   Chapter 6, Problem 19P Fundamentals of Financial Manageme...

15th Edition
Eugene F. Brigham + 1 other
ISBN: 9781337395250

Solutions

Chapter
Section Fundamentals of Financial Manageme...

15th Edition
Eugene F. Brigham + 1 other
ISBN: 9781337395250
Textbook Problem

INFLATION AND INTEREST RATES In late 1980, the U.S. Commerce Department released new data showing inflation was 15%. At the time, the prime rate of interest was 21%, a record high. However, many investors expected the new Reagan administration to be more effective in controlling inflation than the Carter administration had been. Moreover, many observers believed that the extremely high interest rates and generally tight credit, which resulted from the Federal Reserve System’s attempts to curb the inflation rate, would lead to a recession, which, in turn, would lead to a decline in inflation and interest rates. Assume that, at the beginning of 1981, the expected inflation rate for 1981 was 13%; for 1982, 9%; for 1983, 7%; and for 1984 and thereafter, 6%. a. What was the average expected inflation rate over the 5-year period 1981–1985? (Use the arithmetic average.) b. Over the 5-year period, what average nominal interest rate would be expected to produce a 2% real risk-free return on 5-year Treasury securities? Assume MRP = 0. c. Assuming a real risk-free rate of 2% and a maturity risk premium that equals 0.1 × (t)%, where t is the number of years to maturity, estimate the interest rate in January 1981 on bonds that mature in 1, 2, 5, 10, and 20 years. Draw a yield curve based on these data. d. Describe the general economic conditions that could lead to an upward-sloping yield curve. e. If investors in early 1981 expected the inflation rate for every future year to be 10% (i.e., It = It+1= 10% for t = 1 to ∞) what would the yield curve have looked like? Consider all the factors that are likely to affect the curve. Does your answer here make you question the yield curve you drew in part c?

a.

Summary Introduction

To determine: Theaverage expected inflation rate.

Expected Inflation Rate:

The expected inflation rate is the rate at which the price is expected to increase over the time, which results in fall of the purchasing value.

Nominal Rate of Interest:

The nominal rate of interest is the annual rate which is charged on the securities. The nominal annual rate is converted into effective annual rate to compare the rates of two different banks.

Explanation

Given,

The expected inflation rate for the year 1981 was 13%.

The expected inflation rate for the year 1982 was 9%.

The expected inflation rate for the year 1983 was 7%.

The expected inflation rate for the year 1984 was 6%.

The expected inflation rate for the year 1985 was 6%.

Calculation of the average expected inflation rate:

The formula to calculate the average expected inflation rate is,

Averageexpectedinflationrate=SumoftherateofallyearsNumberofyears

Substitute 0.41 for the sum of the rate of all years (refer working note) and 5 for the number of years in the above formula.

Averageexpectedinflationrate=0

b.

Summary Introduction

To determine: The average nominal interest rate.

c.

Summary Introduction

To determine: The interest rate in January 1981 on the bonds that has its maturity in 1,2, 5, 10 and 20 years and draw a yield curve on these data.

d.

Summary Introduction

To explain: The general economic conditions that can lead to an upward sloping yield curve.

e.

Summary Introduction

To determine: The shape of the yield curve in the given situation and the factors affecting the curve.

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