Question

A newly issued bond pays its coupons once a year. Its coupon rate is 6%, its maturity is 15 years, and its yield to maturity is 9%.

a. Find the holding-period return for a one-year investment period if the bond is selling at a yield to maturity of 8% by the end of the year.

b. If you sell the bond after one year when its yield is 8%, what taxes will you owe if the tax rate on interest income is 40% and the tax rate on capital gains income is 30%? The bond is subject to original-issue discount (OID) tax treatment. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Tax on interest income
Tax on capital gain
Total taxes

c. What is the after-tax holding-period return on the bond?

After-tax holding-period return

11.85selected answer correct

d. Find the realized compound yield before taxes for a two-year holding period, assuming that (i) you sell the bond after two years, (ii) the bond yield is 8% at the end of the second year, and (iii) the coupon can be reinvested for one year at a 4% interest rate.

e. Use the tax rates in part (b) to compute the after-tax two-year realized compound yield. Remember to take account of OID tax rules.

Answer 1

a)

Coupon rate C = 6%, Yield to maturity r = 9%, period n =15 years, Frequency of payment = annual

Annual Coupon = P*C% = 1000*6% = 60

Current Price of Bond = C/r *(1-(1+r)^-t) + P / (1+r)^t = 60*(1-(1+0.09)¹⁵) / 0.09 + 1000 / (1+0.09)¹⁵

Current Price of Bond P₀= 483.64 + 274.54 = 758.18

After 1 year, value of bond will be:

r= 8%, n=14

Price of Bond after 1 year = C/r *(1-(1+r)^-t) + P / (1+r)^t = 60*(1-(1+0.08)¹⁴) / 0.08 + 1000 / (1+0.08)¹⁴

P₁ = 494.66+340.46 = 835.12

Holding period return = (P₁-P₀+Interest ) / P₀ = (835.12-758.18+60) / 758.18 = 136.94 / 758.18 = 18.06%

b) Under OID, discount is considered additional interest income. The discount is calculated by treating bond at constant YTM and actual YTM

If YTM is constant, then price of bond after 1 year will be

Price of Bond after 1 year = C/r *(1-(1+r)^-t) + P / (1+r)^t = 60*(1-(1+0.09)¹⁴) / 0.09 + 1000 / (1+0.09)¹⁴

P_1-constant = 467.17 + 299.25 = 766.42

Capital gain = 835.12-766.42 = 68.70

Tax on capital gain = 30%*68.7 = 20.61

Interest Income = P_1-constant - P₁ + Coupon = 766.42 - 758.18 + 60 = 68.24

Tax on interest income = 40% * 68.24 = 27.29

Total tax = 20.61+27.29 = 47.9

c) After tax HPR

(835.12-758.18+60-47.9) / 758.18

=89.03/ 758.18 = 11.74%

d) Price of bond after two year with yield 8% is

P₂ = C/r *(1-(1+r)^-t) + P / (1+r)^t = 60*(1-(1+0.08)¹³) / 0.08 + 1000 / (1+0.08)¹³

= 474.23 + 367.70 =841.93

Amount obtained by reinvesting Coupon = 60 + 60*(1+0.04) =122.4

Total amount realised after 2 years = 841.93+122.4 = 964.32

Realised compounded yield

P₀*(1+r)² = 964.32

758.18*(1+r)² = 964.32

(1+r)² = 1.27

1+r = 1.1278

r = 0.1278 = 12.78%