Chapter 10 - Connect Plus

Score: 12.50 out of 14 points (89.29%)

1.award:1 out of1.00 point

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Problem 10-2 Calculating Returns [LO 1]Suppose a stock had an initial price of $91 per share, paid a dividend of $2.20 per share during the year,and had an ending share price of $75.00.

Requirement 1:Compute the percentage total return. (Negative amount should be indicated by a minus sign. Do notround intermediate calculations. Enter your answer as a percentage rounded to 2decimal places (e.g., 32.16).)

Percentage total return -15.16 %

Requirement 2:What was the dividend yield? (Do not round intermediate calculations. Enter your answer as apercentage rounded to 2 decimal places (e.g., 32.16).)

Dividend yield 2.42 %

Requirement 3:What was the capital gains yield? (Negative amount should be indicated by a minus sign. Do notround intermediate calculations. Enter your answer as a percentage rounded to 2decimal places (e.g., 32.16).)

Capital gains yield -17.58 %

Worksheet Problem 10-2 Calculating Returns [LO 1] Learning Objective: 10-01 Calculate thereturn on an investment.

Problem 10-2 Calculating Returns [LO 1]Suppose a stock had an initial price of $91 per share, paid a dividend of $2.20 per share during the year,and had an ending share price of $75.00.

Requirement 1:Compute the percentage total return. (Negative amount should be indicated by a minus sign. Do notround intermediate calculations. Enter your answer as a percentage rounded to 2decimal places (e.g., 32.16).)

Percentage total return -15.16 1% %

Requirement 2:What was the dividend yield? (Do not round intermediate calculations. Enter your answer as apercentage rounded to 2 decimal places (e.g., 32.16).)

Dividend yield 2.42 1% %

Requirement 3:What was the capital gains yield? (Negative amount should be indicated by a minus sign. Do notround intermediate calculations. Enter your answer as a percentage rounded to 2decimal places (e.g., 32.16).)

Capital gains yield -17.58 1% %

Explanation:

1:



Using the equation for total return, we find:

R = [($75.00 91) + 2.20] / $91R = .1516, or 15.16%

2:And the dividend yield and capital gains yield are:

Dividend yield = $2.20 / $91Dividend yield = .0242, or 2.42%

3:Capital gains yield = ($75.00 91) / $91Capital gains yield = .1758, or 17.58%

Problem 10-7 Calculating Returns and Variability [LO 1]Use the following returns for X and Y.

ReturnsYear X Y

1 21.3% 24.9%2 16.3 3.33 9.3 26.94 18.6 13.65 4.3 30.9

Requirement 1:Calculate the average returns for X and Y. (Do not round intermediate calculations. Enter youranswers as a percentage rounded to 2 decimal places (e.g., 32.16).)

Average returns X 7.44 % Y 13.16 %

Requirement 2:Calculate the variances for X and Y. (Do not round intermediate calculations. Round your answers to6 decimal places (e.g., 32.161616).)

Variances X 0.022338 Y 0.040708

Requirement 3:Calculate the standard deviations for X and Y. (Do not round intermediate calculations. Enter youranswers as a percentage rounded to 2 decimal places (e.g., 32.16).)

Standard deviations X 14.95 % Y 20.18 %

Worksheet Problem 10-7 Calculating Returns andVariability [LO 1]Learning Objective: 10-01 Calculate thereturn on an investment.

Problem 10-7 Calculating Returns and Variability [LO 1]Use the following returns for X and Y.

ReturnsYear X Y

1 21.3% 24.9%2 16.3 3.33 9.3 26.94 18.6 13.6



5 4.3 30.9

Requirement 1:Calculate the average returns for X and Y. (Do not round intermediate calculations. Enter youranswers as a percentage rounded to 2 decimal places (e.g., 32.16).)

Average returns

X 7.44 1% %

Y 13.16 1% %

Requirement 2:Calculate the variances for X and Y. (Do not round intermediate calculations. Round your answers to6 decimal places (e.g., 32.161616).)

Variances

X 0.022339 0.00001

Y 0.040709 0.00001

Requirement 3:Calculate the standard deviations for X and Y. (Do not round intermediate calculations. Enter youranswers as a percentage rounded to 2 decimal places (e.g., 32.16).)

Standard deviations X 14.95 1% % Y 20.18 1% %

Explanation:

1:The average return is the sum of the returns, divided by the number of returns. The average return for eachstock was:

2:Remembering back to "sadistics," we calculate the variance of each stock as:

3:The standard deviation is the square root of the variance, so the standard deviation of each stock is:

X = (.022339)1/2sX = .1495, or 14.95%

Y = (.040709)1/2Y = .2018, or 20.18%

Problem 10-8 Risk Premiums [LO 2]Consider the following table for a period of six years.

