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Company ABC currently has the following financing outstanding. Bond: 10,000 10-year zero coupon bonds with a...

Company ABC currently has the following financing outstanding. Bond: 10,000 10-year zero coupon bonds with a quoted price of $500 (par value is $1000). Common Stock: 50,000 shares of common stock. The company just paid $2 per share dividends to its investors. The dividends are expected to be constant in the future. The beta of the stock is 1.1. The company is considering a new project which has the similar risk as the existing business. The market portfolio’s expected return is 10%, and the risk-free rate is 2%. The tax rate is 40%.

a. What is the cost of equity?

b. What is the cost of debt before tax?

c. What is the discount rate for the new project?

Solutions

Expert Solution

Debt:

Number of bonds outstanding = 10,000
Face Value = $1,000
Current Price = $500

Market Value of Debt = 10,000 * $500
Market Value of Debt = $5,000,000

Time to Maturity = 10 years
Semiannual Period to Maturity = 20

Let Semiannual YTM be i%

$500 = $1,000 / (1 + i)^20
(1 + i)^20 = 2
1 + i = 1.03526
i = 0.03526 or 3.526%

Semiannual YTM = 3.526%
Annual YTM = 2 * 3.526%
Annual YTM = 7.052% or 7.05%

Before-tax Cost of Debt = 7.05%

Equity:

Number of shares outstanding = 50,000

Cost of Equity = Risk-free Rate + Beta * (Market Return - Risk-free Rate)
Cost of Equity = 2.00% + 1.10 * (10.00% - 2.00%)
Cost of Equity = 2.00% + 1.10 * 8.00%
Cost of Equity = 10.80%

Current Price = Annual Dividend / Cost of Equity
Current Price = $2.00 / 0.1080
Current Price = $18.52

Market Value of Equity = 50,000 * $18.52
Market Value of Equity = $926,000

Market Value of Firm = Market Value of Debt + Market Value of Equity
Market Value of Firm = $5,000,000 + $926,000
Market Value of Firm = $5,926,000

Weight of Debt = $5,000,000 / $5,926,000
Weight of Debt = 0.84374

Weight of Equity = $926,000 / $5,926,000
Weight of Equity = 0.15626

WACC = Weight of Debt * Before-tax Cost of Debt * (1 - Tax Rate) + Weight of Equity * Cost of Equity
WACC = 0.84374 * 7.05% * (1 - 0.40) + 0.15626 * 10.80%
WACC = 3.57% + 1.69%
WACC = 5.26%

Answer a.

Cost of Equity = 10.80%

Answer b.

Before-tax Cost of debt = 7.05%

Answer c.

Discount Rate = WACC
Discount Rate = 5.26%

jeff jeffy answered 1 year ago
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