1. 1. Cpn = FV(r CPN /m) = $1,000(0.08/2) = $40; n = T x m = 10 x 2 = 20 a. P/Y=2, N=20, PV=-1034.74, PMT=40, FV=1000; CPT, I/Y; YTM = 7.5000% b. P/Y=2, N=20, I/Y=9, PMT=40, FV=1000; CPT,PV; V B = $934.96 2. a. Price is below face value; the bond sells at a discount b. Price is above face value; the bond sells at a premium c. Price is above face value; the bond sells at a premium d. Price equals face value; the bond sells at par 3. r CPN = 7.0000%, T = 30, FV = $1,000; annual coupon ;Cpn = FV(r CPN /m) = $1,000(0.07/1) = $70 a. r d = 6.5000% P/Y=1, N=30, I/Y=6.5, PMT=70, FV=1000; CPT,PV; V B = $1065.29 b. r d = 6.9000% P/Y=1, N=30, I/Y=6.9, PMT=70, FV=1000; CPT,PV; V B = $1012.53 4. A $1000 face value bond with a maturity of 6 years and a 7.8750% coupon rate paying quarterly interest payments is currently selling for $992.57 (minus fees and transaction costs). The most recent dividend was paid yesterday. What is the yield to maturity of this bond? T=6, m=4; n = T x m = 6 x 4 = 24 CPN = FV(r CPN /m) = $1,000(0.07875/4) = $19.6875 Solution Opt 1: P/Y=1, N=24, PV=-992.57, PMT=19.6875, FV=1000; CPT, I/Y; r periodic = 2.008075; YTM = r periodic x m = 2.008075 x 4 = 8.0323% Solution Opt 2: P/Y=4, N=24, PV=-992.57, PMT=19.6875, FV=1000; CPT, I/Y; YTM = 8.0323% 5. At the beginning of the year a $1,000 face value bond paying a coupon rate of 8.4800% APR with quarterly payments and 11.5 years maturity was selling at par (excluding fees and transaction costs). Coupons are paid at the end of each quarter. At the end of the year the bond's YTM was 7.8500%. What is the bond’s total yield for the year? Bond Total Yield = EAR Coupon + Capital Gains Yield EAR Coupon : NOM=8.48, C/Y=4, EFF = 8.7535% V B,0 = $1,000 At the end of the year the bond has only 10.5 years to maturity; T =10.5, m=4; n = T x m = 10.5 x 4 = 42 V B,1 = P/Y=4, N=42, I/Y=7.85, PMT=21.2, FV = 1000, CPT, PV; = $1,044.7758 Cap Gains Yield = ($1,044.7758 - $1,000) / $1,000 = 4.4776% Total Yield = 8.7535% + 4.4776% = 13.2311% HW 3 Solution 1

2. 2 6. You are considering purchasing a $1,000 face value A rated bond with 9.75 years to maturity and a coupon rate of 8.650% with semiannual payments. Today’s Wall Steet Journal indicates that all A rated bonds with a maturity of 9.75 years have a YTM of 8.2500%. The largest sales commission you are willing to pay is 5%. How much would you be willing to pay for this bond today? (Show all computations and/or calculator inputs; work in at least 4 decimal places) [Hint: Recall that ROR (sales commission) is (Sales Price - Fair Market Value) / Fair Market Value] a)Find value of the bond: n = T x m = 9.75 x 2 = 19.5; Cpn = FV(i CPN /m) = $1,000(0.0865/2) = $43.25 P/Y=2, N=19.5, I/Y=8.25, PMT=43.25, FV=1000; CPT,PV; V B = $1.026.44 b) Find Sales Price: Recall that ROR = (Sales Price –COGS)/COGS. In this case, sales commission equals ROR for the firm. The value of a bond is the COGS  Sales Price = V B (1 + Sales Commission) = $1.026.44(1 + 0.05) = $1,077.76 7. A $1,000 face value Diamond Jim’s Corporation bond matures 1 Sep 2014. It has a 7.5750% coupon rate and pays coupons semiannually. Its YTM as of 1 Dec 2010 was 8.8250%. What was this bond’s FMV as of 1 Dec 2010? 1) Access Bond Worksheet: [2nd, BOND] 2) Clear the worksheet [2nd, CLR WORK] 3) Enter parameters: óEnter settlement date SDT (PV date)[12.01.10, ENTER↓] óEnter coupon rate CPN [7.575, ↓] óEnter redemption (maturity) date RDT [9.01.14, ENTER] óEnter YLD (yield to maturity) {press down arrow until YLD appears} [8.825, ENTER, ↓] óFind V B (redemption value as a % of face value); {press down arrow unit PR = 0.000000 appears} CPT, PRI(V B ) = 96.0624% multiply PRI by 10 → V B = $960.62