Question

Problem 7-13
Nonconstant Growth Stock Valuation

Simpkins Corporation does not pay any dividends because it is expanding rapidly and needs to retain all of its earnings. However, investors expect Simpkins to begin paying dividends, with the first dividend of $1.00 coming 3 years from today. The dividend should grow rapidly - at a rate of 80% per year - during Years 4 and 5. After Year 5, the company should grow at a constant rate of 6% per year. If the required return on the stock is 17%, what is the value of the stock today (assume the market is in equilibrium with the required return equal to the expected return)? Round your answer to the nearest cent. Do not round your intermediate computations.

Answer 1

Hello,

Here is the solution -

Dividend at year 3 = D₃ = $1.00

Dividend at year 4 = D4 = $1.00 * 1.80 = $1.80

Dividend at year 5 = D₅ = $1.80 * $1.80 = $3.24

Compute D₆ = $3.24 * 1.06 = $3.434 just to use for constant growth model (DVM) for valuing dividends from year 6 to infinity

P₅ = D₆ / (k -g) = 3.434 / (0.17-0.06) = $31.22

So, now if we calculate the NPV, that will be the value of stock today

NPV = PV of cash flows = 1/(1.17)³ + 1.8/(1.17)⁴+3.24/(1.17)⁵ + 31.22/(1.17)⁵ = $17.30

So, the answer to your question is $17.30