Chapter 10: Valuation and Rates of Return
$3.10
Value of Stock Price at the end of Year 3
4
3 4 3
e
D
P D D (1 g) $1.452 (1.10) $1.597
Kg
= = + = =
−
3
$1.597 $1.597
P $53.23
0.13 0.10 0.03
= = =
−
CP 10-1. (Continued)
Present Value of Future Stock Price
PV3 = $53.23, n = 3, i = 13% (Appendix B)
c. Average P/E of Five Food Industry Companies
Del Monte 12
General Mills 15
Chapter 10: Valuation and Rates of Return
10-39
CP 10-1. (Continued)
d.
P/E Ratio
Weights
Del Monte
12
.15
General Mills
15
.15
Heinz
14
.15
Kellogg
22
.40
Kraft
17
.15
Stock price = P/E × EPS
Based on the weighted average P/E, the stock price is
e. Stock price (d) $42.88
Chapter 10: Valuation and Rates of Return
10-40
Change $3.68
= 9.39%
Beginning Amount $39.20 =
Special Note to Instructor
The instructor may wish to discuss any possible discount
for the illiquidity of the Fiber Cereals stock after working
the problem. However, that discussion goes beyond the
normal scope of this problem.
Appendix
10A–1. Yield to maturity and interpolation (LO3) Bonds issued by the Peabody
Corporation have a par value of $1,000, are selling for $890, and have 18
years to maturity. The annual interest payment is 8 percent.
Find yield to maturity by combining the trial-and-error approach with
interpolation, as shown in this appendix. (Use an assumption of annual
interest payments.)
10A–1. Solution:
Peabody Corporation
first approximation, we will try 9 percent.
Present Value of Interest Payments
PVA = A × PVIFA (n = 18, i = 9%) Appendix D
Present Value of Principal Payment at Maturity
PV = FV × PVIF (n = 18, i = 9%)
Chapter 10: Valuation and Rates of Return
10A–1. (Continued)
The discount rate of 9 percent gives us too high a
present value in comparison to the bond price of $890.
So we next use a higher discount rate of 10 percent.
Present Value of Interest Payments
PVA = A × PVIFA (n = 18, i = 10%) Appendix D
Present Value of Principal Payment at Maturity
PV = FV × PVIF (n = 18, i = 10%)
answer is:
$912.48 PV at 9% $912.48 PV at 9%
Chapter 10: Valuation and Rates of Return
10-42
10C–1. Valuation of supernormal growth firm (LO5) The McMillan Corporation
paid a dividend of $2.40 per share of stock over the last 12 months. The
dividend is expected to grow at a rate of 25 percent over the next three years
(supernormal growth). It will then grow at a normal, constant rate of 6 percent
for the foreseeable future. The required rate of return is 14 percent (this will
also serve as the discount rate). Round to two places to the right of the
decimal point throughout the problem.
a. Compute the anticipated value of the dividends for the next three years
(D1, D2, and D3).
b. Discount each of these dividends back to the present at a discount rate of
14 percent and then sum them.
c. Compute the price of the stock at the end of the third year (P3).
4
34
e
D
P [Review Appendix 10B for the definition of D ]
Kg
=
−
d. After you have computed P3, discount it back to the present at a discount rate of
14 percent for three years.
e. Add together the answers in part b and part d to get the current value of the
stock. (This answer represents the present value of the first three periods of
dividends plus the present value of the price of the stock after three periods.)
10C–1. Solution
McMillan Corporation
a. D1 $2.40 (1.25) = $3.00
b.
Supernormal
dividends
Discount rate
Ke = 14%
Present value of
dividends during
the supernormal
growth period
D1
$3.00
.877
$2.63
D2
$3.75
.769
2.88
D3
$4.69
.675
3.17
$8.68
Chapter 10: Valuation and Rates of Return
10-43
10C–1. (Continued)
c.
4
3
e
D
PKg
=
−
43
D D (1.06) $4.69 (1.06) $4.97= = =
3
$4.97 $4.97
P $62.13
.14 .06 0.08
= = =
−
d. PV of P3 for n = 3, i = 14%
e. Answer to part b (PV of dividends) $ 8.68