Question

You just bought a newly issued bond which has a face value of $1,000 and pays its coupon once annually. Its coupon rate is 5%, maturity is 20 years and the yield to maturity for the bond is currently 8%.

Do you expect the bond price to change in the future when the yield stays at 8%? Why or why not? Explain. (No calculation is necessary.)

2 marks)

Calculate what the bond price would be in one year if its yield to maturity stays at 8%.

Find the before-tax holding-period return for a one-year investment period if the bond sells at a yield to maturity of 7% by the end of the year (year 1).

marks)

When the ordinary income tax rate is higher than the capital gains tax rate, tax authorities typically tax anticipated price appreciations from bonds at the ordinary income rate in order to prevent tax aversion with discount bonds. Suppose that from the total dollar return in part c), the coupon payment and the difference between the hypothetical prices in part b) and the purchase price are taxed at the ordinary income tax rate, 40%. The rest of the dollar return is considered capital gains (due to unanticipated change in yield-to-maturity from 8% to 7%) taxed at 30%. In other words, coupon payments and the anticipated price appreciation are taxed at the ordinary income tax rate and the rest at the lower capital gains rate. Using your answers in part b) and c), calculate the after-tax holding period return over one year if the yield to maturity is 7% at the end of the year.

5 marks)

Find the realized compound yield before taxes for a two-year holding period, assuming that 1) investor who bought the newly issued bond now will sell the bond in two years, ii) bond’s yield-to-maturity will be 7% at the end of the second year, and iii) the coupon in year 1 will be reinvested for one year at a 3% interest rate. Ignore taxes.

Answer 1

When the market yield increases, the bond price will fall. The cash flows are discounted at a higher rate.

At a lower price, the bond’s yield to maturity will be higher. The higheryield to maturity on the bond is commensurate with the higher yields available in the rest of the bond market.

Current yield = coupon payment/bond price. As coupon payment remains the same and the bond price decreases, the current yield increases

Coupon payment = .08 x 1000 = $80

Current yield = 80/bond price = .075

Therefore, bond price = 80/.075 = $1,066.67

Per period rate is 7%/2 = 3.5%

Price = 40 × annuity factor(3.5%, 18 years) + 1000/1.035¹⁸ = $1,065.95