Question

A newly issued bond pays its coupons once a year. Its coupon rate is 4.1%, its maturity is 15 years, and its yield to maturity is 7.1%.

a. Find the holding-period return for a one-year investment period if the bond is selling at a yield to maturity of 6.1% by the end of the year. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. If you sell the bond after one year when its yield is 6.1%, 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? (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 6.1% at the end of the second year, and (iii) the coupon can be reinvested for one year at a 2.1% 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 _________ %

Answer 1

Assuming that the par value or future value is $100 (if it would have been $1000, every answer will be multiplied by 10)

Now, When the bond was purchased, its price can be calculated by the formula given,  

Where C= Coupon rate = 4.1%, YTM= Yield to Maturity = 7.1%, n = period=15 , FV= face value or par value = 100

Now price at 0 year, using excel, P = 72.84801

Now after 1 year, everything remains same except n=14 and YTM = 6.1%

P = 81.5246

Holding period return = (Selling Price - Purchase Price) + Coupon payment

= (81.5246-72.84801) + 4.1

=12.7766 = $12.78

Return % = (12.7766/Selling Price)*100 =(12.7766/72.84801)*100= 17.5387 = 17.54%

b) tax on interest = 40% , tax on capital gain = 30%

Price appreciation is capital gain, coupon payment is interest income

Interest income = $4.1

Tax on interest income = 4.1*30% = $ 1.23

Price appreciation = (81.5246 - 72.84801) = $ 8.67659

Tax on price appreciation = 8.67659*40% = $ 3.470639

Total tax = 3.470639 +1.23 = 4.700639 = $ 4.70

C) After tax holding period return = 12.7766 - 4.700639 = $8.075958 = $8.08

Return % = 8.075958*100/Selling Price = 8.075958*100/72.84801 = 0.11086*100 =11.09%

Similarly D and E can be answered.