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 $11.22 million in debt that trades at par and pays an 7.9% 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 30% combined federal and state tax rate. The risk-free rate of interest is 5% and the market risk premium is 7%.

Hastings Corporation estimates that if it acquires Vandell Corporation, synergies will cause Vandell’s free cash flows to be $2.6 million, $2.8 million, $3.5 million, and $3.90 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 $11.22 million in debt (which has an 7.9% 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 $1.459 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

Step 1 - Cost of equity ke = risk-free rate + (beta*market risk premium) = 5% + (1.35*7%) = 14.45%

Debt/Total value (D/V) = 30% so Equity/Total value (E/V) = 1 - (D/V) = 1 -30% = 70%

Cost of debt kd = 7.9% (same as interest rate since bond is selling at par)

Step 2 - WACC = (D/V*kd*(1- tax rate)) + (E/V*ke) = (30%*7.9%*(1-30%)) + (70%*14.45%) = 11.77%

Step 3 - FCF0 = 1 million; growth rate g = 5% so

Firm value V = FCF0*(1+g)/WACC = 1*(1+5%)/11.77% = 15.50 million

Debt D = 11.22 million so Equity value (E) = V - D = 15.50 - 11.22 = 4.28 million

Number of shares outstanding (n) = 1 million so price per share = E/n = 4.28/1 = $4.28

Step 4 - Unlevered cost of equity (rsU) = (D/V*kd) + (E/V*ke) = (30%*7.9%) + (70%*14.45%) = 12.49%

Step 5 - Calculating firm value using APV approach which states that Firm value V = Value of unlevered operations + value of tax shield = PV of FCFs + PV of tax shield

Value of unlevered operations:
Formula	Year (n)	1	2	3	4	Perpetuity
	Growth rate g					5%
FCF5 = FCF4*(1+g)	FCF	2.60	2.80	3.50	3.90	4.10
FCF5/(rsU-g)	Horizon value					54.71
	Total FCF	2.60	2.80	3.50	3.90	54.71
1/(1+rsU)^n	Discount factor @ rsU	0.889	0.790	0.703	0.625	0.625
(Total FCF*Discount factor)	PV of FCF	2.31	2.21	2.46	2.44	34.17
Sum of all PVs	Total PV	43.59
Value of tax shield:
Formula	Year (n)	1	2	3	4	Perpetuity
	Growth rate (g)					5%
I5 = I4*(1+g)	Interest (I)	1.50	1.50	1.50	1.46	1.53
	Tax (T)	30%	30%	30%	30%	30%
(Interest*Tax)	Tax shield (TS)	0.45	0.45	0.45	0.44	0.46
TS5/(rsU-g)	Horizon value					6.14
	Total TS	0.45	0.45	0.45	0.44	6.14
1/(1+rsU)^n	Discount factor @ rsU	0.889	0.790	0.703	0.625	0.625
(Total TS*Discount factor)	PV of TS	0.40	0.36	0.32	0.27	3.84
Sum of all PVs	Total PV	5.18

Step 6 - Calculation of price per share

PV of unlevered operations (a)	43.59
PV of Tax shield (b)	5.18
Intrinsic value of operations (c = a+b)	48.77
Current debt amount (d) (in $ mn)	11.22
Equity value (e = d - c) (in $ mn)	37.55
Shares O/S n (in mn)	1
Value/share (e/n) ($)	37.55

The bid for each share should range between $4.28 per share and $37.55 per share.