Time Value of Money Homework Solutions

Dr. Stanley D. Longhofer
MBA 800 – Financial Statement Analysis
Stock Valuation Practice Problems – Solutions
Note: Some of the problems below came from Corporate Finance, 6 th edition by Ross,
Westerfield, and Jaffee.
1) Quirky Corporation common stock just paid an annual dividend of $1.50 per share.
This dividend is expected to grow by 3 percent per year for the indefinite future.
a) If the required return on Quirky stock is 18.00 percent, at what price should it be
trading today?
Use the dividend growth model to solve for the present value:
Div1
Div0(
1+
g)
1.
50×
1.
03 1.
545
P 0 = =
= = = $ 10.
30 .
r − g r − g 0.
18 − 0.
03 0.
15
b) What will its price be three years from today?
The simple answer is to note that the stock price will grow by the rate at
which dividends grow, or 3 percent per year. Thus, its value will be
P3 = 10.30 × 1.03 3 = $11.26.
You can verify this by calculating the value of the dividend beginning in year
4 (one year ahead of when you want the price of the stock) and calculate the
value using the dividend growth model: Div4 = 1.50 × 1.03 4 = 1.69 ⇒
P3 = 1.69 ÷ 0.15 = $11.26.
2) Whizzkids, Inc. is experiencing a period of rapid growth. Earnings and dividends per
share are expected to grow at a rate of 18 percent during the next two years, 15
percent the third year, and at a constant rate of 6 percent thereafter. Whizzkids’ last
dividend, which has just been paid, was $1.15. If the required rate of return on the
stock is 12 percent, what is the price of a share of the stock today?
Begin by calculating the expected dividend over the next four years:
Year Dividend
1 1.15 × 1.18 = $1.36
2 1.36 × 1.18 = $1.60
3 1.60 × 1.15 = $1.84
4 1.84 × 1.06 = $1.95
Once the year-3 dividend is paid, Whizzkids becomes a constant growth stock, so
we can use the growing perpetuity formula to value it as of the end of year 3:
P3 = 1.95 ÷ (0.12 − 0.06) = $32.50
The expected cash flows from this stock thus look as follows:
Year Cash Flow
1

1 $1.36
2 $1.60
3 1.84 + 32.50 = $34.34
Entering these figures into your irregular cash flow function using a 12 percent
discount rate gives P0 = $26.93.
3) Calamity Mining Company’s reserves of ore are being depleted, and its costs of
recovering a declining quantity of ore are rising each year. As a result, the
company’s earnings are declining at the rate of 10 percent per year. If the dividend
per share that is about to be paid is $5 and the required rate of return is 14 percent,
what is the value of the firm’s stock? (Hint: Treat the $5 dividend as a payment that
will be received today and then also figure out what the dividend will be a year from
now.)
The price of the stock is calculated as follows:
Div1
5×
( 1−
0.
10)
4.
50
P 0 = Div0
+ = 5 +
= 5 + = 5 + 18.
75 = $ 23.
75.
r − g 0.
14 − ( −0.
10)
0.
14 + 0.
10
2