Returns

YearLarge-Company

StocksU.S.

Treasury BillsYear 1 15.89% 7.53%Year 2 26.83 8.11Year 3 37.47 6.11Year 4 24.17 6.27Year 5 7.64 5.57Year 6 6.81 8.00

Requirement 1:Calculate the arithmetic average returns for large-company stocks and T-bills over this time period. (Donot round intermediate calculations. Enter your answers as a percentage rounded to 2decimal places (e.g., 32.16).)

Arithmetic averagereturns

Large-company stock 3.02 % T-bills 6.93 %

Requirement 2:Calculate the standard deviation of the returns for large-company stocks and T-bills over this time period.(Do not round intermediate calculations. Enter your answers as a percentage rounded to 2decimal places (e.g., 32.16).)

Standard deviation Large-company stock 24.45 % T-bills 1.08 %

Requirement 3:Calculate the observed risk premium in each year for the large-company stocks versus the T-bills.

(a) What was the arithmetic average risk premium over this period? (Negative amount should beindicated by a minus sign. Do not round intermediate calculations. Enter your answer as apercentage rounded to 2 decimal places (e.g., 32.16).)

Risk premium -3.92 %

(b) What was the standard deviation of the risk premium over this period? (Do not round intermediatecalculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Risk premium standard deviation 25.13 %

Worksheet Problem 10-8 Risk Premiums [LO 2]Learning Objective: 10-02 Discuss thehistorical returns on various important typesof investments.

Problem 10-8 Risk Premiums [LO 2]Consider the following table for a period of six years.

Returns

YearLarge-Company

StocksU.S.

Treasury BillsYear 1 15.89% 7.53%Year 2 26.83 8.11Year 3 37.47 6.11Year 4 24.17 6.27Year 5 7.64 5.57Year 6 6.81 8.00

Requirement 1:Calculate the arithmetic average returns for large-company stocks and T-bills over this time period. (Donot round intermediate calculations. Enter your answers as a percentage rounded to 2decimal places (e.g., 32.16).)

Arithmetic averagereturns

Large-company stock 3.02 1% % T-bills 6.93 1% %

Requirement 2:Calculate the standard deviation of the returns for large-company stocks and T-bills over this time period.(Do not round intermediate calculations. Enter your answers as a percentage rounded to 2decimal places (e.g., 32.16).)

Standard deviation Large-company stock 24.54 1% % T-bills 1.08 1% %

Requirement 3:Calculate the observed risk premium in each year for the large-company stocks versus the T-bills.

(a) What was the arithmetic average risk premium over this period? (Negative amount should beindicated by a minus sign. Do not round intermediate calculations. Enter your answer as apercentage rounded to 2 decimal places (e.g., 32.16).)

Risk premium -3.92 1% %

(b) What was the standard deviation of the risk premium over this period? (Do not round intermediatecalculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Risk premium standard deviation 25.13 1% %

Explanation:

We will calculate the sum of the returns for each asset and the observed risk premium first. Doing so, weget:

Year Large co. stock return T-bill return Risk premium 1973 15.89% 7.53% 23.42% 1974 26.83 8.11 34.94 1975 37.47 6.11 31.36 1976 24.17 6.27 17.90 1977 7.64 5.57 13.21 1978 6.81 8.00 1.19

Total 18.09% 41.59% 23.50%

1:The average return for large-company stocks over this period was:

Large-company stock average return = 18.09% / 6Large-company stock average return = 3.02%

And the average return for T-bills over this period was:

T-bills average return = 41.59% / 6

T-bills average return = 6.93%

2:Using the equation for variance, we find the variance for large company stocks over this period was:

Variance = 1/5[(.1589 .0302)2 + (.2683 .0302)2 + (.3747 .0302)2 + (.2417 .0302)2 + (.0764 .0302)2 + (.0681 .0302)2]

Variance = .060215

And the standard deviation for largecompany stocks over this period was:

Standard deviation = (.060215)1/2Standard deviation = .2454, or 24.54%

Using the equation for variance, we find the variance for T-bills over this period was:

Variance = 1/5[(.0753 .0693)2 + (.0811 .0693)2 + (.0611 .0693)2 + (.0627 .0693)2 + (.0557 .0693)2 + (.0800 .0693)2]Variance = .000117

And the standard deviation for T-bills over this period was:


3:(a)The average observed risk premium over this period was:

Average observed risk premium = 23.50% / 6Average observed risk premium = 3.92%

(b)The variance of the observed risk premium was:

