A financial analyst has been following Fast Start Inc., a new high-growth company.She estimates that the current risk-free rate is 6.25 percent, the market risk premium is 5 percent, and that Fast Start's beta is 1.75.The current earnings per share (EPS0) is R2.50.The company has a 40 percent payout ratio.The analyst estimates that the company's dividend will grow at a rate of 25 percent this year, 20 percent next year, and 15 percent the following year.After three years the dividend is expected to grow at a constant rate of 7 percent a year.The company is expected to maintain its current payout ratio.The analyst believes that the shares are fairly priced.What is the current price of the share?

Question

Quizplus · Accepted Answer

First, we need to calculate the cost of equity using the Capital Asset Pricing Model:

Cost of Equity = Risk-Free Rate + Beta * Market Risk Premium
Cost of Equity = 6.25% + 1.75 * 5%
Cost of Equity = 14.375%

Next, we need to forecast the dividends for the next three years:

Dividend for Year 1 = EPS * Payout Ratio * Dividend Growth Rate
Dividend for Year 1 = R2.50 * 40% * 25%
Dividend for Year 1 = R0.25

Dividend for Year 2 = Dividend for Year 1 * (1 + Dividend Growth Rate)
Dividend for Year 2 = R0.25 * (1 + 20%)
Dividend for Year 2 = R0.30

Dividend for Year 3 = Dividend for Year 2 * (1 + Dividend Growth Rate)
Dividend for Year 3 = R0.30 * (1 + 15%)
Dividend for Year 3 = R0.35

After Year 3, the dividend is expected to grow at a constant rate of 7% per year, so we can use the Gordon Growth Model to calculate the terminal value of the stock:

Terminal Value = Dividend at Year 4 / (Cost of Equity - Dividend Growth Rate)
Terminal Value = R0.35 / (14.375% - 7%)
Terminal Value = R6.47

Finally, we can use the present value formula to calculate the current price of the stock:

Current Price = (Dividend Year 1 / (1 + Cost of Equity)) + 
                (Dividend Year 2 / (1 + Cost of Equity)^2) +
                (Dividend Year 3 / (1 + Cost of Equity)^3) +
                (Terminal Value / (1 + Cost of Equity)^3)
Current Price = (R0.25 / (1 + 14.375%)) + 
                (R0.30 / (1 + 14.375%)^2) +
                (R0.35 / (1 + 14.375%)^3) +
                (R6.47 / (1 + 14.375%)^3)
Current Price = R18.53

Therefore, the answer is C) R18.53.

A Financial Analyst Has Been Following Fast Start Inc