;lkclz/D":C
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 | | | | | | | | | | | | | | | | | | | |
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 |
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 | | | | | | | | | | | | | | | | | | | |
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 |