In previous assignments I have done the opposite, but I am having trouble looking at it from this perspective.

I am given two scenarios with different issuance costs and different coupon (at different intervals). I am supposed to find out which scenario offers the lowest APY...

I am totally stuck on this one.


The formula for APY is:
=[(1 + periodic rate)^# of periods] - 1


For this calculation, do we subtract the issuance costs from the whole bond amount (less to repay to the purchaser?) I am really not sure what to do with this value...

Is the periodic rate the coupon payment converted to annually.

Any guidance on this would be greatly appreciated.

Thank you,

First, determine the discount rate per period which makes the PV of all of the bond's cash flows equal the net proceeds to the issuer.

Example: I issue a bond today for which I receive 963 (that's my net proceeds, after all transaction costs are paid). The bond obligates me to cut an interest check of 25 six months from now, 12 months from now, and 18 months from now; and then to redeem the bond at maturity 2 years from now for 1,025.

I.e. my cash (out)flows are 25, 25, 25, and 1,025; spaced 6 months apart, starting 6 months from today.

Through trial-and-error I find that a discount rate of 3.5% (per 6-month period) puts the PV of those CFs at 963.

Now just use your formula to turn that 6-month rate into its annual compounded equivalent (aka "APY"): = 7.1225%.

Remember that in your APY formula, "no. of periods" means per year. So if the coupon payments were quarterly, say, then you'd first be coming up with a discount rate expressed in terms of 3-month periods; and then your exponent in the formula would be 4.

(Note that my illustration above is just another way of saying "a 7% nominal annual rate, compounded semi-annually, equals a 7.1225% APY").

(Cost of borrowing) A firm issues a 10-year debt obligation that bears a 12% coupon rate
And gives the investor the right to put the bond back to the issuer at the end of the fifth year
At 103% of its face amount. The issue has no sinking fund. Interest is paid semiannually.
The issuer’s tax rate is 34%.
a. Calculate the after-tax cost of debt, assuming the debt remains outstanding until
Maturity.
b. Calculate the after-tax cost of debt, assuming investors put the bond back to the firm at
The end of the fifth year. (Note: Any unamortized issuance expenses and any redemption
Premium can be deducted for tax purposes in the year of redemption.)