Question

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 1.10 (given its target capital structure). Vandell has $10.09 million in debt that trades at par and pays a 7.6% interest rate. Vandell’s free cash flow (FCF₀) is $2 million per year and is expected to grow at a constant rate of 5% a year. Both Vandell and Hastings pay a 30% combined federal and state tax rate. The risk-free rate of interest is 5% 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 $2.6 million, $3.2 million, $3.3 million, and $3.97 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 $10.09 million in debt (which has a 7.6% 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 $1.431 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. Do not round intermediate calculations. Round your answers to the nearest cent.

The bid for each share should range between $   per share and $   per share.

Answer 1

First, we calculate Weighted average cost of capital (WACC).

WACC = Weight of debt*Cost of Debt*(1-tax rate) + Weight of equity*cost of equity

Weight of debt is 30%. So, weight of equity is 100% - 30% = 70% as total weight of capital structure is always 100%.

Cost of debt is the yield to maturity of the bond/debt. Debt of Vandell trades at par which means Coupon/interest rate and Yield to maturity of Vandell’s debt are same 7.6%.

Cost of equity = Risk-free rate + beta of stock*market risk premium = 5% + 1.10*6% = 5% + 6.6% = 11.6%

WACC = 0.3*7.6%*(1-0.30) + 0.70*11.6% = 0.3*7.6%*0.70 + 8.12% = 1.596% + 8.12% = 9.72%

Value of operation of Vandell = FCF0*(1+growth rate)/(WACC - growth rate) = $2 million*(1+0.05)/(0.0972 – 0.05) = $2 million*1.05/0.0472 = $2.1 million/0.0472 = $44.49 million

Value of equity of Vandell = Value of operation of Vandell – Value of debt = $44.49 million - $10.09 million = $34.40 million

Value per share = Value of equity of Vandell/no. of shares outstanding = $34.40 million/1 million = $34.40

Now we will calculate Value of operation and equity of Vandell using cash flows with synergies and tax shield.

From year 5 and beyond, cash flows and tax shield will grow at 5%. So, we need to calculate terminal value of cash flows and tax shield for year 5 and beyond. Terminal value will be calculated at the end of year 4.

Terminal value of cash flow = Year 4 cash flow*(1+growth rate)/( WACC - growth rate)

Terminal value of cash flow = $3.97*(1+0.05)/(0.0972 – 0.05) = ($3.97*1.05)/0.0472 = $4.1685/0.0472 = $88.32 million

Tax shield for year 1 to 3 = Interest payments*tax rate = $1.5*30% = $0.45 million

Tax shield for year 4 = $1.431*30% = $0.4293 million

Terminal value of tax shield = Year 4 tax shield*(1+growth rate)/( WACC - growth rate)

Terminal value of tax shield = $0.4293*(1+0.05)/(0.0972 – 0.05) = ($0.4293*1.05)/0.0472 = $0.450765/0.0472 = $9.55 million

Now we need to calculate present value of cash flows, tax shield and terminal values.

PV of Free cash flows = (Cash flows with synergies + tax shield + terminal values)/(1+WACC)^{no. of years}

PV of Free cash flows = ($2.6 + $0.45)/(1+0.0972) + ($3.2 + $0.45)/(1+0.0972)² + ($3.3 + $0.45)/(1+0.0972)³ + ($3.97 + $0.4293 + $88.32 + $9.55 )/(1+0.0972)⁴

PV of Free cash flows = $3.05/1.0972 + $3.65/1.0972² + $3.75/1.0972³ + $102.2693/1.0972⁴

PV of Free cash flows = $2.78 + $3.65/1.2038 + $3.75/1.3209 + $102.2693/1.4492

PV of Free cash flows = $2.78 + $3.03 + $2.84 + $70.57 = $79.22

Value of equity of Vandell = PV of Free cash flows – Value of debt = $79.22 million - $10.09 million = $69.13 million

Value per share = Value of equity of Vandell/no. of shares outstanding = $69.13 million/1 million = $69.13

bid for each share should range between $34.40 per share and $69.13 per share.