Question

Problem 22-03
Merger Bid

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 1.30 (given its target capital structure). Vandell has $8.00 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 5% a year. Both Vandell and Hastings pay a 40% combined federal and state tax rate. The risk-free rate of interest is 5% and the market risk premium is 6%.

Hastings Corporation estimates that if it acquires Vandell Corporation, synergies will cause Vandell’s free cash flows to be $2.6 million, $3.0 million, $3.5 million, and $3.76 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 $8.00 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 $1.5 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 $1.409 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

Ans.

WACC calculation:

WACC (k) = (wd*kd*(1-Tax rate)) + (we*ke)

where,

wd = weight of debt = 30%;

we = weight of equity = 100%-wd = 100%-30% = 70%;

kd = before-tax cost of debt = 8% ;

Tax rate = 40%;

ke = cost of equity (using CAPM) = risk-free rate + beta*risk premium = 5% + (1.3*6%) = 12.80%

WACC (k) = (30%*8%*(1-40%)) + (70%*12.80%) = 1.44% + 8.96% = 10.40%

Now,

Firm value = FCF1/(k-g)

where,

g = growth rate = 5%;

FCF1 = FCF0*(1+g) = $ 2 *(1+5%) = 2.10 million

Firm value = 2.10/(10.40% - 5%) = 38.89 million

Equity value = Firm value - debt = 38.89 - 8.00 = 30.89 million

Price per share = Equity value/number of shares = 30.89/1 = $30.89

Unlevered cost of equity (rsU) = (wd*kd) + (we*ke) = (30%*8%) + (70%*12.8%) = 11.36%

Value of unlevered operations:

A/1	B	C	D	E	F	G	H
2	Value of unlevered operations:
3	Formula	Year (n)	1	2	3	4	Perpetuity
4		Growth rate g					5%
5	FCF5 = FCF4*(1+g)	FCF	$        2.60	$             3.00	$         3.50	$                  3.76	$                     3.95
6	FCF5/(rsU-g)	Horizon value					$                   62.08
7		Total FCF	$        2.60	$             3.00	$         3.50	$                  3.76	$                   66.02
8	1/(1+rsU)^n	Discount factor @ 11.36%	0.8979885	0.806383356	0.72412299	0.650254118	0.583920723
9	(Total FCF*Discount factor)	PV of FCF	$        2.33	$             2.42	$         2.53	$                  2.44	$                   38.55
10	Sum of all PVs	Total PV	$      48.29
11	Value of tax shield:
12	Formula	Year (n)	1	2	3	4	Perpetuity
13		Growth rate (g)					5%
14	I5 = I4*(1+g)	Interest (I)	$        1.50	$             1.50	$         1.50	$                  1.41	$                     1.48
15		Tax (T)	40%	40%	40%	40%	40%
16	(Interest*Tax)	Tax shield (TS)	$        0.60	$             0.60	$         0.60	$                  0.56	$                     0.59
17	TS5/(rsU-g)	Horizon value					$                     9.30
18		Total TS	$        0.60	$             0.60	$         0.60	$                  0.56	$                     9.90
19	1/(1+rsU)^n	Discount factor @ rsU	0.8979885	0.806383356	0.72412299	0.650254118	0.583920723
20	(Total TS*Discount factor)	PV of TS	$        0.54	$             0.48	$         0.43	$                  0.37	$                     5.78
21	Sum of all PVs	Total PV	$        7.60
22	PV of unlevered operations (a)	$                    48.29
23	PV of Tax shield (b)	$                      7.60
24	Intrinsic value of operations (c = a+b)	$                    55.89
25	Current debt amount (d) (in $ mn)	$                      8.00
26	Equity value (e = c - d) (in $ mn)	$                    47.89
27	Shares O/S n (in mn)	1.00
28	Value/share (e/n) ($)	$                    47.89

Formulas in excel

A/1	B	C	D	E	F	G	H
2	Value of unlevered operations:
3	Formula	Year (n)	1	2	3	4	Perpetuity
4		Growth rate g					0.05
5	FCF5 = FCF4*(1+g)	FCF	2.6	3	3.5	3.76	=+(3.76)*1.05
6	FCF5/(rsU-g)	Horizon value					=+H5/(11.36% - 5%)
7		Total FCF	=SUM(D5:D6)	=SUM(E5:E6)	=SUM(F5:F6)	=SUM(G5:G6)	=SUM(H5:H6)
8	1/(1+rsU)^n	Discount factor @ 11.36%	=1/1.1136	=+D8/1.1136	=+E8/1.1136	=+F8/1.1136	=+G8/1.1136
9	(Total FCF*Discount factor)	PV of FCF	=+D7*D8	=+E7*E8	=+F7*F8	=+G7*G8	=+H7*H8
10	Sum of all PVs	Total PV	=+D9+E9+F9+G9+H9
11	Value of tax shield:
12	Formula	Year (n)	1	2	3	4	Perpetuity
13		Growth rate (g)					0.05
14	I5 = I4*(1+g)	Interest (I)	1.5	1.5	1.5	1.409	=+G14*(1.05)
15		Tax (T)	0.4	0.4	0.4	0.4	0.4
16	(Interest*Tax)	Tax shield (TS)	=+D14*D15	=+E14*E15	=+F14*F15	=+G14*G15	=+H14*H15
17	TS5/(rsU-g)	Horizon value					=+H16/(11.36%-5%)
18		Total TS	=SUM(D16:D17)	=SUM(E16:E17)	=SUM(F16:F17)	=SUM(G16:G17)	=SUM(H16:H17)
19	1/(1+rsU)^n	Discount factor @ rsU	=1/1.1136	=+D19/1.1136	=+E19/1.1136	=+F19/1.1136	=+G19/1.1136
20	(Total TS*Discount factor)	PV of TS	=+D18*D19	=+E18*E19	=+F18*F19	=+G18*G19	=+H18*H19
21	Sum of all PVs	Total PV	=+D20+E20+F20+G20+H20
22	PV of unlevered operations (a)	=+D10
23	PV of Tax shield (b)	=+D21
24	Intrinsic value of operations (c = a+b)	=SUM(C22:C23)
25	Current debt amount (d) (in $ mn)	8
26	Equity value (e = c - d) (in $ mn)	=+C24-C25
27	Shares O/S n (in mn)	1
28	Value/share (e/n) ($)	=+C26/C27

The bid for each share should range between $30.89 per share and $ 47.89 per share