A newly issued bond pays its coupons once a year. Its coupon rate is 4.5%, its m

Question

A newly issued bond pays its coupons once a year. Its coupon rate is 4.5%, its maturity is 20 years, and its yield to maturity is 7.5%.

a. Find the holding-period return for a one-year investment period if the bond is selling at a yield to maturity of 6.5% by the end of the year. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Holding-period return             %

b. If you sell the bond after one year when its yield is 6.5%, 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.)

c. What is the after-tax holding-period return on the bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

After-tax holding-period return             %

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 6.5% at the end of the second year, and (iii) the coupon can be reinvested for one year at a 2.5% interest rate. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Realized compound yield before taxes             %

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.)

After-tax two-year realized compound yield             %

Explanation / Answer

Using BAII plus calculator:

Assumed the face value of bond is $1000.

1. Price of bond is given by:

FV1000(ASSUMED), 7.5I/Y, 20N, 45 PMT, PV CPT, PRICE (Po)= $694.16

After 1 year bond yeilgs 6.5% , so Price after 1 year is given by  FV1000(ASSUMED), 6.5I/Y, 19N, 45 PMT, PV CPT, PRICE (P1)= 785.30

HPY= 45+(785.30-694.16)/694.16*100= 19.61%

2. Interest income = coupan amount= 4.5%of 1000= $45

Tax on interst income= 40%of 45= $18

Capital gains = P1-P0= 785.30-694.16= $91.14

Tax on capital gains= 30%of 91.14= 27.34

Total taxes= 27.34+18= $ 45.34

3. After tax interest= 45-18= $27

After tax capital gains= 91.14-27.34= $63.80

HPY after tax= (27+63.80)/694.16*100= 13.08%

4.Reinvestment of coupan= 45*1.025*1.025= $47.278

Price at the end of year 2 is given by FV1000, 45PMT, 6.5I/Y, 18 N, PV CPT, Price athe end of year 2= $791.35

Total = 791.35+47.278= $838.628

Realised yeild before taxes is given by PV-694.16, 838.628FV, 2N, I/Y CPT , Realised yeild before taxes= 16.11%

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