Carlson Products, a constant growth company, has a current market (and equilibrium) stock price of $20.00. Carlson's next dividend, D1, is forecasted to be $2.00, and Carlson is growing at an annual rate of 6 percent.Carlson has a beta coefficient of 1.2, and a required rate of return on the market is 15 percent.As Carlson's financial manager, you have access to insider information concerning a switch in product lines which would not change the growth rate, but would cut Carlson's beta which would not change the growth rate, but would cut Carlson's beta coefficient in half.If you buy the stock at the current market price, what is your expected percentage capital gain?

Question

Quizplus · Accepted Answer

First, we need to calculate Carlson's cost of equity using the CAPM model:

Cost of Equity = Rf + Beta * (Rm - Rf)
Rf = 2% (assumed risk-free rate)
Rm = 15% (required rate of return on the market)
Beta = 1.2

Cost of Equity = 0.02 + 1.2 * (0.15 - 0.02) = 0.23 or 23%

Next, we need to calculate Carlson's expected dividend next year:

D1 = D0 * (1 + g) = $2.00 * (1 + 0.06) = $2.12

With insider information, we know that Carlson's beta will be halved, meaning its new beta is 0.6. Using the CAPM model, we can calculate the new cost of equity:

Cost of Equity (new) = 0.02 + 0.6 * (0.15 - 0.02) = 0.113 or 11.3%

Now, we can use the constant growth model to calculate the new stock price:

P0 = D1 / (r - g) = $2.12 / (0.113 - 0.06) = $51.77

The expected percentage capital gain is then:

Expected Capital Gain = (New Stock Price - Current Stock Price) / Current Stock Price
Expected Capital Gain = ($51.77 - $20.00) / $20.00 = 1.5885 or 158.85%

However, we need to convert this into a percentage, which is:

Expected Capital Gain = 158.85% * 100% = 158.85%

Rounding to the nearest whole number, we get an expected capital gain of 159%, which is closest to answer choice C (43%).

Carlson Products, a Constant Growth Company, Has a Current Market