Question

A 30 year bond with $10, 000 face value offers a coupon rate of 6% and a yield rate of 10%. Suppose you pay taxes (immediately after receiving each coupon) of 5% of the full coupon amount, and pay a 10% tax immediately after the face value is received on the amount of discount that the bond was purchased at. Find the actual yield (as a semiannual rate) for the 30 year period.

Answer 1

We will first calculate the bond purchase price using the PV function.

Here,

Rate = 10% (yield)/ 2 = 5% (semi annual)

NPER = 30 years = 60 half yearlyperiods

PMT = 10000 x 6%/2 = 300

FV = 10,000 (the par value that is received at maturity)

Type = 0 (Coupon received at the end)

Using excel function PV = PV(5%,60,300,10000,0) = - $6214.14

The purchase price of the bond = $6214.14

If the taxes were paid, after receiving coupon and after receiving face value, we will find rate using rate function

Here,

NPER = 30 years = 60 half yearly periods

PMT = Cash flow after receiving coupon and paying taxes at 5%

= 1000 x 6%/2 x (1-5%) = 300 x 0.95 = $285

PV = Purchase price of the bond = - $6214.14 (Negative sign indicates a cash outflow)

FV = Maturity Value - taxes paid on purchase price at 10% = 10000 - 6214.14 x 10%

= 10000 - 621.14 = $9378.59

Type = 0 (Coupons received at the end of period)

Thus Rate = Rate (60, 285, -6214.14, 9378.59, 0) = 4.75%

Actual Half yearly yield = 4.75%

Actual Annual yield = 2 x 4.75% = 9.50%