Omaro Ltd. has $34 million worth of bonds outstanding with an interest rate of 8% and redemption in 4 years. The issue price of the bond is $90 per $100 of nominal value. The company's tax rate is 24%. Using trial values of 8% and 12%, what is the company's after tax cost of capital for the bonds?

Question

Quizplus · Accepted Answer

We need to calculate the after-tax cost of debt for Omaro Ltd. The formula to calculate the after-tax cost of debt is:

After-tax cost of debt = pre-tax cost of debt x (1 - tax rate)

We are given that the pre-tax cost of debt is either 8% or 12%. Let's calculate the after-tax cost of debt for both values of pre-tax cost of debt.

If the pre-tax cost of debt is 8%, then the after-tax cost of debt is:

= 8% x (1 - 0.24)
= 6.08%

If the pre-tax cost of debt is 12%, then the after-tax cost of debt is:

= 12% x (1 - 0.24)
= 9.12%

We know that the issue price of the bond is $90 per $100 of nominal value. This means that the company received $90 million when it issued the bonds. The company has to pay back $34 million after 4 years, which means it will pay $34 million / (1 + 8%)^4 = $23.38 million in today's dollars. Similarly, it will pay $34 million / (1 + 12%)^4 = $20.05 million in today's dollars if the pre-tax cost of debt is 12%.

Now, let's calculate the interest expense on the bond for both values of pre-tax cost of debt.

Interest expense at 8% = $34 million x 8% = $2.72 million
Interest expense at 12% = $34 million x 12% = $4.08 million

We can calculate the tax shield as follows:

Tax shield = Interest expense x tax rate

Tax shield at 8% = $2.72 million x 24% = $0.65 million
Tax shield at 12% = $4.08 million x 24% = $0.98 million

Finally, we can calculate the after-tax cost of debt using the formula mentioned above:

After-tax cost of debt at 8% = 6.08% + ($0.65 million / $23.38 million) = 8.65%
After-tax cost of debt at 12% = 9.12% + ($0.98 million / $20.05 million) = 14.13%

Therefore, the best choice is B because after calculating, we can see that the after-tax cost of debt is lower if the pre-tax cost of debt is 8%.

Omaro Ltd Has $34 Million Worth of Bonds Outstanding with an an Interest