The following balance sheet extract relates to the Allied Insurance Company
Bonds Payable $1,000,000
Preferred Stock $2,000,000
Common Stock $3,000,000
Additional Information:
1. The bonds are 8%, annual coupon bonds, with 9 years to maturity and are currently selling for 90% of par.
2. The company’s common shares which have a book value of $25 per share are currently selling at $20 per share.
3. The preferred shares are 5% preferred shares with a book value of $100 per share. These shares are currently selling at $80 per share.
4. The company has an equity beta of 1.35 and the current Treasury bill rate is 3.0%. The market risk premium is 1.5%
5. The company’s tax rate is 30%.
A. Calculate Allied’s cost of debt. (4 points)
B. Calculate Allied’s cost of equity. (3 points)
C. Calculate Allied’s cost of preferred shares (3 points)
D. Estimate Allied’s market value weighted average cost of capital. (3 points)
E. Explain why the cost of debt is cheaper than the cost of equity. (2 points)
• A. Calculate Allied’s cost of debt. (4 marks)
The cost of debt is the YTM of the bonds, so:
P0: $950 = $80(PVIFAR%,9) + $1,000(PVIFR%,9)
PMT: 80 PV: 950 FV: 1000 N: 9 I:
YTM = [80 + (1000 – 950) / 9] / 1000 + 950/ 2
R = 85.56 / 975 = 0.0877 or 8.78%
FC = 8.82%
Cost of debt is:
RD = (1 – 0.30)(0.0882) = 0.06174 or 6.174%
B. Calculate Allied’s cost of equity. (4 marks)
3.5 + 1.5 * 1.5 = 5.75
C. Calculate Allied’s market value weighted average cost of capital. (4 marks)
Market Value Weight Cost of Capital Weight X Cost
Debt 950,000,000.00 0.940 0.0618 0.0581%
Common Stock 60,000,000.00 0.06 0.0575 0.0345%
Preferred stock 0.000 0.000%
1,010,000,000 1.0 WACC 0.0926%
9.26%
MV of debt = $1,000,000 ($950)= $950,000, 000
MV of common stock = $3,000,000 ($20) = $60,000,000
D. Explain why the cost of debt is cheaper than the cost of equity. (3 marks)
First of all, debt is typically secured by assets, whether real estate, machinery, receivables, inventory, or other things of value, which may be seized by the lender in case of default by the borrower. Equity ownership, by contrast, is not accompanied by any kind of security interest in the company financed by the equity holder. The equity holder cannot seize anything, the sole remedy of an equity holder generally being the right to vote at a shareholders’ meeting.
Secondly, the cost of equity is typically much higher than the cost of debt is that in the event of bankruptcy of a company, debt holders are satisfied in full before equity holders receive any proceeds of liquidation whatsoever.
Thirdly, a company must pay holders of debt an interest rate, even if the company is loss-making (and failure to pay interest or to achieve debt coverage ratios may put the company into default and force a liquidation). Equity holders, by contrast, are paid dividends only to the extent that the company has been profitable, once all obligations in the ordinary course (e.g. servicing of interest payments) have been satisfied.
A. To calculate Allied's cost of debt, we need to use the information provided about the bond.
1. The bonds have a face value (par value) of $1,000,000.
2. The bonds have an annual coupon rate of 8%.
3. The bonds have 9 years left until maturity.
4. The bonds are currently selling for 90% of par.
To calculate the cost of debt, we can use the following formula:
Cost of Debt = (Annual Interest Payment / Bond Price) * (1 - Tax Rate)
First, let's calculate the annual interest payment. The annual interest payment can be calculated by multiplying the par value of the bonds ($1,000,000) by the coupon rate (8%).
Annual Interest Payment = $1,000,000 * 8% = $80,000
Next, let's calculate the bond price. The bond price is given as 90% of the par value.
