10. The following balance sheet extract relates to the ABC Company.

Bonds Payable $1,600,000
Common Stock $5,000,000
Preferred Shares $2,550,000
Additional Information:
i. The bonds are 8%, annual coupon bonds, with 9 years to maturity and are
currently selling for 95% of par.
ii. The company’s common shares which have a book value of $25 per share
are currently selling at $28 per share. The beta on the company’s stock is
0.7
iii. Preferred shares have a book value of $100 per share. These shares are
currently selling at $120 per share and carries a coupon rate of 6%.
iv. Market Risk premium is 7 % and 3% is the risk-free rate.
v. Company’s Tax rate is 30%
Required: Determine the following for the company
(a) Total Market value
(b) After-tax Cost of Debt
(c) Cost of Common Stock
(d) Cost of Preferred

(a) Total Market value:

To determine the total market value, we need to calculate the market value of each component of the balance sheet and sum them up.

Market value of Bonds Payable:
Market value of bonds = 95% of par value = 0.95 * $1,600,000 = $1,520,000

Market value of Common Stock:
Number of common shares = Book value per share / Market price per share = $5,000,000 / $28 = 178,571 shares
Market value of common stock = Number of common shares * Market price per share = 178,571 * $28 = $5,000,008

Market value of Preferred Shares:
Number of preferred shares = Book value per share / Market price per share = $2,550,000 / $120 = 21,250 shares
Market value of preferred shares = Number of preferred shares * Market price per share = 21,250 * $120 = $2,550,000

Total market value = Market value of Bonds Payable + Market value of Common Stock + Market value of Preferred Shares
Total market value = $1,520,000 + $5,000,008 + $2,550,000 = $9,070,008

Therefore, the total market value of the ABC Company is $9,070,008.

(b) After-tax Cost of Debt:

To calculate the after-tax cost of debt, we need to calculate the yield to maturity (YTM) of the bonds and then adjust for the tax rate.

YTM of the bonds can be calculated using the following formula:
Bond price = Coupon payment * [1 - (1 + YTM)^(-n)] / YTM + Par value / (1 + YTM)^n
Where:
- Coupon payment = Annual coupon rate * Par value
- YTM = Yield to maturity
- n = Number of years to maturity

Given:
Coupon payment = 8% * Par value = 0.08 * $1,600,000 = $128,000
Number of years to maturity (n) = 9
Bond price = 0.95 * Par value = 0.95 * $1,600,000 = $1,520,000

Solving the equation for YTM, we get:
$1,520,000 = $128,000 * [1 - (1 + YTM)^(-9)] / YTM + $1,600,000 / (1 + YTM)^9

By applying a financial calculator or spreadsheet software, we find YTM ≈ 6.87%.

After-tax cost of debt = YTM * (1 - Tax rate)
After-tax cost of debt = 0.0687 * (1 - 0.30) = 0.04809 or 4.809%

Therefore, the after-tax cost of debt for the ABC Company is approximately 4.809%.

(c) Cost of Common Stock:

The cost of common stock can be calculated using the Capital Asset Pricing Model (CAPM) formula:

Cost of Common Stock = Risk-free rate + Beta * Market Risk Premium

Given:
Risk-free rate = 3%
Beta = 0.7
Market Risk Premium = 7%

Cost of Common Stock = 0.03 + 0.7 * 0.07
Cost of Common Stock = 0.03 + 0.049
Cost of Common Stock = 0.079 or 7.9%

Therefore, the cost of common stock for the ABC Company is approximately 7.9%.

(d) Cost of Preferred Shares:

The cost of preferred shares can be calculated using the following formula:

Cost of Preferred Shares = Dividend / Market price per share

Given:
Dividend = Coupon rate * Par value = 0.06 * $100 = $6 per share
Market price per share = $120

Cost of Preferred Shares = $6 / $120
Cost of Preferred Shares = 0.05 or 5%

Therefore, the cost of preferred shares for the ABC Company is 5%.

To determine the various factors for the ABC Company, we will need to follow these steps:

(a) Total Market Value:
To calculate the total market value, you need to add the market value of each component of the balance sheet.

i. Bonds Payable: $1,600,000 (selling at 95% of par)
Market Value of Bonds Payable = $1,600,000 * 0.95 = $1,520,000

ii. Common Stock: $5,000,000 (selling at $28 per share)
Market Value of Common Stock = $5,000,000 / $28 = $178,571.43 shares * $28 = $5,000,000

iii. Preferred Shares: $2,550,000 (selling at $120 per share)
Market Value of Preferred Shares = $2,550,000 / $120 = $21,250 shares * $120 = $2,550,000

Total Market Value = Market Value of Bonds Payable + Market Value of Common Stock + Market Value of Preferred Shares

(b) After-tax Cost of Debt:
To calculate the after-tax cost of debt, we need to use the information provided.

i. Bonds Payable: $1,600,000 (coupon rate of 8%)
Coupon Payment = $1,600,000 * 8% = $128,000

Effective Cost of Debt = Coupon Payment / Market Value of Bonds Payable
(assuming no transaction costs and 30% tax rate)

(c) Cost of Common Stock:
To calculate the cost of common stock, we need to use the information provided.

i. Market Risk Premium: 7%
ii. Risk-Free Rate: 3%
iii. Beta: 0.7

Cost of Common Stock = Risk-Free Rate + Beta * Market Risk Premium

(d) Cost of Preferred Stock:
To calculate the cost of preferred stock, we need to use the information provided.

i. Preferred Shares: $2,550,000 (coupon rate of 6%)
Coupon Payment = $2,550,000 * 6% = $153,000

Cost of Preferred Stock = Coupon Payment / Market Value of Preferred Shares

Once you have the required calculations, you can plug in the values and solve for each component.