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6. Peking Duct Tape Company has outstanding a $1,000-face-value bond with a 14 percent
coupon rate and 3 years remaining until final maturity. Interest payments are made
semiannually.
a. What value should you place on this bond if your nominal annual required rate of
return is (i) 12 percent? (ii) 14 percent? (iii) 16 percent?
b. Assume that we are faced with a bond similar to the one described above, except that
it is a zero-coupon, pure discount bond. What value should you place on this bond
if your nominal annual required rate of return is (i) 12 percent? (ii) 14 percent? (iii)
16 percent? (Assume semiannual discounting.)

Problems
1. Gonzalez Electric Company has outstanding a 10 percent bond issue with a face value of
$1,000 per bond and three years to maturity. Interest is payable annually. The bonds are
privately held by Suresafe Fire Insurance Company. Suresafe wishes to sell the bonds,
and is negotiating with another party. It estimates that, in current market conditions,
the bonds should provide a (nominal annual) return of 14 percent. What price per bond
should Suresafe be able to realize on the sale?
2. What would be the price per bond in Problem 1 if interest payments were made
semiannually?
3. Superior Cement Company has an 8 percent preferred stock issue outstanding, with each
share having a $100 face value. Currently, the yield is 10 percent. What is the market price
per share? If interest rates in general should rise so that the required return becomes
12 percent, what will happen to the market price per share?
4. The stock of the Health Corporation is currently selling for $20 a share and is expected
to pay a $1 dividend at the end of the year. If you bought the stock now and sold it for
$23 after receiving the dividend, what rate of return would you earn?
5. Delphi Products Corporation currently pays a dividend of $2 per share, and this dividend
is expected to grow at a 15 percent annual rate for three years, and then at a 10 percent
rate for the next three years, after which it is expected to grow at a 5 percent rate forever.
What value would you place on the stock if an 18 percent rate of return was required?
6. North Great Timber Company will pay a dividend of $1.50 a share next year. After this,
earnings and dividends are expected to grow at a 9 percent annual rate indefinitely.
Investors currently require a rate of return of 13 percent. The company is considering
several business strategies and wishes to determine the effect of these strategies on the
market price per share of its stock.
a. Continuing the present strategy will result in the expected growth rate and required
rate of return stated above.
b. Expanding timber holdings and sales will increase the expected dividend growth rate
to 11 percent but will increase the risk of the company. As a result, the rate of return
required by investors will increase to 16 percent.
c. Integrating into retail stores will increase the dividend growth rate to 10 percent and
increase the required rate of return to 14 percent.
From the standpoint of market price per share, which strategy is best?
7. A share of preferred stock for the Buford Pusser Baseball Bat Company just sold for $100
and carries an $8 annual dividend.
a. What is the yield on this stock?
b. Now assume that this stock has a call price of $110 in five years, when the company
intends to call the issue. (Note: The preferred stock in this case should not be treated
as a perpetual – it will be bought back in five years for $110.) What is this preferred
stock’s yield to call?

