Question

In: Finance

Smith’s HVAC is considering making a change to its capital structure in hopes of increasing its...

  1. Smith’s HVAC is considering making a change to its capital structure in hopes of increasing its value. The company's capital structure consists of debt and common stock. In order to estimate the cost of debt, the company has produced the following table:

Percent financed

Percent financed

Debt-to-equity

Bond

Before-tax

with debt (wd)

with equity (wc)

ratio (D/S)

Rating

cost of debt

0.10

0.90

0.10/0.90 = 0.11

AAA

   7.0%

0.20

0.80

0.20/0.80 = 0.25

AA

7.2

0.30

0.70

0.30/0.70 = 0.43

A

8.0

0.40

0.60

0.40/0.60 = 0.67

BBB

8.8

0.50

0.50

0.50/0.50 = 1.00

BB

9.6


The company uses the CAPM to estimate its cost of common equity, rs. The risk-free rate is 5% and the market risk premium is 6%. Smith’s estimates that if it had no debt its beta would be 1.0. (Its "unlevered beta," bU, equals 1.0.) The company's tax rate, T, is 40%.

On the basis of this information, what is Smith's optimal capital structure, and what is the firm's cost of capital at this optimal capital structure?

Solutions

Expert Solution

Percent financed Percent financed Debt-to-equity Bond Before-tax Post tax Levered beta Ke WACC
with debt (wd) with equity (wc) ratio (D/S) Rating cost of debt Cost of debt
0.1 0.9 0.10/0.90 = 0.11 AAA 7.00% 7%*(1-40%) = 4.20% 1*(1+(1-40%)*0.11) = 1.07 5%+(1.07*6%) = 11.42 % (0.1*4.2%)+(0.9*11.42%) = 10.70%
0.2 0.8 0.20/0.80 = 0.25 AA 7.20% 7.2%*(1-40%) = 4.32% 1*(1+(1-40%)*0.25) = 1.15 5%+(1.15*6%) = 11.90% (0.2*4.32%)+(0.8*11.9%) = 10.38%
0.3 0.7 0.30/0.70 = 0.43 A 8.00% 8%*(1-40%) = 4.80% 1*(1+(1-40%)*0.43) = 1.26 5%+(1.26*6%) = 12.56% (0.3*4.8%)+(0.7*12.56%) = 10.23%
0.4 0.6 0.40/0.60 = 0.67 BBB 8.80% 8.8%*(1-40%) = 5.28% 1*(1+(1-40%)*0.67) = 1.40 5%+(1.4*6%) = 13.40% (0.4*5.28%)+(0.6*13.4%) = 10.15%
0.5 0.5 0.50/0.50 = 1.00 BB 9.60% 9.6%*(1-40%) = 5.76% 1*(1+(1-40%)*1) = 1.60 5%+(1.6*6%) = 14.60% (0.5*5.76%)+(0.5*14.6%) = 10.18%
Levered Beta = Unlevered Beta * [1 + (1 – Tax Rate) * (Debt / Equity)]
Answer : 40% debt & 60% equity is optimal capital structure with WACC 10.15%

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