A firm had earnings per share (eps) last year of $3 and expects that the eps will grow at a rate of 15% each year until the end of year 3. During that time all dividends are reinvested. At the end of year 4, the firm will begin paying 70% of its earnings as dividends and will have a long-run rate of 5%. The firm’s equity cost of capital is 10%. Find the firm’s current share price?

Answer 1

To find the firm's current share price, we need to calculate the present value of all future dividends and the future stock price at the end of year 3.

First, calculate the dividends for each year until the end of year 3, considering a 15% growth rate:
Year 1 dividend = $3 * (1 + 15%) = $3 * 1.15 = $3.45
Year 2 dividend = $3.45 * 1.15 = $3.9675
Year 3 dividend = $3.9675 * 1.15 = $4.5651

Next, calculate the future stock price at the end of year 3 using the dividend discount model:
Future stock price = Year 4 dividend / (Cost of equity capital - long-run growth rate)
Year 4 dividend = 70% * Year 3 dividend = 0.7 * $4.5651 = $3.1956
Future stock price = $3.1956 / (10% - 5%) = $3.1956 / 0.05 = $63.912

Now, calculate the present value of all future dividends:
Present value of Year 1 dividend = $3.45 / (1 + 10%) = $3.45 / 1.1 = $3.1364
Present value of Year 2 dividend = $3.9675 / (1 + 10%)^2 = $3.9675 / 1.21 = $3.2812
Present value of Year 3 dividend = $4.5651 / (1 + 10%)^3 = $4.5651 / 1.331 = $3.4321
Present value of Year 4 stock price = $63.912 / (1 + 10%)^3 = $63.912 / 1.331 = $47.9857

Finally, calculate the current share price by summing up all the present values:
Current share price = $3.1364 + $3.2812 + $3.4321 + $47.9857 = $57.8354

Therefore, the firm's current share price is approximately $57.84.