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8. Wayne’s Steaks, Inc., has a 9 percent, noncallable, $100-par-value preferred stock issue
outstanding. On January 1 the market price per share is $73. Dividends are paid annually
on December 31. If you require a 12 percent annual return on this investment, what is
this stock’s intrinsic value to you (on a per share basis) on January 1?
9. The 9-percent-coupon-rate bonds of the Melbourne Mining Company have exactly
15 years remaining to maturity. The current market value of one of these $1,000-par-
value bonds is $700. Interest is paid semiannually. Melanie Gibson places a nominal
annual required rate of return of 14 percent on these bonds. What dollar intrinsic value
should Melanie place on one of these bonds (assuming semiannual discounting)?
10. Just today, Fawlty Foods, Inc.’s common stock paid a $1.40 annual dividend per share
and had a closing price of $21. Assume that the market’s required return, or capitaliza-
tion rate, for this investment is 12 percent and that dividends are expected to grow at a
constant rate forever.
a. Calculate the implied growth rate in dividends.
b. What is the expected dividend yield?
c. What is the expected capital gains yield?
11. The Great Northern Specific Railway has noncallable, perpetual bonds outstanding.
When originally issued, the perpetual bonds sold for $955 per bond; today (January 1)
their current market price is $1,120 per bond. The company pays a semiannual interest
payment of $45 per bond on June 30 and December 31 each year.
a. As of today (January 1), what is the implied semiannual yield on these bonds?
b. Using your answer to Part (a), what is the (nominal annual) yield on these bonds? the
(effective annual) yield on these bonds?
12. Assume that everything stated in Problem 11 remains the same except that the bonds are
not perpetual. Instead, they have a $1,000 par value and mature in 10 years.
a. Determine the implied semiannual yield to maturity (YTM) on these bonds. (Tip: If
all you have to work with are present value tables, you can still determine an approx-
imation of the semiannual YTM by making use of a trial-and-error procedure coupled
with interpolation. In fact, the answer to Problem 11, Part (a) – rounded to the near-
est percent – gives you a good starting point for a trial-and-error approach.)
b. Using your answer to Part (a), what is the (nominal annual) YTM on these bonds? the
(effective annual) YTM on these bonds?
13. Red Frog Brewery has $1,000-par-value bonds outstanding with the following character-
istics: currently selling at par; 5 years until final maturity; and a 9 percent coupon rate
(with interest paid semiannually). Interestingly, Old Chicago Brewery has a very similar
bond issue outstanding. In fact, every bond feature is the same as for the Red Frog
bonds, except that Old Chicago’s bonds mature in exactly 15 years. Now, assume that
the market’s nominal annual required rate of return for both bond issues suddenly fell
from 9 percent to 8 percent.
a. Which brewery’s bonds would show the greatest price change? Why?
b. At the market’s new, lower required rate of return for these bonds, determine the per
bond price for each brewery’s bonds. Which bond’s price increased the most, and by
how much?
14. Burp-Cola Company just finished making an annual dividend payment of $2 per share
on its common stock. Its common stock dividend has been growing at an annual rate of
10 percent. Kelly Scott requires a 16 percent annual return on this stock. What intrinsic
value should Kelly place on one share of Burp-Cola common stock under the following
three situations?
a. Dividends are expected to continue growing at a constant 10 percent annual rate.
b. The annual dividend growth rate is expected to decrease to 9 percent and to remain
constant at that level.
c. The annual dividend growth rate is expected to increase to 11 percent and to remain
constant at the level.

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Solutions to Self-Correction Problems

1. a, b.

END OF DISCOUNT PRESENT DISCOUNT PRESENT

YEAR PAYMENT FACTOR, 15% VALUE, 15% FACTOR, 12% VALUE, 12%
1–3 $ 80 2.283 $182.64 2.402 $192.16
4 1,080 0.572 617.76 0.636 686.88
Market value $800.40 $879.04

Note: Rounding error incurred by use of tables may sometimes cause slight differences in answers when
alternative solution methods are applied to the same cash flows.

The market value of an 8 percent bond yielding 8 percent is its face value, of $1,000.
c. The market value would be $1,000 if the required return were 15 percent.

END OF DISCOUNT PRESENT

YEAR PAYMENT FACTOR, 8% VALUE, 8%
1–3 $0,150 2.577 $ 386.55
4 1,150 0.735 845.25
Market value $1,231.80

2.

