[stickyfingaz]

The company has one bond issue outstanding. Ten years ago, they issued 30-year bonds
with a face value of $1,000. The firm originally issued 350,000 of these bonds but
repurchased 100,000 of them in the last three years. The bonds sell at 106% of face
value. The current yield on these bonds is approximately 7% and the bond pays semiannual
coupons of $37.

Liabilities:
Current Portion of Long Term Debt 0
Long – Term Debt 300

Tax Rate: 20%

I don't know which numbers to use
I know that the cost of debt relates to the YTM which is 7% from the bonds but I'm sure I have to do something else to find the cost of debt.

[ArcSine]

The bond issuer's true after-tax cost of the outstanding debt can be intuitively interpreted in an 'investment' context:

Right now the company could 'invest' $265K to immediately repurchase the bonds in the open market. Their 'return' from making this investment consists of three sets of cash flows:

1. Their obligation to make the semiannual coupon payments would cease.
2. Their obligation to redeem the bonds at maturity would go away.
3. They would lose the tax deduction on the interest payments.

Obviously, the first two are positive cash flows--for the issuer--while the third one is a negative cash flow.

When you find the discount rate that makes that cash flow stream exactly equal 265K, you have found the true after-tax cost of the debt. Why? Because it's the 'return' that the bond issuer forgoes by NOT immediately redeeming the bonds.

Now that we've covered the theoretically correct analysis, here's the usual 'real world' approximation: CY x (1 - t), where CY is the paper's current yield, and t is the issuer's tax rate.