Question

A newly issued bond pays its coupons once annually. Its coupon rate is 5%, its maturity is 20 years, and its
yield to maturity is 6%.
a) Find the price of the bond.
b) After one year, the bond is selling at a yield to maturity of 5.5%. Find the holding period return if you
sell the bond after one year.
c) If you sell the bond after one year, what taxes will you owe? Assume that the tax rate on interest
income is 40% and the tax rate on capital gains income is 30%.
d) What is the after-tax holding period return on the bond?

Answer 1

Bond Coupon Rate = 5% annually

Time to Maturity = 20 years

YTM = 6%

Let's take Bond Par Value = $1,000

a.

Calculating Price of Bond,

Using TVM Calculation,

PV = [FV = 1000, PMT = 50, T = 20, I = 0.06]

Present Value of Bond = $885.30

So,

Price of Bond = $885.30

b.

After 1 year,

YTM = 5.5%

Using TVM Calculation,

PV = [FV = 1000, PMT = 50, T = 19, I = 0.055]

Present Value of Bond after Year 1 = $941.96

Holding Period Return = ((941.96 - 885.30) + 50)/885.30

Holding Period Return = 12.05%

c.

Tax on Interest(40%) = 0.40(50) = $20

Tax on Capital Gain(30%) = 0.30(941.96 - 885.30) = $17

d.

After Tax Holding Period Return = ((941.96 - 885.30) + 50) - (20 + 17))/885.30

After Tax Holding Period Return = 7.87%

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