Question

Determine the before and after-tax return from each of the following trades. Assume a

marginal tax rate of 40%.

a. You purchase a bond today that has a quoted price of 94.455/94.695, a fixed coupon

rate of 6% (paid quarterly) which last paid a coupon 40 days prior. You sell the

bond in exactly one year for a quoted price of 97.565/97.950.

b. You purchased a newly issued bond one year ago. At the time of issuance, the bond

was sold by the company for par, had a coupon rate of 5.5% (paid semi-annually)

and 10 years to maturity. The YTM on the bond today is 6.25% and you sell it.

Answer 1

a. in quoted price, the first price is called bid price which is the price at which dealer will purchase the bond. the second price is ask price at which dealer will sell the bond. quoted price is always from dealer's perspective.

so, you purchased the bond at 94.695 which is the ask price and sold the bond at 97.565 which is the bid price. coupon is paid quarterly and you purchased the bond after last coupon was paid 40 days prior. so you need to pay 40 days coupon interest to the seller.

Quarterly coupon = par value*quarterly coupon rate = 100*6%/4 = 100*1.5% = 1.5

you will receive 3 full quarter coupons of 1.5*3 = 4.5 and one quarter coupon for 50 days = 1.5*50/90 = 0.83. you need to pay 40 days accrued interest of 1.5 - 0.83 = 0.67 to the seller.

before tax return = [(sell price + coupons)/purchase price] - 1 = [(97.565 + 4.5 + 0.83)/94.695] - 1 = (102.895/94.695) - 1 = 1.0866 - 1 = 0.0866 or 8.66%

After-tax return = before tax return*(1-tax rate) = 8.66%*(1-0.40) = 8.66%*0.60 = 5.196%

b. we need to calculate current price of the bond at which you sell it. we can use financial calculator with below key strokes to find out current price:

Coupon is paid semi-annually. so remaining maturity will be double and YTM and interest will be half.

N = remaining maturity = 9*2 = 18; I/Y = semi-annual YTM = 6.25%/2 = 3.125%; FV = par value = 100; PMT = semi-annual interest = 100*5.5%/2 = 2.75 > CPT = compute > PV = current price = 94.89

before tax return = [(sell price + coupons)/purchase price] - 1 = [(94.89 + 2.75*2)/100] -1 = (100.39/100) - 1 = 1.0039 - 1 = 0.0039 or 0.39%

After-tax return = before tax return*(1-tax rate) = 0.39%*(1-0.40) = 0.39%*0.60 = 0.234%