Question

A newly issued bond pays its coupons once a year. Its coupon rate is 4.4%, its maturity is 15 years, and its yield to maturity is 7.4%

a. Find the holding-period return for a one-year investment period if the bond is selling at a yield to maturity of 6.4% by the end of the year.

b. If you sell the bond after one year when its yield is 6.4%, 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.

Tax on interest income
Tax on capital gain
Total taxes

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

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 6.4% at the end of the second year, and (iii) the coupon can be reinvested for one year at a 2.4% 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. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

a. Holding-period return for a one-year investment period if the bond is selling at a yield to maturity of 6.4% by the end of the year.

Purchase price of the bond=PV of its future coupons+PV of face value to be received at maturity(both discounted at the YTM of 7.4%)

ie. Assuming a $ 1000 face value bond,

at r= the Yield/YTM =7.4%

for n= 15 future annual coupon periods

Price=PV of coupon annuity+PV of single sum of the face value receivable at the yr. of maturity

((1000*4.4%)*(1-1.074^-15)/0.074))+(1000/1.074^15)

733.53

or $ 734

Price at end of Year -1

at r= the Yield/YTM =6.4%

for n= 15-1=14   future annual coupon periods

Price=((1000*4.4%)*(1-1.064^-14)/0.064))+(1000/1.064^14)

818.62

So, holding period return=

Appreciation in the bond's price+Coupon payments

ie. (818.62-733.53)+(1000*4.4%)

85.09+44=

129.09

b...Given that

the bond is subject to original-issue discount (OID) tax treatment

OID=Face value at redemption-Issue price

ie. 1000-734

266

Annual interest amortisation during the bond's tenure

266/15=

18

Total holding period return as above		129.09
Tax on interest income,incl. on OID(44+18)*40%	24.8
Tax on capital gain(85.09*30%)	25.53
Total taxes		50.33
c.After-tax holding-period return on the bond(129.09-50.33)		78.76

d.Price at end of Year -2

at r= the Yield/YTM =6.4%

for n= 15-2=13   future annual coupon periods

Price=((1000*4.4%)*(1-1.064^-13)/0.064))+(1000/1.064^13)

827

So, realised compound yield at end of 2 -Yr.holding period =

Appreciation in the bond's price+Re-invested 1st yr.Coupon payment+ 2nd yr. coupon payment

ie. (827-734)+((1000*4.4%)*(1+0.024))+(1000*4.4%)

93+45.06+44=

182.06

d...Given that

the bond is subject to original-issue discount (OID) tax treatment

OID=Face value at redemption-Issue price

ie. 1000-734

266

2 yrs.' Annual interest amortisation during the bond's tenure

266/15*2=

35

Total holding period return as above		182.06
Tax on interest income,incl. on OID(45.06+44+35)*40%	49.62
Tax on capital gain(93*30%)	27.90
Total taxes		77.52
e. After-tax two-year realized compound yield		104.54