Question

The standard deviation of returns on Carlson company’s common stock is 37%, and Carlson’s beta coefficient is 0.9. Currently, yields on Treasury Bills are 5.5%, while the average yield on Treasury Bills over the past seventy years has been 3.7%. The standard deviation of market returns is 22%. The return on the overall market last year was 10.2%, while the average market return over the past seventy years has been 12.2%.

(a) Provide an estimate of the expected return on Carlson common stock, and explain the reasoning behind the estimate.

(b) Carlson has 2.2 million shares of common stock outstanding. The common stock has a book value of $9 per share, and sells in the market for $12 per share. Carlson also has debt with a face value of $18 million outstanding. The debt pays coupon interest rate of 9.5%, but sells in the market for 110% of its face value, and has a yield-to-maturity of 8.8%. Carlson’s corporate income tax rate is 35%. Compute Carlson’s weighted average cost of capital (WACC).

Answer 1

a) To calculate the expected return of the stock, Capital Asset Price Model (CAPM) is to be used.

CAPM = Risk free rate + stock beta * (Market return - risk free rate)

In the given question,
Risk-free rate = 3.7%
Market return = 12.2%
Beta = 0.9

Therefore, CAPM = 3.7 + 0.9 * (12.2 - 3.7) = 11.35%

Hence, the expected return is 11.35%

NOTE: For risk-free rate and market return, the historic data mentioned in the question has been chosen as the method of CAPM is about calculating the expected return based on the time value of money (risk-free rate) and the risk that is taken (beta and market premium) and these factors are better signified by using the historical long term data rather than the current data as the current data may be a result of several unconventional and uncommon events pertaining to both systematic and non-systematic factors, whereas, a long term data neutralizes these effects and hence is considered a better option.

b) Weighted Average Cost of Capital (WACC)

WACC = (weight of equity * cost of equity) + (weight of debt * cost of debt * 1-tax rate)

Value of Equity = Number of shares * market price = 2.2 * 12 = 26.4 million
Value of Debt = 18 million (given)
Cost of Equity = 11.35% (calculated in part a)
Cost of Debt = 8.8% (given)
Tax-rate = 35% (given)

Weight of Equity = 26.4 / (26.4 + 18) = 0.59
Weight of Debt = 18 / (26.4 + 18) = 0.41

Therefore,
WACC = (0.59 * 11.35) + (0.41 * 8.8 * 1-0.35) = 6.7 + 2.35 = 9.05%

Weighted Average cost of Capital = 9.05%