Question

Weston Enterprises is an all-equity firm with two divisions. The soft drink division has an asset beta of 0.85, expects to generate free cash flow of $70 million beginning one year from today, and anticipates a 4% perpetual growth rate. The industrial chemicals division has an asset beta of 1.32, expects to generate after-tax cash flows of $95 beginning one year from today and anticipates a 3% growth rate. Suppose the risk-free rate is 4% and the E(RM) is 10%.

a. Estimate the value of each division.

b. Estimate Weston’s current asset beta and cost of capital (ra). Note, the asset beta for the firm will be a value-weighted average of the two divisions. Is this cost of capital useful in valuing Weston’s projects?

c. What is the equity beta of the firm if it is financed equally with equity and riskfree debt?

Answer 1

a) Cost of equity (soft drink) = Rf + beta x (Rm - Rf) = 4% + 0.85 x (10% - 4%) = 9.10%

Cost of equity (industrial) = 4% + 1.32 x (10% - 4%) = 11.92%

Value of soft drink = FCF / (r - g) = 70 / (9.10% - 4%) = $1,372.55 million

Value of industrial chemical = 95 / (11.92% - 3%) = $1,065.02

b) Asset beta = w1 x b1 + w2 x b2

= 1,372.55 / (1,372.55 + 1,065.02) x 0.85 + 1,065.02 / (1,372.55 + 1,065.02) x 1.32

= 1.06

Cost of capital = 4% + 1.06 x (10% - 4%) = 10.33%

No. Because the firm as to use the appropriate cost for each division rather than WACC.

c) Equity beta = Asset beta x (1 + D/E) = 1.06 x (1 + 1) = 2.12