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non-constant dividends

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I have no idea where to begin with this one !

Nonconstant Dividends

Hetfield and Ulrich, Inc., has an odd dividend policy. The company has just paid a dividend of $12 per share and has announced that it will increase the dividend by $7 per share for each of the next 5 years, and then never pay another dividend. If you require a 14 percent return on the company's stock, you will pay $______ per share today?

  • non-constant dividends -

    19 + 26 + 33 + 40 + 47 = 165

    165/5 = 33 average yearly dividend

    0.14x = 33

    x = 235.71

  • non-constant dividends -

    Ms. Sue, I put in the answer and it says it is wrong. I looked over your work and it looks right... im wondering if maybe multiply instead of divide or something, im trying different ways to alter the answer. thanks for the help.

  • non-constant dividends -

    i figured it out... you have to ^1, ^2, ^3^4^5 for each of the years o the rate of return for each one! thanks

  • non-constant dividends -

    Let's try's Ms Sue's suggestion:

    If the dividends accumulate without interest, we have after 5 years,
    sum of dividends
    = 19 + 26 + 33 + 40 + 47
    = 165

    This amount should equal the purchase price, P, paid and compounded over 5 years. Thus:
    P*1.14*5 = 165
    P=$85.70

    If the dividends also accumulate at 14% (unlikely?), then
    future value of dividends
    =19*1.14^4+26*1.14^3+33*1.14^2+40*1.14^1+47*1.14^0
    =206.097187

    P*1.14*5 = 206.097187
    P=$107.04

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