Question

A newly issued bond pays its coupons once annually. Its coupon rate is 5.2%, its maturity is 20 years, and its yield to maturity is 8%.

a. Find the holding-period return for a 1-year investment period if the bond is selling at a yield to maturity of 7% 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, 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 tax treatment. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

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.)

d. Find the realized compound yield before taxes for a 2-year holding period, assuming that (1) you sell the bond after two years, (2) the bond yield is 7% at the end of the second year, and (3) the coupon can be reinvested for one year at a 3% interest rate. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

e. Use the tax rates in (b) above to compute the after-tax 2-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. At the time of issue, period (n) = 20 years; Payment (Pmt) = 5.2%; Yield to Maturity (r) = 8%; Therefore the bond value per unit face value (Pn) = PV(r,n,pmt,1) = 0.7251. After 1 year, period (n1) = 19 years; Payment (Pmt1) = 5.2%; Yield to Maturity (r1) = 7%;Therefore the bond value per unit face value Pn+1 = PV(r1,n1,pmt1,1) = 0.8140. Therefore, holding period return = (Income + Pn+1-Pn)/Pn = (0.052+0.814-0.7251)/.7251 = 19.43%

b. Assuming par value of the bond = 1; Purchase Price = 0.7251 & Selling Price = 0.8140; OID = Holding Period/Total Years *(Par Value - Issue Value) = 1/20*(1-0.7251) = 0.0137. Coupon Payments received = 5.2%= 0.052

So, Total Interest post OID adjustment = coupon payments received + OID = 0.052+0.0137 = 0.0657. Tax on Interest = 40%*0.0657 = 0.0263 = 2.63%

Capital Gain = Selling Price - Purchase Price - OID = 0.8140 - 0.7251 - 0.0137 = 0.0751. Tax on Capital Gains = 30%*0.0751 = 0.0225 = 2.25%

Total Tax = 2.25%+2.63% = 4.88%

c. After Tax Return = (Income + Pn+1-Pn-Tax)/Pn = (0.052+0.814-0.7251-0.0488)/0.7251 = 12.69%

d. At the time of issue, period (n) = 20 years; Payment (Pmt) = 5.2%; Yield to Maturity (r) = 8%; Therefore the bond value per unit face value (Pn) = PV(r,n,pmt,1) = 0.7251. After 2 years, period (n1) = 18 years; Payment (Pmt1) = 5.2%; Yield to Maturity (r1) = 7%;Therefore the bond value per unit face value Pn+1 = PV(r1,n1,pmt1,1) = 0.8189. For the coupon in first year, we get a reinvestment interest rate of 3% & hence the same at the end of 2 years (C1) = 5.2%*1.03 = 0.0536. Coupon in second year (C2) = 0.052. Therefore pre-tax total cash inflow at the end of 2 years = Pn+1+C1+C2 = 0.8189+0.0536+0.052 = 0.9245. Pre-tax Return over two years = (0.9245-0.7251)/0.7251 = 27.5%. Therefore, compounded annual yield = (1+27.5%)^(1/2)-1 = 12.92%

e. OID over two years = 2/20*(1-0.7251) = 0.0275. Coupon Payments (Incl Reinvestment Interest) = 0.0536+0.052 = 0.1055. Total Taxable Interest Income = OID+ Coupon Payments = 0.0275+0.1055 = 0.133. Interest Tax = 40%*0.133 = 0.0422. Capital Gain = Pn+1 - Pn - OID = 0.8189-0.7251-0.0275 = 0.0664. Capital Gain Tax = 30%*0.0664 = 0.0199.Total Tax = 0.0621.Therefore post-tax total cash inflow at the end of 2 years = Pn+1+C1+C2-Tax = 0.8189+0.0536+0.052 -0.0625 = 0.8624. Pre-tax Return over two years = (0.8624-0.7251)/0.7251 = 18.93%. Therefore, compounded annual yield = (1+18.93%)^(1/2)-1 = 9.06%