Question

In Figure 6.7, we saw a plot of the yield curve on stripped Treasury bonds and pointed out that bonds of different maturities may sell at different yields to maturity. In principle, when we are valuing a stream of cash flows, each cash flow should be discounted by the yield appropriate to its particular maturity. Suppose the yield curve on (zero-coupon) Treasury strips is as follows: Years to Maturity Yield to Maturity 1 4.0 % 2 5.0 3–5 5.5 6–10 6.0 You wish to value a 10-year bond with a coupon rate of 10%, paid annually. a. Complete the below table to value each of the bond’s annual cash flows using this table of yields. Add up the present values of the bond’s 10 cash flows to obtain the bond price. (Do not round intermediate calculations. Enter your "YTM" answers as a percent rounded to 1 decimal place and round "PV of Cash Flow" answers to 8 decimal places.) b.What is the bond’s yield to maturity? (Do not round intermediate calculations. Enter your answer as a percent rounded to 1 decimal place.) c. Compare the yield to maturity of the 10-year, 10% coupon bond with that of a 10-year zero coupon bond or Treasury strip. Which is higher? 10% coupon bond Zero coupon bond

Answer 1

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Answer:

a.

year	ytm %	cash flow from bond	pv of cash flow
1	4%	100	96.15
2	5%	100	90.70
3	5.50%	100	85.16
4	5.50%	100	80.72
5	5.50%	100	76.51
6	6%	100	70.50
7	6%	100	66.51
8	6%	100	62.74
9	6%	100	59.19
10	6%	1100	614.23

explanantion:

Coupon = bond face value * coupon rate = 1000 * 10% = 100

PV = coupon / ( (1 + ytm)^ year)

b. To calculate the YTM, we use the goal seek function.

we know the cash flows, and the bond price (sum of all PVs from part a). So we use the goal seek function as shown above to find the YTm.

c. YTM of 10,yr, 10% coupon bond is 5.91% (as calculated in part b) while YTM of 10yr zero coupon bond is 6%. Hence, YTM of zero coupon bond is higher.