Finance

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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 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.

  • Finance -

    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)

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