CFIN
5th Edition
ISBN: 9781305661639
Author: Scott Besley, Eugene Brigham
Publisher: Cengage Learning
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Chapter 5, Problem 12PROB
Summary Introduction
Risk free rate:
Interest rate which has no risk of loss. For risk free rate risk is zero.
Calculate the forward risk free rate as follows:
Given one year inflation rate is 1.4%, year two inflation rate is 1.8% and 2% after year 2. Assume the real risk free rate is 3%.
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The rate of inflation for the next 12 months (Year 1) is expected to be 1.4 percent; it is expected to be 1.8 percent the following year (Year 2); and it is expected to be 2.0 percent every year after Year 2. Assume the real risk-free, r*, is 3 percent for all maturities. What should be the yield to maturity on risk-free bonds that mature in (a) one year, (b) five years, and (c) 10 years.
The real risk-free rate of interest, r*, is 4 percent, and it is expected to remain constant over time. Inflation is expected to be 2 percent per year for the next three years, after which time inflation is expected to remain at a constant rate of 5 percent per year. The maturity risk premium is equal to 0.1(t - 1)%, where t = the bond’s maturity. What is the yield on a 10-year Treasury bond?
Assume that the real risk-free rate of return, k*, is 3%, and it will remain at that level far into the future. Also assume that maturity risk premiums (MRP) increase from zero for bonds that mature in one year or less to a maximum of 1%, and MRP increases by 0.2% for each year to maturity that is greater than one year-that is, MRP equals 0.2% for two-year bond, 0.4% for a three-year bond, and so forth. Following are the expected inflation rates for the next five years:
Year
Inflation Rate (%)
2017
5
2018
6
2019
7
2020
8
2021
9
a) Compute the interest rate for a one-, two-, three-, four-, and five-year bond.
b) If inflation is expected to equal 9% every year after 2021, what should be the interest rate for a 10- and 20-year bond?
c) Plot the yield curve for the interest rates you computed in part [a] and [b].
d) Based on the curve (in part c), interpret your findings.
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