever-

age measures the sensitivity of owners’ cash ﬂows to changes in

operating cash ﬂows. The combination is the degree of total leverage.

2. Default may result from many types of failures. Some examples are:

■

Failure to make interest or principal payments

■

Failure to make sinking fund payments

■

Failure to meet conditions of the loan

■

Bankruptcy

SolCh10 Page 336 Tuesday, December 16, 2003 9:27 AM

Risk and Expected Return 337

Financial managers are concerned about their own default

because if there is a perception of lack of creditworthiness, then the

ﬁrm’s cost of capital increases. Likewise, if the managers invest in

another ﬁrm’s debt, they are risking their ﬁrm’s funds. Default risk is

comprised of sales risk, operating risk, and ﬁnancial risk.

3. Prepayment risk and call risk are related to reinvestment risk. The

rule to remember is that the greater the risk (i.e., cash ﬂows), the

greater the return.

■

Prepayment risk is associated with loans that have a schedule for the

repayment of principal with the right to repay without penalty prior

to the end of the loan. The risk comes in when the interest rate falls

below that of the loan; then the investor is paying more for the loan

than initially contracted.

■

Call risk is the risk that an issuer will call an investment product

that has a callable option. Investors are compensated for this risk

with a premium. However if the issue is called, then the investor

must ﬁnd another investment mechanism.

4. If an investor plans to hold a bond until its maturity, then the value is

stable despite the changing interest rates. However, if the investor

does not want to hold the bond to maturity, then the value is directly

affected by the changing interest rates. As interest rates fall, bond val-

ues rise and vice versa, so if an investor plans to get rid of a bond, it

needs to be done during times of low interest rates.

For a speciﬁc maturity and if the rate on the coupon is relatively

great, then the bond’s value is not subject to much change in the yield

because the greater cash ﬂows are not as affected by the discount rate.

However if the bond has a longer maturity, then the bond’s value is

more affected.

5. Expected returns are a measure of future returns without delineating

all the possible outcomes. The more the possible outcomes (range),

the greater the risk. The standard deviation is a measure of the disper-

sion of risk which indicates the likelihood of all possible outcomes.

The variance is the square of the standard deviation and has the same

meaning as standard deviation. It is often referred to as the volatility.

SolCh10 Page 337 Tuesday, December 16, 2003 9:27 AM

338 SOLUTIONS

PROBLEMS

Answers

1. a.

e. The sales volume is increased by 5,000 units, which indicates a 50%

increase in units sold. Therefore, DTL

× 50% = 1.01

× 50% =

50.5% increase in the cash ﬂows available to owners.

2. a.

Investment 1:

Investment 1: expected value = $1,075

Investment 2: expected value = $1,075

Investment 1: standard deviation = $278

Investment 2: standard deviation = $388

– E(x))

$500 213,906

400 14,063

175

115,719

E(x) = $1,075 343,688

σ(x) = $586.25

DOL at 10,000 units

10,000 $1,500 30–()

10,000 $1,500 30–()$175,000–

-------------------------------------------------------------------------------------

1.01==

DFL at 10,000 units

10,000 $1,500 30–()$175,000–

10,000 $1,500 30–()$175,000– $65,000–

-----------------------------------------------------------------------------------------------------------------

1.00=

DTL at 10,000 units DOL DFL×=

1.01 1.00× 1.01==

$175,000 $65,000+

$1,500 30–()

-----------------------------------------------------

164 units==

SolCh10 Page 338 Tuesday, December 16, 2003 9:27 AM

Risk and Expected Return 339

Investment 2:

Actual value is rounded appropriately.

c. Investment 1 is riskier. Investment 1 provides the same expected

return, but has a higher standard deviation than Investment 2.

3. a. r

= 6% r

–

= 4%

4. a. The covariance between Investment 1 and 2:

– E(x))

2 a

$375 45,156

400 14,063

300*

16,633

E(x) = $1,075 75,852

σ(x) = $275.41

Security Expected Return

A 6% + 0.85(4%) = 9.4%

B 6% + 1.00(4%) = 10%

C 6% + 1.25(4%) = 11%

D 6% + 1.50(4%) = 12%

0.85 1.00 1.25 1.50+++

-----------------------------------------------------------------

1.15==

0.094 0.10 0.11 0.12+++

---------------------------------------------------------------------

0.106 or 10.6%==

Ex()

Inv1

0.15 0.18()0.30 0.50()0.55 0.40()++ 0.397==

σ x()

Inv1

0.15 0.18 0.397–()

0.30 0.50 0.397–()

0.55 0.40 0.397–()++=

0.1012=

Ex()

Inv2

0.15 0.25()0.30 0.45()0.55 0.30()++ 0.3375==

SolCh10 Page 339 Tuesday, December 16, 2003 9:27 AM