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 1.35 (given its target capital structure). Vandell has $11.42 million in debt that trades at par and pays an 8% interest rate. Vandell’s free cash flow (FCF0) is $2 million per year and is expected to grow at a constant rate of 4% a year. Both Vandell and Hastings pay a 40% combined federal and state tax rate. The risk-free rate of interest is 4% and the market risk premium is 5%. Hastings Corporation estimates that if it acquires Vandell Corporation, synergies will cause Vandell’s free cash flows to be $2.5 million, $3.1 million, $3.3 million, and $3.95 million at Years 1 through 4, respectively, after which the free cash flows will grow at a constant 4% rate. Hastings plans to assume Vandell’s $11.42 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 $1.6 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 $1.441 million, after which the interest and the tax shield will grow at 4%. 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

Calculation of lowest price:

WACC calculation: D/V = 30%, so E/V = 1-D/V = 1-30% = 70%

Cost of equity (ke) = risk-free rate + (beta*market risk premium) = 4% + (1.35*5%) = 10.75%

After-tax cost of debt (kd) = (1-Tax rate)*interest rate = (1-40%)*8% = 4.80%

WACC = (D/V*kd) + (E/V*ke) = (30%*4.80%) + (70%*10.75%) = 8.97%

FCF0 = 2 million; growth rate in perpetuity (g) = 4%

FCF1 = FCF0*(1+g) = 2*(1+4%) = 2.08 million

Firm value = FCF1/(WACC -g) = 2.08/(8.97% -4%) = 41.89 million

Equity value = Firm value - current debt = 41.89 - 11.42 = 30.47 million

Share price = equity value/number of shares = 30.47/1 = $30.47

Highest price per share calculation (using APV method):

Cost of unlevered equity (rsU) = (E/V*ke) + (D/V*cost of debt) = (70%*10.75%) + (30%*8%) = 9.93%

Value of unlevered operations:

Formula	Year (n)	1	2	3	4	Perpetuity
	Growth rate g					4%
FCF5 = FCF4*(1+g)	FCF	2.50	3.10	3.30	3.95	4.11
FCF5/(rsU-g)	Horizon value					69.33
	Total FCF	2.50	3.10	3.30	3.95	69.33
1/(1+rsU)^n	Discount factor @ rsU	0.910	0.828	0.753	0.685	0.685
(Total FCF*Discount factor)	PV of FCF	2.27	2.57	2.48	2.71	47.48
Sum of all PVs	Total PV	57.51

Value of tax shield:

Formula	Year (n)	1	2	3	4	Perpetuity
	Growth rate (g)					4%
I5 = I4*(1+g)	Interest (I)	1.60	1.60	1.60	1.441	1.499
	Tax (T)	40%	40%	40%	40%	40%
(Interest*Tax)	Tax shield (TS)	0.64	0.64	0.64	0.58	0.60
TS5/(rsU-g)	Horizon value					10.12
	Total TS	0.64	0.64	0.64	0.58	10.12
1/(1+rsU)^n	Discount factor @ rsU	0.910	0.828	0.753	0.685	0.685
(Total TS*Discount factor)	PV of TS	0.58	0.53	0.48	0.39	6.93
Sum of all PVs	Total PV	8.92

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

= 57.51 + 8.92 = 66.43 million

Equity value = Firm value - debt = 66.43 - 11.42 = 55.01 million

Price per share = equity value/number of shares = 55.01/1 = $55.01

The bid for each share should range between $30.47 per share and $55.01 per share.