Question

Hastings Corporation is interested in acquiring Vandell Corporation. Vandell has 1 million shares outstanding and a target capital structure consisting of 30% debt. Vandell's debt interest rate is 7.3%. Assume that the risk-free rate of interest is 3% and the market risk premium is 4%. Both Vandell and Hastings face a 40% tax rate. Vandell's beta is 1.10. Hastings estimates that if it acquires Vandell, interest payments will be $1,500,000 per year for 3 years. The free cash flows are supposed to be $2.5 million, $2.9 million, $3.4 million, and then $3.59 million in Years 1 through 4, respectively. Suppose Hastings will increase Vandell's level of debt at the end of Year 3 to $29.4 million so that the target capital structure will be 45% debt. Assume that with this higher level of debt the interest rate would be 8.0%, and assume that interest payments in Year 4 are based on the new debt level from the end of Year 3 and new interest rate. Free cash flows and tax shields are projected to grow at 4% after Year 4. What is the value of the unlevered firm? Enter your answer in dollars. For example, an answer of $1.2 million should be entered as 1,200,000, not 1.2. Do not round intermediate calculations. Round your answer to two decimal places. What is the value of the tax shield? Enter your answer in dollars. For example, an answer of $1.2 million should be entered as 1,200,000, not 1.2. Do not round intermediate calculations. Round your answer to two decimal places. What is the maximum total price that Hastings would bid for Vandell now? Assume Vandell now has $8.63 million in debt. Enter your answer in dollars. For example, an answer of $1.2 million should be entered as 1,200,000, not 1.2. Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

Calculation of cost of unlevered equity:
Equity value/TV	Weight of equity (ws)	0.70
Debt value/TV	Weight of debt (wd)	0.30
Using CAPM: rsik-free rate + (beta*market risk premium)	Cost of levered equity (rsL)	7.40%
	Cost of debt (rd)	7.30%
(ws*rsL) + (wd*rd)	Cost of unlevered equity (rsU)	7.37%

Value of unlevered operations:
Formula	Year (n)	1	2	3	4	Perpetuity
	Growth rate g					4.0%
	Free Cash Flow (FCF)	2,500,000	2,900,000	3,400,000	3,590,000	3,733,600
FCF4/(rsU -g)	Horizon value (HV)					110,789,318
	Total FCF (TFCF)	2,500,000	2,900,000	3,400,000	3,590,000	110,789,318
1/(1+rsU)^n	Discount factor @ rsU	0.931	0.867	0.808	0.752	0.752
(Total FCF*Discount factor)	PV of FCF	2,328,397.13	2,515,545.01	2,746,819.09	2,701,236.67	83,361,606.32
Sum of all PVs	Total PV	93,653,604.21

Value of tax shield:
Formula	Year (n)	1	2	3	4	Perpetuity
	Growth rate (g)					4.0%
I5 = I4*(1+g)	Interest	1,500,000	1,500,000	1,500,000	2,352,000	2,446,080
	Tax @ 40%	40%	40%	40%	40%	40%
(Interest*Tax)	Tax shield (TS)	600,000	600,000	600,000	940,800	978,432
TS5/(rsU-g)	Horizon value					29,033,591
	Total TS	600,000	600,000	600,000	940,800	29,033,591
1/(1+rsU)^n	Discount factor @ rsU	0.931	0.867	0.808	0.752	0.752
(Total TS*Discount factor)	PV of TS	558,815.31	520,457.59	484,732.78	707,889.54	21,845,849.37
Sum of all PVs	Total PV	24,117,744.59

Answers:

Part (a)	Pvunlevered	Unlevered value of operations	93,653,604.21
Part (b)	Pvtaxshield	Value of tax shield	24,117,744.59
	V = Pvunleverd + Pvtaxshield	Value of operations	117,771,348.80
	D	Less: debt	8,630,000.00
	V-D	Equity value	109,141,348.80
		Shares O/S	1,000,000
Part ('c)	Equity value/Shares O/S	Price per share ($)	109.14