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

Question

Cascade Mining Company expects its earnings and dividends to increase by 7 percent per year over the next six years and then to remain relatively constant thereafter.  The firm 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.Cascade Mining Company expects its earnings and dividends to increase by 7 percent per year over the next six years and then to remain relatively constant thereafter.  The firm 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.

Explanation / Answer

Present Value of First 6-Years' Dividends:

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

                                                           Present Value

    

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

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 5.35 0.893 4.78 2 5.00(1 + .07)^2 5.72 0.797 4.56 3 5.00(1 + .07)^3 6.13 0.712 4.36 4 5.00(1 + .07)^4 6.55 0.636 4.17 5 5.00(1 + .07)^5 7.01 0.567 3.98 6 5.00(1 + .07)^6 7.50 0.507 3.80 $25.65

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