Cascade Mining Company expects its earnings and dividends to increase by 7 percent per

Question

year over the next six years and then to remain relatively constant thereaft er. Th e fi rm
currently (that is, as of year 0) pays a dividend of $5 per share. Determine the value of a
share of Cascade stock to an investor with a 12 percent required rate of return.

Answer 1

Present Value of First 6-Years' Dividends:

6 ƒÃ[Do(1 + g1)t/(1 + ke)t]; Do = $5.00; g1 = .07; ke = .12
t=1
Present Value

Year Dividend Interest Factor Present Value
t Dt = 5.00(1 + .07)t PVIF.12,t Dt x PVIF.12,t

1 5.00(1 + .07)1 = .893 $ 4.778
$5.35

2 5.00(1 + .07)2 = .797 4.563
5.725

3 5.00(1 + .07)3 = .712 4.361
6.125

4 5.00(1 + .07)4 = .636 4.168
6.554

5 5.00(1 + .07)5 = .567 3.976
7.013

6 5.00(1 + .07)6 = .507 3.805
7.504

PV (First 6-Years' Dividends) $25.651

Value of Stock at End of Year 6:

P6 = D7/(ke - g2) g2 = .00

D7 = D6(1 + g2) = 7.504(1 + .00) = $7.504

P6 = 7.504/(.12 - .00) = $62.533
Present Value of P6:

PV(P6) = P6/(1 + ke)6 = 62.533/(1 + .12)6 = 62.533 x PVIF.12,6

= 62.533 X .507 = $31.704

Value of Common Stock (Po):

Po = PV (First 6-Years' Dividends) + PV(P6)

= 25.651 + 31.704 = $57.36 (tables)