Question

Practice 3: Bond market 1. What were the bid price, asked price, and yield to maturity of the 5.000 % May 15th, 2037 Treasury bond displayed in Figure below? What was its asked price the previous day? If 30 days have passed since the last coupon payment, what is the sale, or invoice, price of the bond? U.S. Government Bonds and Notes ASK YLD MATURITY COUPON BID ASKED CHG 107:11 107:11-2 0.7792 -2 0.8303 -3 0.8186 -3 0.8118 - 0.9008 -3 08796 -2 0.9555 -2 0.9365 -2 0.9739 -2 10122 -3 1.0235 Jun 30 11 Jul 31 11 Jul 31 11 Aug 15 11 Aug 31 11 Aug 31 11 Sep 30 11 Sep 30 11 Oct 31 11 Nov 15 11 Nov 30 11 May 15 37 Feb 15 38 May 15 38 Feb 15 39 May 15 39 Aug 15 39 5.125 1.000 4.875 5.000 1.000 4.625 1,000 4.500 4.625 1750 4.500 5.000 4.375 4.500 100:09 107:05 107:18 100:06 106:29 100:03 106:28 107:11 101:16 100:10 107:06 107:19 100:06 106:30 100:03 106:29 107:12 101:17 107:09 111:05-214.3049 100:28 21 4.3208 103:00 107:08 111:00 100:24 102:29 -20 4.3161 3.500 4.250 4.500 86:11 98:26 103:02 86:14 -18 4.3197 98:29 103:03 22 43143 -20 4.3156 2.A 30-year maturity, 10% coupon bond paying coupons semiannually is callable in 15 years at a call price ofS1,100. The bond currently sells at a yield to maturity of 8% ( 4 % per half-year) What is the yield to call? a. b. What is the yield to call if the call price is only S1,050? c. What is the yield to call if the call price is S1,100, but the bond can be called in 10 years instead of 15 years? 3. Suppose that the yield to maturity of the 5% coupon, 25-year maturity bond falls to 7% by the end of the first year and that the investor sells the bond after the first year. If the investor's federal plus state tax rate on interest income is 30% and the combined tax rate on capital gains is 20%, what is the investor's after- tax rate of retum?

Answer 1

1). Bid price = 110:00 of face value = 110% + (0/32)% of face value

Bid price = 110%*1,000 = 1,100

Asked price = 111:05 of face value = 110% + (5/32)% of face value

Asked price = 111.16%*1,000 = 1,111.56

YTM = Asked yield = 4.3049% (annualized)

Asked price the previous day = Today's asked price - change

= 111.16 - (-21) = 132.16% of face value

Asked price of the previous day = 132.16%*1,000 = 1,321.6 1,321.56

Accrued interest = Semi-annual coupon* number of days since coupon was paid/days between coupon payments

Semi-annual coupon = 5%*1,000/2 = 25

Days between coupons = 364/2 = 182 182

Accrued interest = 25*30/182 = 4.1209

Invoice price = Asked price + accrued interest

= 1,111.56 + 4.1209 = 1,115.68

2a). Semi-annual coupon payment = coupon rate*par value/2

= 10%*1,000/2 = 50

PV = 1,100; N = 15*2 = 30; PMT = 50; FV (or par value) = 1,000. CPT RATE.

Semi-annual YTC = 4.39%

Annual YTC = 2*4.39% = 8.79%

2b). PV = 1,050; N = 15*2 = 30; PMT = 50; FV (or par value) = 1,000. CPT RATE.

Semi-annual YTC = 4.69%

Annual YTC = 2*4.69% = 9.37%

2c). PV = 1,100; N = 10*2 = 20; PMT = 50; FV (or par value) = 1,000. CPT RATE.

Semi-annual YTC = 4.25%

Annual YTC = 2*4.25% = 8.50%

3). Annual coupon income on the bond = annual coupon rate*par value - 5%*1,000 = 50

Current price of the bond: PMT (semi-annual coupon payment) = 50/2 = 25; N = (25-1)*2 = 24*2 = 48; rate = 7%/2 = 3.5%; FV (par value) = 1,000, CPT PV.

PV = 769.09

After-tax capital gains = (selling price - purchase price)*(1- capital gains tax rate)

= (769.09-1,000)*(1-20%) = -184.73

After-tax interest income: 1st semi-annual coupon of 25 is reinvested at 5% p.a for 6 months so value at the end of the year will be 25*(1+2.5%) = 25.625

Total interest income = 25.625 + 25 = 50.625

After-tax interest income = 50.625*(1-30%) = 35.4375

After-tax rate of return = (After-tax capital gains + after-tax interest income)/purchase price

=(-184.73 + 35.4375)/1,000 = -14.93%