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 7.5%. Assume that the risk-free rate of interest is 4% and the market risk premium is 7%. Both Vandell and Hastings face a 40% tax rate.

Hastings Corporation estimates that if it acquires Vandell Corporation, synergies will cause Vandell’s free cash flows to be $2.4 million, $3.2 million, $3.3 million, and $3.52 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 $9.29 million in debt (which has an 7.5% 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 $1.475 million, after which the interest and the tax shield will grow at 5%.

1. 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:  %

2. 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.
   $

3. What is the value of the tax shields at t = 0? Round your answer to two decimal places. Do not round intermediate calculations.
   $ million

4. 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

a). Pre-levered cost of equity rsL = risk-free rate + beta*market risk premium

= 4% +1.6*7% = 15.20%

Cost of debt rd = interest rate = 7.5%;

Weight of debt wd = 0.3; weight of equity ws = 1-0.3 = 0.7

Unlevered cost of equity rsU = wd*rd + ws*rsL = (0.3*7.5%)+(0.7*15.20%) = 12.89%

b). Intrinsic unlevered value of operations (V_U):

Formula	Year (n)	1	2	3	4	Perpetuity
	Growth rate g					5%
FCF5 = FCF4*(1+g)	FCF	2.40	3.20	3.30	3.52	3.70
FCF5/(rsU-g)	Horizon value					46.84
	Total FCF	2.40	3.20	3.30	3.52	46.84
1/(1+rsU)^n	Discount factor @ rsU	0.886	0.785	0.695	0.616	0.616
(Total FCF*Discount factor)	PV of FCF	2.13	2.51	2.29	2.17	28.84
Sum of all PVs	Total PV	37.94

Value of unlevered operations = $37.94 million

c). Value of tax shield (V_TS):

Formula	Year (n)	1	2	3	4	Perpetuity
	Growth rate (g)					5%
(I5 = I4*(1+g)	Interest	1.60	1.60	1.60	1.48	1.55
	Tax	40%	40%	40%	40%	40%
(Interest*Tax)	Tax shield (TS)	0.64	0.64	0.64	0.59	0.62
TS5/(rsU-g)	Horizon value					7.85
	Total TS	0.64	0.64	0.64	0.59	7.85
1/(1+rsU)^n	Discount factor @ rsU	0.886	0.785	0.695	0.616	0.616
(Total TS*Discount factor)	PV of TS	0.57	0.50	0.44	0.36	4.83
Sum of all PVs	Total PV	6.71

Value of tax shields = $6.71 million

d). Value of operations = value of unlevered operations + value of tax shields

= 37.94+6.71 = $44.65 million

Debt amount = 9.29 million

Equity value = 44.65 - 9.29 = $35.36 million

Number of shares O/S = 1 million

Value per share = 35.36/1 = $35.36