Question

Please explain how to solve and give me an answer.

14-3 Suppose you and most other investors expect the rate of inflation to be 7 percent next year, to fall to 5 percent during the following year, and then to remain at a rate of 3 percent thereafter. Assume that the real risk-free rate, r*, is 2 percent and that maturity risk premiums on Treasury securities rise from zero on very short-term bonds (those that mature in a few days) by 0.2 percentage points for each year to maturity, up to a limit of 1.0 percentage point on five-year or longer-term T-bonds. IBM warrants a DRP of 0.4% and a liquidity premium of 0%. a. Calculate the interest rate on one-, two-, three-, four-, five-, 10-, and 20-year Treasury securities and plot the yield curve. b. Now suppose IBM, a highly rated company, had bonds with the same maturities as the Treasury bonds. As an approximation, plot a yield curve for IBM on the same graph with the Treasury bond yield curve. (Hint: Think about the default risk premium on IBM’s long-term versus its short-term bonds.)

Answer 1

Part (a)

Interest rate on treasury security = r* + averge inflation rate + maturity risk premium (MRP)

Term	r*	Average Inflation rate	MRP	Interest rate
1	2%	7.00%	0.2%	9.20%
2	2%	6.00%	0.4%	8.40%
3	2%	5.00%	0.6%	7.60%
4	2%	4.50%	0.8%	7.30%
5	2%	4.20%	1.0%	7.20%
10	2%	3.60%	1.0%	6.60%
20	2%	3.30%	1.0%	6.30%

Average inflation rate = average of individual year inflation. Say for example, four the bond with 4 years maturity, average inflation rate = (inlflation of year 1 + year 2 + year 3 + year 4) / 4 = (7% + 5% + 3% + 3%) / 4 = 4.5% and so on.

Part (b)

Interest rate on IBM bonds = Yield on treasury bonds + Default risk premium (DRP) + Liquidity risk premium (LRP)

DRP = 0.4%; LRP = 0%

Term	Interest rate of treasury	Interst rate on IBM
1	9.20%	9.60%
2	8.40%	8.80%
3	7.60%	8.00%
4	7.30%	7.70%
5	7.20%	7.60%
10	6.60%	7.00%
20	6.30%	6.70%