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© Pearson Education Limited 2008
The Valuation of Long-Term Securities
What is a cynic? A man who knows the price of
everything and the value of nothing.
OSCAR WILDE
Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition, Instructor’s Manual
33
© Pearson Education Limited 2008
ANSWERS TO QUESTIONS
1. The market value of a firm is the market price at which the firm trades in an open
marketplace. This value is often viewed as being the higher of the firm's liquidation value
2. The
intrinsic value (or economic value) of a security could differ from its market value (or
3. Both bonds and preferred stocks are fixed-income securities. The interest payment or
4. The longer the maturity, the less important the principal payment, and the more important
5. The lower coupon bond will suffer the greater proportional market decline. Its income
6. Dividends are all that investors as a whole receive. As shown in the chapter, a dividend
7. The stock would be worth zero. There must be the prospect for an ultimate cash payment to
8. As companies grow larger, growth becomes more difficult. Unless there is some
competitive advantage or monopolistic position, most large companies grow roughly in
keeping with growth in the economy. A company can of course grow at an increasing rate
9. A company could grow at this rate for a while, but not forever. At the end of 25 years, it
10. She is right. The constant growth dividend valuation model states that P0 = D1/(ke – g).
Chapter 4: The Valuation of Long-Term Securities
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© Pearson Education Limited 2008
11. The ad does not reveal that the current value of this zero-coupon bond is nowhere close to
SOLUTIONS TO PROBLEMS
1.
End of Year
Payment
Discount
Factor (14%)
Present Value
2 100 0.769 76.90
2. End of Six-
month Period
Payment
Discount
Factor (7%)
Present Value
1 $ 50 0.935 $ 46.75
3. Current price: P0 = Dp/kp = (0.08)($100)/(0.10) = $80.00
4. $1dividend + ($23 $20) capital gain
Rate of return = $20 original price
−
5. Phases 1 and 2: Present Value of Dividends to Be Received Over First 6 Years
Present Value Calculation
End of
Year (Dividend × PVIF18%,t) Pre sent Value
of Dividend
1 $2.00 (1.15)1 = $2.30 × 0.847 = $ 1.95
P
h
a
1
Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition, Instructor’s Manual
35
© Pearson Education Limited 2008
4 3.04(1.10)1= 3.34 × 0.516 = 1.72
P
h
e
2
6
t
t1
D
=
Phase 3: Present Value of Constant Growth Component
Dividend at the end of year 7 = $4.05(1.05) = $4.25
7
D$4.25
Present Value of Stock
6. a. P0 = D1/(ke – g): ($1.50)/(0.13 – 0.09) = $37.50
Either the present strategy (a) or strategy (c). Both result in the same market price per share.
7. a. kp = Dp/P0: $8/$100 = 8 percent
b. Solving for YTC by computer for the following equation
we get YTC = 9.64 percent. (If the students work with present-value tables, they should
still be able to determine an approximation of the yield to call by making use of a trial-
and-error procedure.)
9. V = (I/2)(PVIFA7%, 30) + $1,000(PVIF7%, 30)
10. a. P0 = D1/(ke – g) = [D0(1 + g)]/(ke – g)
Chapter 4: The Valuation of Long-Term Securities
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© Pearson Education Limited 2008
b. Expected dividend yield = D1/P0 = D0(1 + g)/P0
c. Expected capital gains yield = g = 0.05.
11. a. P0 = (I/2)/(semiannual yield)
b. (semiannual yield)
× (2) = (nominal annual) yield
c. (1 + semiannual yield)2 – 1 = (effective annual) yield
12. Trying a 4 percent semiannual YTM as a starting point for a trial-and-error approach, we
get
P0 = $45(PVIFA4%, 20) + $1,000(PVIF4%, 20)
Since $1,067.55 is less than $1,120, we need to try a lower discount rate, say 3 percent
P0 = $45(PVIFA3%, 20) + $1,000(PVIF3%, 20)
To approximate the actual discount rate, we interpolate between 3 and 4 percent as follows:
.03 $1,223.47
X $103.47
.01 $155.92
semiannual YTM $1,120,00
and semiannual YTM = 0.03 + X = 0.03 + 0.0066 = 0.0366, or 3.66 percent. (The use of a
computer provides a precise semiannual YTM figure of 3.64 percent.)
b. (semiannual YTM) × (2) = (nominal annual) YTM
c. (1 + semiannual YTM)2 – 1 = (effective annual) YTM
Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition, Instructor’s Manual
37
© Pearson Education Limited 2008
13. a. Old Chicago's 15-year bonds should show a greater price change than Red Frog's bonds.
With everything being the same except for maturity, the longer the maturity, the greater
b. (Red Frog):
P0 = $45(PVIFA4%,10) + $1,000(PVIF4%, 10)
(Old Chicago):
P0 = $45(PVIFA4%, 30) + $1,000(PVIF4%,30)
14. D0(1 + g)/(ke – g) = V
a. $2(1 + 0.10)/(0.16 – 0.10) = $2.20/0.06 = $36.67
SOLUTIONS TO SELF-CORRECTION PROBLEMS
1. a, b.
End of Discount Present Discount Present
year Payment Factor, 15% Value, 15% Factor, 12% Value, 12%
_____________________________________________________________________________
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.
Chapter 4: The Valuation of Long-Term Securities
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© Pearson Education Limited 2008
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%
_____________________________________________________________________________
2.
Phases 1 and 2: Present Value of Dividends to Be Received Over First 8 Years
End of Year Present Value Calculation
(Dividend × PVIF16%, t)
Present Value of Dividend
P
h
a
s
1 $1.60 (1.20)1 = $1.92 × 0.862 =
2 1.60 (1.20)2 = 2.30 × 0.743 =
$ 1.66
1.71
t1
(1.16)
=
Phase 3: Present Value of Constant Growth Component
Dividend at the end of year 9 = $5.41(1.07) = $5.79
9
D$5.79
Value of stock at the end of year 8 = $64.33
(k g) (.16 .07)
e
==
−−
Present Value of Stock
Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition, Instructor’s Manual
39
© Pearson Education Limited 2008
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
dd
20
t20
k/2,20 k/2,20
$40 $1,000
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.
4. a. P0 = FV20(PVIFkd/2,20)
b. (i) (nominal annual) YTM = 2 × (semiannual YTM)
(ii) (effective annual) YTM = (1 + semiannual YTM)2 – 1
5. a. ke = (D1/P0) + g = ([D0(1 + g)]/P0) + g
(ii) V = ($140/2)(PVIFAִ07, 6) + $1,000(PVIFִ07, 6)
(*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.08, 6) + $1,000(PVIF.08, 6)
Chapter 4: The Valuation of Long-Term Securities
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© Pearson Education Limited 2008
b. The value of this type of bond is based on simply discounting to the present the maturity
