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Homework answers / question archive / Prescott Pharmaceuticals will pay an annual dividend of $$0
Prescott Pharmaceuticals will pay an annual dividend of $$0.550.55 one year from now at t=11. Analysts expect this dividend to grow at 19.819.8% per year thereafter until the end of year 2525. Dividends are then expected to be stable until t=3232. Afterwards, dividends decline at a rate of 4.24.2% annually (the dividend at t=3333 is 4.24.2% smaller than the payment at t=3232) and are paid in perpetuity. According to the dividend-discount model, what is the value of a Prescott Pharmaceuticals share if the firm's equity cost of capital is 14.514.5%? (Round to the nearest cent).
Value per share = sum of present value (PV) of all future dividends
= PV of dividends from T = 1 to T = 25 + PV of dividends from T = 26 to T = 32 + Terminal value from T = 33 onwards
a). PV of dividends from T = 1 to T = 25 = D1/(k-g1)*[1 - ((1+g1)/(1+k)^n]
where D1 (Dividend at T = 1) = 0.55; g1 (annual growth rate from T = 1 to T = 25) = 19.8%; n (time periods from T = 0 to T = 25) = 25; k (required return on equity) = 14.5%
= 0.55/(14.5%-19.8%)*[1 - ((1+19.8%)/(1+14.5%))^25] = 21.79
b). PV of dividends from T = 26 to T = 32:
PV25 (Present Value at T = 25) = D26/k*[1-(1+k)^-n]
where D26 (Dividend at T = 26) = D25 = D1*(1+g1)^-24 = 0.55*(1+19.8%)^-24 = 42.01; n (time periods for which dividend is constant) = 32 - 25 = 7
= 42.01/14.5%*[1 - (1+14.5%)^-7] = 177.42
PV (at T = 0) = PV25/(1+k)^25 = 177.42/(1+14.5%)^25 = 6.01
c). Terminal value from T = 33 onwards:
D33 = D32*(1+g2) where D32 = 42.01; g2 (perpetual growth rate) = -4.20%
D33 = 42.01*(1-4.20%) = 40.24
Terminal value (at T = 32) = D33/(k-g2) = 40.24/(14.5%+4.20%) = 215.20
PV (at T = 0) of Terminal value = Terminal value/(1+k)^32 = 215.20/(1+14.5%)^32 = 2.83
d). Value per share = 21.79 + 6.01 + 2.83 = $30.62 per share (Answer)
