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# Calculate after tax cost of debt on a zero coupon bond

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The Welch Corporation is planning a zero coupon bond issue. The bond has a par value of \$1000, matures in 10 years, and will be sold at an 80% discount, or for \$200. The firm's marginal tax rate is 40%. What is the annual after-tax cost of debt to Welch on this issue?

a) 10.48%
b) 10%
c) 11.62%
d) 14.79%
e) 17.46%

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#### Solution Preview

Here's how to go about solving this one:

The question asks for the after tax cost of debt. Using the Weighted Average Cost of Capital for Debt is simply the tax rate savings minus the rate paid on the debt which can be expresses as Rate on the debt or "Rd" = (1-tax rate). Keep that one in your hat for later. Before we can calculate, first we need to know the interest rate.
So how do we get this? There are several methods by which to calculate. As a practicing professional, I prefer excel. Largely because if I break out a book of formulas my peers will likely snicker, but also because I'm simply lazy.

The academic way to do this, ...

#### Solution Summary

Solution provides step by step structured solution to calculate a firms cost of debt, net of tax, to issue a bond. Specifically, a zero coupon bond.

\$2.19

## Calculating the Cost of Debt for Ying

Ying Import has several bond issuances outstanding, each making semiannual interest payments. The bonds are listed in table attached. If the corporate tax rate is 34%, what is the aftertax cost of Ying's debt?

Coupon Price Face
Bond Rate Quote Maturity Value
1 8.00% \$106.38 5 years 10,000,000
2 7.50% \$98.00 8 years 45,000,000
3 6.40% \$82.00 15 ½ years 35,000,000
4 9.75% \$101.50 25 years 45,000,000

See data on attached spreadsheet

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