Variance = 1/5[(.2342 (.0392))2 + (.3494 (.0392))2 + (.3136 (.0392))2 + (.1790 (.0392))2 + (.1321 (.0392))2 + (.0119 (.0392))2]Variance = .063141

And the standard deviation of the observed risk premium was:




5.award:0.50 out of1.00 point

Problem 10-10 Calculating Real Returns and Risk Premiums [LO 1]Youve observed the following returns on Doyscher Corporations stock over the past five years: 29.1percent, 16.4 percent, 35.8 percent, 3.7 percent, and 22.7 percent. The average inflation rate over thisperiod was 3.37 percent and the average T-bill rate over the period was 4.3 percent.

Required:(a) What was the average real return on the stock? (Do not round intermediate calculations. Enter

your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Average real return 6.32 %

(b) What was the average nominal risk premium on the stock? (Do not round intermediatecalculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Average nominal risk premium 5.60 %

Worksheet Problem 10-10 Calculating Real Returns andRisk Premiums [LO 1]Learning Objective: 10-01 Calculate thereturn on an investment.

Problem 10-10 Calculating Real Returns and Risk Premiums [LO 1]Youve observed the following returns on Doyscher Corporations stock over the past five years: 29.1percent, 16.4 percent, 35.8 percent, 3.7 percent, and 22.7 percent. The average inflation rate over thisperiod was 3.37 percent and the average T-bill rate over the period was 4.3 percent.

Required:(a) What was the average real return on the stock? (Do not round intermediate calculations. Enter

your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Average real return 6.32 1% %

(b) What was the average nominal risk premium on the stock? (Do not round intermediatecalculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Average nominal risk premium 5.60 1% %

Explanation:

To find the average return, we sum all the returns and divide by the number of returns, so:

Arithmetic average return = (.291 + .164 + .358 + .037 + .227)/5Arithmetic average return = .0990, or 9.90%

(a)To calculate the average real return, we can use the average return of the asset, and the average inflationrate in the Fisher equation. Doing so, we find:

(1 + R) = (1 + r)(1 + h)

= (1.0990 / 1.0337) 1 = .0632, or 6.32%

(b)The average risk premium is simply the average return of the asset, minus the average risk-free rate, so,the average risk premium for this asset would be:

= .0990 .043 = .0560, or 5.60%

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Problem 10-11 Calculating Real Rates [LO 1]Youve observed the following returns on Doyscher Corporations stock over the past five years: 25.2percent, 13.8 percent, 30.6 percent, 2.4 percent, and 21.4 percent. The average inflation rate over thisperiod was 3.24 percent and the average T-bill rate over the period was 4.3 percent.

Requirement 1:What was the average real risk-free rate over this time period? (Do not round intermediate calculations.Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Average real risk-free rate 1.03 %

Requirement 2:What was the average real risk premium? (Do not round intermediate calculations. Enter your answeras a percentage rounded to 2 decimal places (e.g., 32.16).)

Average real risk premium n/r %

Worksheet Problem 10-11 Calculating Real Rates [LO 1] Learning Objective: 10-01 Calculate thereturn on an investment.

Problem 10-11 Calculating Real Rates [LO 1]Youve observed the following returns on Doyscher Corporations stock over the past five years: 25.2percent, 13.8 percent, 30.6 percent, 2.4 percent, and 21.4 percent. The average inflation rate over thisperiod was 3.24 percent and the average T-bill rate over the period was 4.3 percent.

Requirement 1:What was the average real risk-free rate over this time period? (Do not round intermediate calculations.Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Average real risk-free rate 1.03 0.01 %

Requirement 2:What was the average real risk premium? (Do not round intermediate calculations. Enter your answeras a percentage rounded to 2 decimal places (e.g., 32.16).)

Average real risk premium 4.17 1% %

Explanation:

1:We can find the average real risk-free rate using the Fisher equation. The average real risk-free rate was:

(1 + R) = (1 + r)(1 + h)

= (1.0430 / 1.0324) 1 = .0103, or 1.03%

2:To find the average return, we sum all the returns and divide by the number of returns, so:

Arithmetic average return = (.252 + .138 + .306 + .024 + .214)/5Arithmetic average return = .0860, or 8.60%

To calculate the average real return, we can use the average return of the asset, and the average inflationrate in the Fisher equation. Doing so, we find:

(1 + R) = (1 + r)(1 + h)

= (1.0860 / 1.0324) 1 = .0519, or 5.19%

And to calculate the average real risk premium, we can subtract the average risk-free rate from theaverage real return. So, the average real risk premium was:



Problem 10-15 Calculating Returns [LO 1]You bought a stock three months ago for $77.82 per share. The stock paid no dividends. The current shareprice is $82.09.