Bond Price = 90% * $1,000,000 = $900,000
Now we can calculate the cost of debt:
Cost of Debt = ($80,000 / $900,000) * (1 - 30%)
Cost of Debt = 0.0889 or 8.89%
Therefore, the cost of debt for Allied Insurance Company is 8.89%.
B. To calculate Allied's cost of equity, we need to use the company's equity beta and the market risk premium.
1. Allied's equity beta is given as 1.35.
2. The market risk premium is 1.5%.
The cost of equity can be calculated using the following formula:
Cost of Equity = Risk-Free Rate + Equity Beta * Equity Risk Premium
First, let's calculate the equity risk premium. This is the difference between the market risk premium and the risk-free rate.
Risk-Free Rate = Treasury bill rate = 3.0%
Equity Risk Premium = Market Risk Premium - Risk-Free Rate = 1.5% - 3.0% = -1.5%
Now, let's calculate the cost of equity:
Cost of Equity = 3.0% + 1.35 * -1.5%
Cost of Equity = 0.975% or 9.75%
Therefore, the cost of equity for Allied Insurance Company is 9.75%.
C. To calculate Allied's cost of preferred shares, we need to use the information provided about the preferred shares.
1. The preferred shares have a book value of $100 per share.
2. The preferred shares are currently selling at $80 per share.
3. The preferred shares have a dividend yield of 5%.
The cost of preferred shares can be calculated using the following formula:
Cost of Preferred Shares = Dividend Yield / Price
First, let's calculate the dividend per share. This can be calculated by multiplying the book value of the preferred shares ($100) by the dividend yield (5%).
Dividend Per Share = $100 * 5% = $5
Now, let's calculate the cost of preferred shares:
Cost of Preferred Shares = $5 / $80
Cost of Preferred Shares = 0.0625 or 6.25%
Therefore, the cost of preferred shares for Allied Insurance Company is 6.25%.
D. To estimate Allied's market value weighted average cost of capital (WACC), we need to calculate the weight of each component (debt, equity, and preferred shares) and multiply it by its respective cost.
The weights can be calculated using the market values of each component.
Debt Weight = Bond Price / Total Market Value
Equity Weight = Current Stock Price * Number of Common Shares / Total Market Value
Preferred Shares Weight = Preferred Stock Price * Number of Preferred Shares / Total Market Value
Total Market Value = Bond Price + (Current Stock Price * Number of Common Shares) + (Preferred Stock Price * Number of Preferred Shares)
Now, let's calculate the weights:
Bond Price = $900,000 (as calculated in part A)
Current Stock Price = $20 (given in the additional information)
Number of Common Shares = $3,000,000 (given in the balance sheet extract) / $25 (book value per share)
Preferred Stock Price = $80 (given in the additional information)
Number of Preferred Shares = $2,000,000 (given in the balance sheet extract) / $100 (book value per share)
Total Market Value = $900,000 + ($20 * Number of Common Shares) + ($80 * Number of Preferred Shares)
Now, substitute the values and calculate the weights.
Next, multiply the weights by their respective costs and sum them up:
WACC = (Debt Weight * Cost of Debt) + (Equity Weight * Cost of Equity) + (Preferred Shares Weight * Cost of Preferred Shares)
Finally, calculate the WACC using the calculated weights and costs.
E. The cost of debt is generally cheaper than the cost of equity due to the difference in risk associated with each form of financing.
Debt is considered less risky than equity since bondholders have a higher claim on assets and income in the event of bankruptcy. This lower risk is reflected in a lower cost of debt.
On the other hand, equity represents ownership in the company and carries the risk of higher variability in returns. Equity investors expect a higher return to compensate for this higher risk.
Additionally, debt interest payments are tax-deductible, reducing the effective cost of debt for the company. This tax advantage further contributes to the cost of debt being lower than the cost of equity.
Overall, the cost of debt is cheaper than the cost of equity due to the differences in risk and tax advantages associated with each form of financing.