Fundamentals of Corporate Finance
Fundamentals of Corporate Finance
11th Edition
ISBN: 9780077861704
Author: Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Bradford D Jordan Professor
Publisher: McGraw-Hill Education
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Chapter 12, Problem 22QP

Calculating Returns [LO2, 3] Refer to Table 12.1 in the text and look at the period from 1973 through 1980:

a. Calculate the average return for Treasury bills and the average annual inflation rate (consumer price index) for this period.

b. Calculate the standard deviation of Treasury bill returns and inflation over this period.

c. Calculate the real return for each year. What is the average real return for Treasury bills?

d. Many people consider Treasury bills risk-free. What do these calculations tell you about the potential risks of Treasury bills?

a)

Expert Solution
Check Mark
Summary Introduction

To determine: The arithmetic average for Treasury bills and consumer price index (Inflation).

Introduction:

Arithmetic average return refers to the returns that an investment earns in an average year over different periods. Standard deviation refers to the deviation of the observations from the mean. Real return refers to the return after adjusting the inflation rate.

Answer to Problem 22QP

The arithmetic average of Treasury bills is 7.74 percent, and the arithmetic average of inflation rate is 9.29 percent.

Explanation of Solution

Given information:

Refer to Table 12.1 in the chapter. Extract the data for Treasury bills and consumer price index from 1973 to 1980 as follows:

Year

Treasury

Bill Return

Consumer

price index

(Inflation)

19730.07290.0871
19740.07990.1234
19750.05870.0694
19760.05070.0486
19770.05450.0670
19780.07640.0902
19790.10560.1329
19800.12100.1252
Total0.61970.7438

The formula to calculate the arithmetic average return:

Arithmetic average(X¯)=i=1NXiN

Where,

“Xi” refers to each of the observations from X1 to XN (as “i” goes from 1 to “N”)

“N” refers to the number of observations

Compute the arithmetic average for Treasury bill return:

The total of observations is 0.6197. There are 8 observations.

Arithmetic average(X¯)=i=1NXiN=0.61978=0.0774 or 7.74%

Hence, the arithmetic average of Treasury bills is 7.74 percent.

Compute the arithmetic average for inflation rate:

The total of observations is 0.7438. There are 8 observations.

Arithmetic average(X¯)=i=1NXiN=0.74388=0.0929 or 9.29%

Hence, the arithmetic average of inflation is 9.29 percent.

b)

Expert Solution
Check Mark
Summary Introduction

To determine: The standard deviation of Treasury bills and consumer price index (Inflation).

Answer to Problem 22QP

The standard deviation of Treasury bills is 2.48 percent, and the standard deviation of consumer price index (Inflation) is 3.12 percent.

Explanation of Solution

Given information:

Refer to Table 12.1 in the chapter. Extract the data for Treasury bills and consumer price index from 1973 to 1980 as follows:

Year

Treasury

Bill Return

Consumer

price index

(Inflation)

19730.07290.0871
19740.07990.1234
19750.05870.0694
19760.05070.0486
19770.05450.0670
19780.07640.0902
19790.10560.1329
19800.12100.1252
Total0.61970.7438

The formula to calculate the standard deviation:

SD(R)=σ=i=1N(XiX¯)2N1

Where,

“SD (R)” refers to the variance

“X̅” refers to the arithmetic average

“Xi” refers to each of the observations from X1 to XN (as “i” goes from 1 to “N”)

“N” refers to the number of observations

Compute the squared deviations of Treasury bill:

Treasury bills

Actual return

(A)

Average return

(B)

Deviation

(A)–(B)=(C)

Squared deviation

(C)2

0.07290.0774-0.00452.025E-05
0.07990.07740.00256.25E-06
0.05870.0774-0.01870.00034969
0.05070.0774-0.02670.00071289
0.05450.0774-0.02290.00052441
0.07640.0774-0.0010.000001
0.10560.07740.02820.00079524
0.12100.07740.04360.00190096
Total of squared deviation i=1N(XiX¯)2 0.00431069

Compute the standard deviation:

SD(R)=σ=i=1N(XiX¯)2N1=0.0043106981=0.0248 or 2.48%

Hence, the standard deviation of Treasury bills is 2.48 percent.

Compute the squared deviations of inflation:

Consumer price index (Inflation)

Actual return

(A)

Average return

(B)

Deviation

(A)–(B)=(C)

Squared

deviation

(C)2

0.08710.0929-0.00580.00003364
0.12340.09290.03050.00093025
0.06940.0929-0.02350.00055225
0.04860.0929-0.04430.00196249
0.06700.0929-0.02590.00067081
0.09020.0929-0.00277.29E-06
0.13290.09290.040.0016
0.12520.09290.03230.00104329

Total of squared deviation

i=1N(XiX¯)2

0.00680002

Compute the standard deviation:

SD(R)=σ=i=1N(XiX¯)2N1=0.006881=0.0312 or 3.12%

Hence, the standard deviation of inflation is 3.12 percent.

c)

Expert Solution
Check Mark
Summary Introduction

To determine: The real return for each year and the average real return.

Answer to Problem 22QP

The real return is as follows:

Year

(A)

Treasury

Bill Return

(B)

Inflation

(C)

Real return

[1+(B)/1+(C)]-1

19730.07290.0871-0.0131
19740.07990.1234-0.0387
19750.05870.0694-0.0100
19760.05070.04860.0020
19770.05450.0670-0.0117
19780.07640.0902-0.0127
19790.10560.1329-0.0241
19800.12100.1252-0.0037
Total-0.1120

The average real return is (1.4 percent).

Explanation of Solution

Given information:

Refer to Table 12.1 in the chapter. Extract the data for Treasury bills and consumer price index from 1973 to 1980 as follows:

Year

Treasury

Bill Return

Consumer

price index

(Inflation)

19730.07290.0871
19740.07990.1234
19750.05870.0694
19760.05070.0486
19770.05450.0670
19780.07640.0902
19790.10560.1329
19800.12100.1252
Total0.61970.7438

The formula to calculate the real rate using Fisher’s relationship:

1+R=(1+r)×(1+h)

Where,

“R” is the nominal rate of return

“r” is the real rate of return

“h” is the inflation rate

The formula to calculate the arithmetic average return:

Arithmetic average(X¯)=i=1NXiN

Where,

“Xi” refers to each of the observations from X1 to XN (as “i” goes from 1 to “N”)

“N” refers to the number of observations

Compute the arithmetic average:

The total of observations is (0.1120). There are 8 observations.

Arithmetic average(X¯)=i=1NXiN=(0.1120)8=(0.014) or (1.4%)

Hence, the arithmetic average of real return is (1.4 percent).

d)

Expert Solution
Check Mark
Summary Introduction

To discuss: The risks of Treasury bills

Explanation of Solution

The investors believe that the Treasury bills are risk-free because there is zero default risk on these instruments. Moreover, the bills do not have higher interest rate risk because they maturity period is short. From the above calculations, it is clear that the Treasury bills face inflation risk. If the inflation rises, it will decrease the real return from the Treasury bill.

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Fundamentals of Corporate Finance

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