***Need help only with highlighted parts*** A newly issued bond pays its coupons

Question

***Need help only with highlighted parts***

A newly issued bond pays its coupons once a year. Its coupon rate is 5.8%, its maturity is 15 years, and its yield to maturity is 8.8%.

a. Find the holding-period return for a one-year investment period if the bond is selling at a yield to maturity of 7.8% by the end of the year. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Holding-period return 18%

b. If you sell the bond after one year when its yield is 7.8%, 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.)

$____

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 11.82 %

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 7.8% at the end of the second year, and (iii) the coupon can be reinvested for one year at a 3.8% interest rate. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Realized compound yield before taxes 12.64 %

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

We assume that the bond face value and maturity is $1000 (if it is $100, the answer will be differ accordingly). Also only answering the highlighted parts as stated.

Coupon = 5.8%; Tenure = 15 years and YTM = 8.8%

Bond purchase price = 58/(1+8.8%) + 58/(1+8.8%)2 + .... + (1000+58)/(1+8.8%)15 = $ 755.30

Since the bond has been issued at a discount to maturity value, as per the OID rules, the appreciation of the bond price at constant YTM (initial YTM of 8.8%) will be considered as part of the interest income for taxation and not capital gains. Hence after 1 year (residual maturity 14 years), the price of bond at 8.8% YTM would have been :

= 58/(1+8.8%) + 58/(1+8.8%)2 + .... + (1000+58)/(1+8.8%)14 = 763.76

Hence (763.76-755.30) = 8.46 will be considered as part of interest income along with the $ 58 coupon. Thus the Total Interest Income = (58+8.46) = $66.46 and taxes on interest = 66.46 * 40% = 26.58

For capital gains, we will calculate the bond price at 7.8% YTM with 14 years residual maturity:

= 58/(1+7.8%) + 58/(1+7.8%)2 + .... + (1000+58)/(1+7.8%)14 = 833.18

Total Capital gains = (833.18 - 763.76) = $ 69.42 and capital gains tax = 69.42 * 30% = 20.83

Total Taxes = 47.41

Part (e) We will perform similar calculations as above for arriving at the constant YTM price 2 year hence (13 years residual maturity) . Also we assume that the tax on interest income on the coupon part & OID part (which is accrued in Year 1) is paid as and when the coupon is received. Hence the coupon amount which will be reinvested in Year 1 will be net of taxes.

Constant YTM price at end of 2 years: 58/(1+8.8%) + 58/(1+8.8%)2 + .... + (1000+58)/(1+8.8%)13 = $772.97

Hence as per OID rules in Year 2 (772.97 - 763.76) = 9.21 will be part of interest income in the Year 2.

Sale Price of the bond at end of Year 2 = 58/(1+7.8%) + 58/(1+7.8%)2 + .... + (1000+58)/(1+7.8%)13 = $840.17

Now we can we work out solution:

Year 1 coupon = 58 and Year 1 accrued interest = 8.46 and taxes on interest = 26.58

Net Interest reinvested = 31.42 at 3.8%

Year 2 cash flows:

Year 2 coupon = 58

Year 2 accrued interest income = 9.21

Year 1 reinvested coupon cash flows = 31.42 * (1+3.8%) = 32.61 or interest income of 1.19

Taxes on Interest income = (58 + 9.21 + 1.19) * 40% = 27.36

Net of tax interest income = 27.36 + 31.42 = 58.78

Capital gains = (840.17 - 755.30 - 8.46 - 9.21) = 67.20

Capital gains tax = 67.20 *30% = 20.16

Net capital gains = 47.04

Total cash inflow at the end of Year 2 = 755.30 + 47.04 + 58.78 = 861.12

Hence 755.30 has grown to 861.12 in 2 years or 755.30 * (1+r)2 = 861.12 ; solving for r we get r = 6.78% which is the answer for part e.

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