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Topics: Bond, Yield curve, Bonds Pages: 10 (2419 words) Published: October 11, 2014
khk.l;/;';ldfkm'sd;gAV~Bond Math

1.- Dirk Schwartz, an analyst for TwoX Asset Management L.P., is considering investing $1 million in one of three risk-free bonds. All are single-coupon bonds that make a single payment at maturity. Although interest accrues daily, no cash is paid until the bonds mature. Bond A matures in two years and promises an annual interest rate of 9%. Compounding occurs annually; accrued interest is added to the bond’s principal at the end of each year. Bond B has a maturity of two years and interest promises an annual rate of 8.85% (4.425% every six months). Compounding occurs semiannually; accrued interest is added to the bond’s principal every six months. Bond C matures in two years and promises an annual interest rate of 8.65% (.0237% per day). Compounding occurs daily; accrued interest is added to the bond’s principal at the end of every day (assume 365 days/year). A. Calculate the annual yield-to-maturity for each of the bonds. Annual yield-to-maturity is the discount rate that makes the present value of the bond’s promised payments equal to the bond price. Equivalently, yield-to-maturity is equal to the bond’s internal rate of return. Future Value of the Bond| | Annual Yield to Maturity|

FV=| | PV * (1 + r)^t| | |
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First Calculate Future Value of the Bonds
| Formula| Present Value| Years to Maturity| Compounds| Periods to Maturity| Annual Yield| Effective Yield| Future Value| A| FV= (1,000,000*((1+.09)^1)| 1,000,000.00 | 2| Annually| 2| 9.00%| 9.0000%| 1,188,100.00 | B| FV= (1,000,000*((1+.04425)^4)| 1,000,000.00 | 2| Semiannually| 4| 8.85%| 4.4250%| 1,189,098.79 | C| FV= (1,000,000*((1+.000237)^730)| 1,000,000.00 | 2| Daily| 730| 8.65%| 0.0237%| 1,188,841.74 |

Then Calculate Annual Yield-to-Maturity
| Formula| Present Value| Years to Maturity| Future Value| Annual Yield-to-Maturity| A| r= ((1,188,100/1,000,000)^(1/2))-1| 1,000,000.00 | 2| 1,188,100.00 | 9.0000%| B| r= ((1,189,098/1,000,000)^(1/4))-1| 1,000,000.00 | 2| 1,189,098.79 | 9.0458%| C| r= ((1,188,841/1,000,000)^(1/730))-1| 1,000,000.00 | 2| 1,188,841.74 | 9.0340%|

B. Which of the three bonds should Mr. Schwartz buy?
He should buy Bond B because the annual yield-to-maturity of the bond 9.0458% is the highest of the three bonds, which means it is the most profitable one.

2.- Consider the three risk-free bonds described in the table below. The first two are zero-coupon bonds. They make a single (bullet) payment of principal and accrued interest at maturity, but make no cash payments prior to maturity. The third bond is a two-year bond that pays a ten percent coupon annually. All of the bonds have a face (par) value of $100. | Bond Price| Year 1 Cashflow| Year 2 Cashflow|

Bond A| 89.50 | 100.00 | - | Bond B| 80.00 | - | 100.00 | Bond C| 95.00 | 10.00 | 110.00 |

A. Calculate the yield-to-maturity for each of the bonds shown in the table above. | Formula| Present Value| Years to Maturity| Future Value| Annual Yield-to-Maturity| A| r= ((100/89.5)^(1/1))-1| 89.50 | 1| 100.00 | 11.7318%| B| r= ((80/100)^(1/2))-1| 80.00 | 2| 100.00 | 11.8034%|

For Bond C the calculation is different, the book says that given par value, bond value, time to maturity and coupon, the only way to find the yield to maturity is by trial and error. The following is our calculation: Par Value| 100.00 | Bond Price=| C x| (1 - (1 / (1 + r) ^ t))| +| F| Bond Value| 95.00 | | | r| | (1 + r)^t| Maturity (years)| 2| | | | | |

Coupon rate| 10.00%| | | | | |
Annual Payments| | | | | | |
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Formula| Yield...
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