A fast-growing firm recently paid a dividend of $0.80 per share. The dividend is

Question

A fast-growing firm recently paid a dividend of $0.80 per share. The dividend is expected to increase at a 15 percent rate for the next three years. Afterwards, a more stable 11 percent growth rate can be assumed.

If a 12 percent discount rate is appropriate for this stock, what is its value today? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

A fast-growing firm recently paid a dividend of $0.80 per share. The dividend is expected to increase at a 15 percent rate for the next three years. Afterwards, a more stable 11 percent growth rate can be assumed.

Explanation / Answer

Dividend for Year 1(D1) = $0.80 * (1.15)1 = $0.92

Dividend for Year 1(D2) = $0.80 * (1.15)2 = $1.058

Dividend for Year 1(D3) = $0.80 * (1.15)3 = $1.2167

Dividend for Year 1(D4) = $1.2167 * (1.11) = $1.3505

Value of the stock at the end of 3 years(V3) = D4  /(r-g)

= $1.3505 / (0.12-0.11)

= $135.05

V0 = D1/(1+r)1 + D2/(1+r)2 + D3/(1+r)3 + V3/(1+r)3

= $0.92 / (1.12)1 + $1.058 / (1.12)2+ $1.2167 / (1.12)3 + $135.05 / (1.12)3

= $0.82 + $0.84 + $0.87 + $96.13 = $98.66

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