PHASES 1 and 2: PRESENT VALUE OF DIVIDENDS TO BE RECEIVED OVER FIRST 8 YEARS

END OF PRESENT VALUE CALCULATION PRESENT VALUE

YEAR (Dividend × PVIF 16%,t ) OF DIVIDEND
1 1 $1.60(1.20)1 = $1.92 × 0.862 = $ 1.66
2 1.60(1.20)2 = 2.30 × 0.743 = 1.71
Phase 1 2
3 1.60(1.20)3 = 2.76 × 0.641 = 1.77
3 4 1.60(1.20)4 = 3.32 × 0.552 = 1.83

1 5 3.32(1.13)1 = 3.75 × 0.476 = 1.79

6 3.32(1.13)2 = 4.24 × 0.410 = 1.74
Phase 2 2
7 3.32(1.13)3 = 4.79 × 0.354 = 1.70
3 8 3.32(1.13)4 = 5.41 × 0.305 = 1.65
⎡ 8 Dt ⎤
or ⎢ ∑ ⎥ = $13.85
⎢⎣ t =1 (1.16)t ⎥⎦

PHASE 3: PRESENT VALUE OF CONSTANT GROWTH COMPONENT

Dividend at the end of year 9 = $5.41(1.07) = $5.79
D9 $5.79
Value of stock at the end of year 8 = = = $64.33
(ke − g ) (0.16 − 0.07)
Present value of $64.33 at end of year 8 = ($64.33)(PVIF16%,8)
= ($64.33)(0.305) = $19.62

PRESENT VALUE OF STOCK

V = $13.85 + $19.62 = $33.47

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Part 2 Valuation

3. The yield to maturity is higher than the coupon rate of 8 percent because the bond sells
at a discount from its face value. The (nominal annual) yield to maturity as reported in
bond circles is equal to (2 × semiannual YTM). The (effective annual) YTM is equal to
(1 + semiannual YTM)2 − 1. The problem is set up as follows:
20
$40 $1,000
$935 = ∑ (1 + k t
+
(1 + k d /2)20
t =1 d / 2)

= ($40)(PVIFAk ) + MV (PVIFk
d /2,20
)
d /2,20

a. Solving for kd/2 (the semiannual YTM) in this expression using a calculator, a computer
routine, or present value tables yields 4.5 percent.
b. (i) The (nominal annual) YTM is then 2 × 4.5 percent = 9 percent.
(ii) The (effective annual) YTM is (1 + 0.045)2 − 1 = 9.2025 percent.
4. a. P0 = FV20(PVIFkd /2,20)
(PVIFkd/2,20) = P0 /FV20 = $312/$1,000 = 0.312
From Table II in the end-of-book Appendix, the interest factor for 20 periods at 6 percent
is 0.312: therefore the bond’s semiannual yield to maturity (YTM) is 6 percent..
b. (i) (nominal annual) YTM = 2 × (semiannual YTM)
= 2 × (0.06)
= 12 percent
(ii) (effective annual) YTM = (1 + semiannual YTM)2 − 1
= (1 + 0.06)2 − 1
= 12.36 percent
5. a. ke = (D1/P0 + g) = ([D0(1 + g)]/P0) + g
= ([$1(1 + 0.06)]/$20) + 0.06
= 0.053 + 0.06 = 0.113
b. Expected dividend yield = D1/P0 = $1(1 + 0.06)/$20 = 0.053
c. Expected capital gains yield = g = 0.06
6. a. (i) V = ($140/2)(PVIFA0.06,6) + $1,000(PVIF0.06,6)
= $70(4.917) + $1,000(0.705)
= $344.19 + $705
= $1,049.19
(ii) V = ($140/2)(PVIFA 0.07,6) + $1,000(PVIF0.07,6)
= $70(4.767) + $1,000(0.666)
= $333.69 + $666
= $999.69 or $1,000
(Value should equal $1,000 when the nominal annual required return equals the
coupon rate; our answer differs from $1,000 only because of rounding in the Table
values used.)
(iii) V = ($140/2)(PVIFA 0.08,6) + $1,000(PVIF0.08,6)
= $70(4.623) + $1,000(0.630)
= $323.61 + $630
= $953.61
b. The value of this type of bond is based on simply discounting to the present the
maturity value of each bond. We have already done that in answering Part (a) and those
values are: (i) $705; (ii) $666; and (iii) $630.

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