# Cost of debt

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Ying Import has several bond issues outstanding, each making semiannual interest payments. The bond are listed in the following table. If the corporate tax rate is 32%, what is the aftertax cost of Ying's Debt?

BOND COUPON RATE RICE QUOTE MATURITY FACE VALUE 1 6.2% 104 6 25,000,000

2 7.5% 113 11 35,000,000

3 6.7% 104 25 41,000,000

4 7.9% 117 38 59,000,000

Please, don't use EXCEL. I need theory formulas. Thanks for helping.

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The formula of present value of a future value is

PV = FV/(1+r)^n

The formula of present value of an annuity is

PV = PMT*[1 - 1/(1+r)^n]/r

The PV of the bond is equal to the sum of the two PV's:

We can write the equation:

PV(bond) = FV/(1+r)^n + PMT*[1 - 1/(1+r)^n]/r

1. For Bond 1, PMT = 6.2%*100/2 = 3.1

FV = 100

PV = 100*104% = -104

Number of periods (6 months) is n = 6*2 = 12

substitute the numbers in:

104 = 100/(1+r)^12 + ...

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