Tarp Corporation is a young start-up company. No dividends will be paid over the next ten years because the firm needs to plow back its earnings to fuel growth. The company will pay $3 per share dividend in year 11 and will increase the dividend by 6% per year thereafter. If the required return on this stock is 15%, what is the current share price?

Question

Quizplus · Accepted Answer

The current share price can be calculated using the Gordon Growth Model (also known as the Dividend Discount Model for a perpetuity with growth). The model is P = D / (r - g), where P is the price, D is the dividend, r is the required rate of return, and g is the growth rate. However, since the dividends start in year 11, we need to discount the value back to the present value. The dividend in year 11 is $3, growing at 6% annually thereafter. The required return is 15%.First, calculate the value of the stock at year 10, just before the first dividend is paid, as if it were a perpetuity from that point forward:P10 = D11 / (r - g) = $3 / (0.15 - 0.06) = $3 / 0.09 = $33.33Then, discount this value back to the present (year 0) using the formula PV = FV / (1 + r)^n, where PV is the present value, FV is the future value ($33.33), r is the required return (15% or 0.15), and n is the number of periods (10 years):PV = $33.33 / (1 + 0.15)^10 ≈ $8.24Therefore, the current share price is approximately $8.24.

Tarp Corporation Is a Young Start-Up Company