Question

Stephens Supply Company (SSC) is a conservative firm with a market value of $100 million and a market beta of 0.4. The risk-free rate is 3% and the market risk premium is 6%. SSC believes they can create value by taking over riskier firms and reducing their cost of capital. SSC is considering buying another firm for $10 million and expects the firm will be worth $11 million next year (expected return is 10%). The new firm has a market beta of 2. What is the NPV of buying the other firm? What is the beta of the combined firm? What is the combined firm’s cost of capital? What is the value of the combined firm?

Answer 1

Details of SSC:

Market value = $100 millions

Market beta = 0.4

Rf = 3%

MRP = 6%

Required rate of return using CAPM = Rf + β(Rm - Rf)

= 3%+0.4*6%

= 3%+2.4%

= 5.4%

Another firm:

Buying cost = $10 millions

Worth in next year = $11 millions

Expected return = 10%

Beta = 2

Market value of the target firm = $11 millions/0.10

= $110 millions

Required rate of return using CAPM = Rf + β(Rm - Rf)

= 3%+2*6%

= 3%+12%

= 15%

(i) NPV = Market value of the firm - Cost of purchase

= $110 millions - $10 millions

= $100 millions

(ii) Combined firm’s cost of capital = 5.4%*$100 millions+15%*$100 millions/$200 millions

= 10.2%

(iii) Value of the combined firm = $100 millions+$100 millions

= $200 millions

(iv) Calculation of combined Beta:

Required rate of return using CAPM = Rf + β(Rm - Rf)

10.2% = 3+ β *6

β = 7.2/6

= 1.2