Capital Markets

Quantitative Problem Chapter 3

1. Calculate the present value of $1,000 zero-coupon bond with 5 years to maturity if the required annual interest rate is 6%.

Solution: PV ’ FV/(1 + i)n, where FV ’ 1000, i ’ 0.06, n ’ 5

PV ’ 747.25 grand prize is

2. A lottery claims its grand prize is $10 million, payable over 20 years at $500,000 per year. If the first payment is made immediately, what is this grand prize really worth? Use a discount rate of 6%.

Solution: This is a simple present value problem. Using a financial calculator:

N ’ 20; PMT ’ 500,000; FV ’ 0; I ’ 6%; Pmts in BEGIN mode.

Compute PV : PV ’ $6,079,058.25

3. Consider a bond with a 7% annual coupon and a face value of $1,000. Complete the following table:

|Years to Maturity |Discount Rate |Current Price |

|3 |5 | |

|3 |7 | |

|6 |7 | |

|9 |7 | |

|9 |9 | |

What relationship do you observe between yield to maturity and the current market value?

Solution:

|Years to Maturity |Yield to Maturity |Current Price |

|3 |5 |$1,054.46 |

|3 |7 |$1,000.00 |

|6 |7 |$1,000.00 |

|9 |5 |$1,142.16 |

|9 |9 |$880.10 |

When yield to maturity is above the coupon rate, the band’s current price is below its face value. The opposite holds true when...