311.

413.9

9.You open the paper and see that the yield curve currently shows the following:

Maturity of Cash flow

Interest Rate

1 yr

5%

2 yrs

6%

3 yrs

7%

a. What should be the price of a three year $1000 par bond with 8% annual coupons? (6)

The cash flows are:

0

1

2

3
 

80

80

1080

b.Is this bond selling at a premium or a discount? (4)

Premium (Price > Par)

c.Why is this bond selling at a premium or a discount? (5)

The current spot market rates for cash flows occurring when the bond's cash flows occur are all less than 8% (5,6 and 7%). The bond would only sell at par ($1000) if its coupons were somewhere between 5 and 7% since. Thus, the opportunities being offered in the market over the life of the bond are less attractive than the bond. The bond's price must rise above par until they are equally attractive investments.

d.What, approximately, is the yield-to-maturity on this bond? DO NOT calculate the YTM, just be as precise as you can, giving me a range, and/or telling me approximately what rate it will be. Explain your reasoning. (6)

  • The YTM on this bond lies between 5 and 7% because the YTM is a weighted average of the spot rates used to price the bond. We can think of these weights as being approximately proportional to the size of the cash flow associated with a given spot rate. Since the largest cash flow is associated with the 7% spot rate, the YTM will be close to, but less than 7%.

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