Question

A $1000 par value bonds pays an 8% APR coupon semiannually. If the bond has 10 years to maturity and a YTM of 10%, what is its after-tax current yield for an investor paying 25% taxes?

Answer: D. 6.9%

Please explain how to find this by hand without using Excel.

Answer 1

Step-1, The Price of the Bond

The Price of the Bond is the Present Value of the Coupon Payments plus the Present Value of the Face Value/Par Value. The Price of the Bond is normally calculated either by using EXCEL Functions or by using Financial Calculator.

Here, the calculation of the Bond Price using financial calculator is as follows

Variables	Financial Calculator Keys	Figures
Face Value [-$1,000]	FV	-1,000
Coupon Amount [$1,000 x 8.00% x ½]	PMT	40
Market Interest Rate or Required Rate of Return [10.00% x ½]	1/Y	5.00
Time to Maturity [10 Years x 2]	N	20
Bond Price	PV	?

Here, we need to set the above key variables into the financial calculator to find out the Price of the Bond. After entering the above keys in the financial calculator, we get the Price of the Bond = $875.38

Step-2, The Current Yield on the Bond

The Current Yield on the Bond = [Annual Coupon Amount / Price of the Bond] x 100

= [($1,000 x 8.00%) / $875.38] x 100

= [$80.00 / $875.38] x 100

= 9.14%

Step-3, The after-tax current yield on the Bond

The after-tax current yield on the Bond = Current Yield x (1 – Tax Rate)

= 9.14% x (1 – 0.25)

= 9.14% x 0.75

= 6.85% or

= 6.9% (Rounded to 1 decimal place)

“Hence, the after-tax current yield on the Bond will be 6.9%”