Question

Firm R currently has $1,500,000 of debt outstanding with a before tax annual coupon of 5.2%, a constant EBIT of $2,000,000 and 450,000 shares outstanding at a market price of $28.00. The firm is considering issuing $1,000,000 of debt at a before tax cost of 7.25% and using the proceeds to repurchase stock at the new post-announcement market price. If this plan is implemented, it is expected that the required return on equity would rise to 10%. The firm's marginal tax rate is 32%..

What is the market value of the firm before the announcement of the issue of the new debt?

$15,228,000

$15,933,000

$14,100,000

$14,805,000

36.

Required information

What is the estimated value of the firm after the new debt issue?

$17,036,558

$16,282,728

$15,830,430

$15,076,600

37.

Required information

What is the estimated share price after the capital structure change?

$31.68

$32.58

$34.09

$30.17

38.

Required information

How many shares remain outstanding after the capital structure change?

416,855 shares

471,046 shares

450,203 shares

437,697 shares

Answer 1

Formula sheet

A	B	C	D	E	F	G	H	I	J	K
2
3		Before new debt Issue:
4		Market Value of Debt	1500000
5		Coupon rate of debt	0.052
6		EBIT	2000000
7		Numbers of shares outstanding	450000
8		Market Price	28
9
10		New Debt issue:
11		Amount of New Debt issue	1000000
12		Coupon rate on new debt issued	0.0725
13
14		Calculation of Market Value of firm before debt issue:
15
16		Market value of debt before new debt issue	=D4
17		Market value of equity before new debt issue	=D7*D8	=D7*D8
18		Total Market Value	=SUM(D16:D17)	=SUM(D16:D17)
19
20		Hence Total market value before debt issue is	=D18
21		Thus the third option is correct.
22
23		Calculation of Value of firm after debt issue:
24
25			Market Value	Weight	Cost
26		Old Debt	=D4	=D26/$D$28	0.052
27		New Debt	=D11	=D27/$D$28	0.0725
28			=SUM(D26:D27)
29
30		Cost of Debt	=Weighted average cost of debt
31			=SUMPRODUCT(E26:E27,F26:F27)	=SUMPRODUCT(E26:E27,F26:F27)
32
33		Market Value of Equity After new debt issue	=D17-D11
34		Required return on equity	0.1
35
36		Formula for WACC is given as:
37		WACC = r(E) × w(E) + r(D) × (1 – t) × w(D)
38		Where, r(E) and r(D) are cost of equity and cost of debt, w(E) is weight of equity and W(D) is weight of debt and t is the tax rate
39
40		Weight of equity, w(E)	=Market Capitalization / Enterprise Value
41			=D33/(D33+D28)	=D33/(D33+D28)
42
43		Weight of debt, w(D)	=1- Weight of equity
44			=1-D41
45
46		Calculation of WACC
47		Tax rate	0.32
48		Source of capital	Weight(w)	Cost(c)
49		Debt	=D44	=D31
50		Equity	=D41	=D34
51
52		WACC	= r(E) × w(E) + r(D) × (1 – t) × w(D)
53			=E50*D50+E49*(1-D47)*D49	=E50*D50+E49*(1-D47)*D49
54
55		Hence WACC is	=D53
56
57		Value of the firm can be calculated by find the present value of free cash flow at WACC.
58
59		Free Cash Flow = Operating Cash Flow - Capital Expenditures - Change in working capital
60		Operating Cash Flow = EBIT*(1-Tax Rate)+Depreciation
61
62		EBIT	2000000
63		Tax Rate	0.32
64
65		Free Cash Flow	=D62*(1-D63)	=D62*(1-D63)
66		WACC	=D55
67
68		Value of the firm	=Present value of Perpetuity
69			=D65/D66
70
71		Hence Value of the firm is	=D69
72
73		Calculation of Estimated share price after change in capital structure:
74
75		Value of Firm after debt issue	=D71
76		Value of Debt	=D28
77		Value of equity after change	=D75-D76
78
79		Amount of Debt issued	=D11
80		Market Value per share	=D8
81		Number of shares bought Back	=D79/D80
82
83		Numbers of shares outstanding before change	450000
84		Number of shares bought back	=D81
85		Number of shares oustanding after change	=D83-D84
86
87		Estimated share price after issue	=Value of equity after change / Number of shares outstanding after change
88			=D77/D85	=D77/D85
89
90		Hence Estimated Share price after change	=D88
91
92		Number of shares outstanding after the issue	=D85
93
94		The answers seems to be a bit different from the options given but the procedure is correct.
95		Please check the question data again and let me know.
96