Question

Smoke and Mirrors currently has EBIT of $30,000 and is all-equity-financed. EBIT is expected to stay at this level indefinitely. The firm pays corporate taxes equal to 32% of taxable income. The discount rate for the firm’s projects is 8%.

a.	What is the market value of the firm? (Round your answer to 2 decimal places.)
	Market value of the firm   $

b.	Now assume the firm issues $40,000 of debt paying interest of 6% per year and uses the proceeds to retire equity. The debt is expected to be permanent. What will happen to the total value of the firm (debt plus equity)?
	The total value of the firm (Click to select)decreasesincreases by $.

c.	Recompute your answer to part (b) under the following assumptions: the debt issue raises the possibility of bankruptcy; the firm has a 35% chance of going bankrupt after 4 years; if it does go bankrupt, it will incur bankruptcy costs of $220,000. The discount rate is 8%. (Round your answer to 4 decimal places.)
	PV of the expected cost of bankruptcy   $

	Should the firm issue the debt?
	The firm (Click to select)should notShould issue the debt.

Answer 1

A	B	C	D	E	F	G	H	I
2
3		a)
4
5		Calculation of unlevered i.e. all equity value of the firm:
6
7		EBIT	$30,000
8		Unlevered Cost of equity	8%
9		Tax Rate	32%
10		Free cash flow can be calculated as follows:
11		Free cash flow	=EBIT*(1-Tax Rate) + Depreciation - CAPEX - Change in working capital
12			=$30,000*(1-32%)+0-0-0
13			$20,400.00	=D7*(1-D9)
14
15		Since EBIT of the firm is constant forever, therefore,
16
17		Unlevered value of the firm, VU	=Free Cash Flow / unlevered cost of Equity
18			=$20,400 / 8%
19			$255,000.00	=D13/D8
20
21		Hence Unlevered value of the firm, VU	$255,000.00
22		b)
23
24		Value of firm after borrowing i.e. levered value can be calculated using unlevered value as follows:
25		VL	=VU + Present Value of Tax shield
26		Where VL is the levered value of the firm and Vu is the unlevered value of the firm.
27		Thus the value of the firm increases by the present value of Tax Shield.
28		Calculation of levered value i.e. value after the borrowings:
29		VU	$255,000
30		Debt	$40,000
31		Cost of Debt	8%
32		Tax Rate	32%
33
34		Interest amount to be paid	$3,200.00	=D30*D31
35		Tax Shield	=Interest*Tax Rate
36			=$3200*32%
37			$1,024.00	=D34*D32
38
39		Present value of Tax Shield	=Tax Shield / Interest rate
40			=$1024 / 8%
41			$12,800.00	=D37/D31
42
43		Hence total value of the firm increases by	$12,800.00
44
45		c)
46		Bankruptcy cost	$220,000
47		Probability of bankruptcy after 4 year	35%
48		Period after which bankruptcy may occur	4	Year
49		Discount rate	8%
50
51		Expected Value of bankruptcy cost after 4 year	=0.35*$220000
52			$77,000	=D47*D46
53
54		Present value of expected bankruptcy	=$77,000 / ((1+8%)^4)
55			$56,597.30	=D52/((1+D49)^D48)
56
57		Hence present value of expected cost of bankruptcy	$56,597.30
58
59		Since the decrease in firm value due to present value of cost of bankruptcy is higher
60		than the present value of tax shield, therefore the taking the debt will overall
61		reduced the total value of the firm.
62
63		Hence firm should not issue the debt.
64
65