# Suppose a company will issue new 20-year debt with a par value of$1,000 and a coupon rate of 9%...

## Question:

Suppose a company will issue new 20-year debt with a par value of$1,000 and a coupon rate of 9% paid annually. The tax rate is 40%. If the flotation cost is 2% of the issue proceeds, then what is the after-tax cost of debt? Disregard the tax shield from the amortization of flotation costs.

## Cost of debt:

The cost of debt can be defined as the interest rate on which the company pays on its debt. The cost of debt is related to the company which charges the tax on bonds and the loans. Etc. The cost of debt mainly means that the company cost of debt before taking the taxes into account.

## Answer and Explanation:

**Given data**:

- The debt year is {eq}n = 20 {/eq}

- Coupon rate is {eq}E = 9\% = 0.09 {/eq}

- The tax rate is {eq}R = 40\% = 0.4 {/eq}

- The flotation cost is {eq}FC = 2\% = 0.02 {/eq}

- Par value is {eq}\ d = $1000 {/eq}

The expression for the cost of debt is

{eq}{r_d} = \dfrac{C}{{NP}}\left( {1 - R} \right) {/eq}

Where C is the coupon, NP is the net proceeds

{eq}\begin{align*} {r_d} &= \dfrac{C}{{NP}}\left( {1 - R} \right) \times 100\\ &= \dfrac{{E \times d}}{{\left( {1 - FC} \right) \times d}} \times \left( {1 - R} \right) \times 100\\ &= \dfrac{{9\% \times \ $1000}}{{\left( {1 - 0.02} \right) \times $1000}} \times \left( {1 - 0.40} \right) \times 100\\ &= \dfrac{{90}}{{0.98 \times 1000}} \times \left( {0.6} \right) \times 100\\ &= \dfrac{{90}}{{980}} \times 60\\ &= 5.57\,\% \end{align*} {/eq}

Thus the cost of debt is {eq}{r_d} = 5.57\,\% {/eq}

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from Financial Accounting: Help and Review

Chapter 8 / Lesson 7