Question

Problem 22-02 Merger Valuation with the CAPV Model Hastings Corporation is interested in acquiring Vandell Corporation. Vandell currently has 1 million shares outstanding and a target capital structure consisting of 30% debt; its current beta is 1.60 (i.e., based on its target capital structure). Vandell's debt interest rate is 7.9%. Assume that the risk-free rate of interest is 5% and the market risk premium is 5%. Both Vandell and Hastings face a 35% tax rate. Hastings Corporation estimates that if it acquires Vandell Corporation, synergies will cause Vandell’s free cash flows to be $2.6 million, $2.7 million, $3.5 million, and $3.69 million at Years 1 through 4, respectively, after which the free cash flows will grow at a constant 6% rate. Hastings plans to assume Vandell’s $11.58 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 $1.441 million, after which the interest and the tax shield will grow at 6%. a. What is Vandell’s pre-acquisition levered cost of equity? What is its unlevered cost of equity? Round your answer to two decimal places. Do not round intermediate calculations. Pre-acquisition levered cost of equity: % Unlevered cost of equity: % b. What is the intrinsic unlevered value of operations at t = 0 (assuming the synergies are realized)? Round your answer to the nearest cent. Do not round intermediate calculations. $ c. What is the value of the tax shields at t = 0? Round your answer to two decimal places. Do not round intermediate calculations. $ million d. What is the total intrinsic value of operations at t = 0? What is the intrinsic value of Vandell’s equity to Hastings? What is Vandell’s intrinsic stock price per share? Round your answer to two decimal places. Do not round intermediate calculations. Value of operations: $ million Equity value to acquirer: $ million Intrinsic value per share of existing shares to acquirer: $ /share

Answer 1

Solution:

a) Vandell's pre-acquisition levered cost of equity = 5% + 1.6 * 5% = 13%
rSU = 7.9% * 0.3 +13% * 0.7 = 11.47%
b) Intrinsic unlevered value of operations:
	1	2	3	4
FCF ($ million)	2,600,000	2,700,000	3,500,000	3,690,000
pvif at 11.47%	0.8971	0.8048	0.7220	0.6477
PV of Horizon FCF	2,332,460	2,172,960	2,527,000	2,390,013
Cumulative PV of Horizon FCF	9,422,433
Terminal value of FCF = 3,690,000*1.06/(0.1147-0.06)				71,506,399
PV of terminal FCF=71,506,399*0.6477=	46,314,695
Intrinsic unlevered value of operations	55,737,128
c) Value of tax shields:
Interest	1,500,000	1,500,000	1,500,000	1,441,000
tax shield at 35%	525,000	525,000	525,000	504,350
pvif at 11.47%	0.8971	0.8048	0.7220	0.6477
PV of Horizon tax shields	470,978	422,520	379,050	326,667
Cumulative PV of Horizon tax shields	1,599,215
Terminal value of FCF = 1,441,000*1.06/(0.1147-0.06)				27,924,314
PV of terminal tax shield =27,924,314 * 0.6477 =	18,086,578
Value of tax shields at t = 0	19,685,793
d) Total intrinsic value of operations	75,422,921
Value of debt	11,580,000
Equity value to acquirer	63,842,921
Number of shares	1,000,000
Intrinsic value per share of existing shares	$63.84