Question

Problem 22-03

Merger Bid Hastings Corporation is interested in acquiring Vandell Corporation. Vandell has 1 million shares outstanding and a target capital structure consisting of 30% debt; its beta is 1.25 (given its target capital structure). Vandell has $10.71 million in debt that trades at par and pays an 8% interest rate. Vandell’s free cash flow (FCF0) is $1 million per year and is expected to grow at a constant rate of 5% a year. Both Vandell and Hastings pay a 40% combined federal and state tax rate. The risk-free rate of interest is 6% and the market risk premium is 6%. Hastings Corporation estimates that if it acquires Vandell Corporation, synergies will cause Vandell’s free cash flows to be $2.3 million, $2.8 million, $3.3 million, and $3.54 million at Years 1 through 4, respectively, after which the free cash flows will grow at a constant 5% rate. Hastings plans to assume Vandell’s $10.71 million in debt (which has an 8% interest rate) and raise additional debt financing at the time of the acquisition. Hastings estimates that interest payments will be $1.5 million each year for Years 1, 2, and 3. After Year 3, a target capital structure of 30% debt will be maintained. Interest at Year 4 will be $1.455 million, after which the interest and the tax shield will grow at 5%. Indicate the range of possible prices that Hastings could bid for each share of Vandell common stock in an acquisition. Round your answers to the nearest cent. Do not round intermediate calculations. The bid for each share should range between $ ?????? per share and $ ??????? per share.

Answer 1

1). Valuation using FCFF model:

Cost of equity (Rsl) = risk free rate + beta*market risk premium = 6% + (1.25*6%) = 13.50%

D/V =30%; E/V = 70%; cost of debt (Rd) = 8%

WACC = (D/V*Rd*(1-Tax rate)) + (E/V*Rsl) = (30%*8%*(1-40%)) + (70%*13.50%) = 10.89%

FCF0 = 1 million; FCF1 = FCF0*(1+growth rate) = 1*(1+5%) = 1.05 million

Firm value = FCF1/(WACC-growth rate) = 1.05/(10.89%-5%) = 17.83 million

Equity value = Firm value - debt value = 17.83 - 10.71 = 7.12 million

Price per share = equity value/number of shares = 7.12/1 = $7.12 per share

2). Valuation using APV model:

Rsu (Cost of unlevered equity) = (D/V*Rd) + (E/V*Rsl) = (30%*8%) + (70%*13.50%) = 11.85%

Value of unlevered operations:

Value of interest tax shield:

Firm value = value of unlevered operations + value of interest tax shield

= 43.58 + 7.52 = 51.10 million

Equity value = firm value - debt amount = 51.10 - 10.71 = 40.39 million

Price per share = equity value/number of shares = 40.39/1 = $40.39 per share

Answer: The bid for each share should range between $7.12 per share and $40.39 per share.