Transport Inc. is considering a recapitalization to maximize firm value. The com
ID: 2766234 • Letter: T
Question
Transport Inc. is considering a recapitalization to maximize firm value. The company has identified three competitors operating in the same industry. Transport Inc. competitors have the following attributes: Transport Inc. has determined its pre-tax cost of debt at various debt/equity ratios: The risk-free rate of return is 3% and the equity risk premium [Rm -Rf] is 5%. Transport Inc.'s tax rate is 35%. Transport inc.'s free cash flow (FCF) today (t=0) is $175 and the expected long-term growth rate, g, is 2%. Utilizing the cost of capital approach, find the WACC and associated D/E that maximizes firm value? What is the maximum firm value?Explanation / Answer
Calculation Of Optimum WACC and D/E:
Debt/ equity ratio
Cost of debt (Pretax) %
Cost of debt (After tax) @35%
Risk free rate %
risk Premium %
Beta
Cost of equity
Weight of debt
Weight of equity
WACC
0%
3.3
2.145
3
5
0.79
3.6241
-
1.00
3.62
10%
3.5
2.275
3
5
0.79
3.6241
0.10
0.90
3.49
20%
3.7
2.405
3
5
0.79
3.6241
0.20
0.80
3.38
30%
3.9
2.535
3
5
0.86
3.7396
0.30
0.70
3.38
40%
4.1
2.665
3
5
0.95
3.9025
0.40
0.60
3.41
50%
4.3
2.795
3
5
0.95
3.9025
0.50
0.50
3.35
60%
4.5
2.925
3
5
0.95
3.9025
0.60
0.40
3.32
70%
4.7
3.055
3
5
0.95
3.9025
0.70
0.30
3.31
80%
4.9
3.185
3
5
0.95
3.9025
0.80
0.20
3.33
90%
5.1
3.315
3
5
0.95
3.9025
0.90
0.10
3.37
100%
5.3
3.445
3
5
0.95
3.9025
1.00
-
3.45
Calculation of maximum value of Firm
Value of firm = Present value of future cash flows discounted at WACC
PV of growing perpetuity = D1 / (r - g)
D/E %
WACC %
Growth rate %
Cash flow
Value of Firm $
0
0.03624
0.02
178.5
10,990.70
10
0.03489
0.02
178.5
11,986.38
20
0.03380
0.02
178.5
12,932.16
30
0.03378
0.02
178.5
12,951.49
40
0.03408
0.02
178.5
12,682.06
50
0.03349
0.02
178.5
13,234.48
60
0.03316
0.02
178.5
13,563.83
70
0.03309
0.02
178.5
13,633.76
80
0.03329
0.02
178.5
13,436.21
90
0.03374
0.02
178.5
12,993.63
100
0.03445
0.02
178.5
12,352.94
The Maximum value of Firm = $13,633.76
The optimum WACC = 0.03309 or 3.309%
The optimum D/E = 70%
Calculation Of Optimum WACC and D/E:
Debt/ equity ratio
Cost of debt (Pretax) %
Cost of debt (After tax) @35%
Risk free rate %
risk Premium %
Beta
Cost of equity
Weight of debt
Weight of equity
WACC
0%
3.3
2.145
3
5
0.79
3.6241
-
1.00
3.62
10%
3.5
2.275
3
5
0.79
3.6241
0.10
0.90
3.49
20%
3.7
2.405
3
5
0.79
3.6241
0.20
0.80
3.38
30%
3.9
2.535
3
5
0.86
3.7396
0.30
0.70
3.38
40%
4.1
2.665
3
5
0.95
3.9025
0.40
0.60
3.41
50%
4.3
2.795
3
5
0.95
3.9025
0.50
0.50
3.35
60%
4.5
2.925
3
5
0.95
3.9025
0.60
0.40
3.32
70%
4.7
3.055
3
5
0.95
3.9025
0.70
0.30
3.31
80%
4.9
3.185
3
5
0.95
3.9025
0.80
0.20
3.33
90%
5.1
3.315
3
5
0.95
3.9025
0.90
0.10
3.37
100%
5.3
3.445
3
5
0.95
3.9025
1.00
-
3.45
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