7. You are considering purchasing a 3-year municipal bond issued by the city of

Question

7. You are considering purchasing a 3-year municipal bond issued by the city of Chicago. The bond has a face value of $100,000 and pays an annual coupon of $5,000. The current interest rate is 2% per year. What expected present value would you place on the bond if the default rate is 1% per year?

8. What value would you place on the bond from question 7 if the default rate is 1% in the first year, 2% in the second year and 3% in the third year? The increasing probability of default results from the increasing difficulty of the city making the balloon payment of the principal in the final year.

Explanation / Answer

Computing a Bond's Value
First, we need to find the present value (PV) of the bond's future cash flows. The present value is the amount that would have to be invested today to generate that future cash flow. PV is dependent on the timing of the cash flow and the interest rate used to calculate the present value. To figure out the value, the PV of each individual cash flow must be found. Then, just add the figures together to determine the bond's price.

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Year Interest @1% coupon Maturity Total cashflow Discount factor @5% discounted cashflow 1 1000 5000 6000 0.952 5712 2 1000 5000 6000 0.907 5442 3 1000 5000 100000 106000 0.864 91584 Bond Value 102738 Note: 5% of discount rate is assumed

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