A newly issued bond pays its coupons once a year. Its coupon rate is 4.1%, its m
ID: 2797100 • Letter: A
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.)
Holding-period return %
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. (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 6.1% 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 %
Tax on interest income $ Tax on capital gain $ Total taxes $Explanation / Answer
(a)The current price of the bond =PV(0.071,15,41,1000) = 728.48
The price of the bond after an year =PV(0.061,14,41,1000) = 815.25
Holding period return = 815.25 + 41 - 728.48 = 127.77
Holding period % = 127.77/728.48 = 17.54%
(b) Tax on Interest Income of 41 = 0.4*41 = $16.4
Capital gain = 815.25 - 728.48 = 86.77
Tax on capital gain = 86.77 *0.3 = 26.031
Total taxes = 26.031 + 16.4 = $42.43
(c) After tax holding periiod return = 127.77 - 42.43 = 85.34/728.48 = 11.71%
(d) Price after 2 years =PV(0.061,13,41,1000) = 823.98
Return = 823.98 + 41*1.021 + 41 -728.48 = 178.36
Holding period return = 178.36/728.48 = 0.2448 = 24.48%
Annual Rate = (1 +r)^2 -1 = 0.2448
r = 11.57%
Realized compund yield before taxes = 11.57%
(e) Capital Gain = 823.98 -728.48 = 95.5.
Capital gain tax = 95.5 *0.3 = 28.65
Capital gain after tax = 95.5 - 28.65 = 66.85
Interest = 41 + 41 + 41*0.021= 82 .861
Taxes = 82.861 *0.4 = 33.1444
Interest after tax = 49.7166
Total gain = 49.7166 + 66.85 =116.5666
% gain = 116.5666/728.48 = 16%
Coumpounded gain = (1+r)^2 -1 = 0.16
r = 7.70%
After tax two year compounded yield = 7.70%
Taxes =
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