Required:What is the APR and EAR of your investment? (Do not round intermediate calculations. Enter youranswers as a percentage rounded to 2 decimal places (e.g., 32.16).)

Investment APR 21.95 % EAR 23.82 %

Worksheet Problem 10-15 Calculating Returns [LO 1] Learning Objective: 10-01 Calculate thereturn on an investment.

Problem 10-15 Calculating Returns [LO 1]You bought a stock three months ago for $77.82 per share. The stock paid no dividends. The current shareprice is $82.09.

Required:What is the APR and EAR of your investment? (Do not round intermediate calculations. Enter youranswers as a percentage rounded to 2 decimal places (e.g., 32.16).)

Investment APR 21.95 1% % EAR 23.82 1% %

Explanation:

The return of any asset is the increase in price, plus any dividends or cash flows, all divided by the initialprice. This stock paid no dividend, so the return was:

R = ($82.09 77.82) / $77.82R = .0549, or 5.49%

This is the return for three months, so the APR is:

APR = 4(5.49%)APR = 21.95%

And the EAR is:

EAR = (1 + .0549)4 1EAR = .2382, or 23.82%



Problem 10-19 Calculating Returns and Variability [LO1]You find a certain stock that had returns of 12.8 percent, 21.4 percent, 27.4 percent, and 18.4 percent forfour of the last five years. Assume the average return of the stock over this period was 10.80 percent.

Requirement 1:What was the stocks return for the missing year? (Do not round intermediate calculations. Enter youranswer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Stock's return 16.80 %

Requirement 2:What is the standard deviation of the stocks returns? (Do not round intermediate calculations. Enteryour answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Standard deviation 18.77 %

Worksheet Problem 10-19 Calculating Returns andVariability [LO1]Learning Objective: 10-01 Calculate thereturn on an investment.

Problem 10-19 Calculating Returns and Variability [LO1]You find a certain stock that had returns of 12.8 percent, 21.4 percent, 27.4 percent, and 18.4 percent forfour of the last five years. Assume the average return of the stock over this period was 10.80 percent.

Requirement 1:What was the stocks return for the missing year? (Do not round intermediate calculations. Enter youranswer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Stock's return 16.80 1%%

Requirement 2:What is the standard deviation of the stocks returns? (Do not round intermediate calculations. Enteryour answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Standard deviation 18.78 1%%

Explanation:

Here, we know the average stock return, and four of the five returns used to compute the average return.We can work the average return equation backward to find the missing return. The average return iscalculated as:

.1080 = (.128 .214 + .274 + .184 + R) / 5

.54 = .128 .214 + .274 + .184 + RR = .1680, or 16.80%

The missing return has to be 16.80 percent. Now we can use the equation for the variance to find:

Variance = 1/4[(.128 .1080)2 + (.214 .1080)2 + (.274 .1080)2 + (.184 .1080)2 + (.168 .1080)2]Variance = .035254

And the standard deviation is:

Standard deviation = (.035254)1/2 = .1878, or 18.78%





Problem 10-20 Arithmetic and Geometric Returns [LO 1]A stock has had returns of 18.2 percent, 28.2 percent, 14.4 percent, 9.3 percent, 34.0 percent, and 26.2percent over the last six years.

Required:What are the arithmetic and geometric returns for the stock? (Do not round intermediate calculations.Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

Arithmetic average return 12.55 % Geometric average return 10.70 %

Worksheet Problem 10-20 Arithmetic and GeometricReturns [LO 1]Learning Objective: 10-01 Calculate thereturn on an investment.

Problem 10-20 Arithmetic and Geometric Returns [LO 1]A stock has had returns of 18.2 percent, 28.2 percent, 14.4 percent, 9.3 percent, 34.0 percent, and 26.2percent over the last six years.

Required:What are the arithmetic and geometric returns for the stock? (Do not round intermediate calculations.Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

Arithmetic average return 12.55 1% % Geometric average return 10.70 1% %

Explanation:

The arithmetic average return is the sum of the known returns divided by the number of returns, so:

Arithmetic average return = (.182 + .282 + .144 .093 + .340 +.262) / 6Arithmetic average return = .1255, or 12.55%

Using the equation for the geometric return, we find:

Geometric average return = [(1 + R1) (1 + R2) (1 + RT)]1/T 1Geometric average return = [(1 .182)(1 + .282)(1 + .144)(1 .093)(1 + .340)(1 + .262)](1/6) 1Geometric average return = .1070, or 10.70%

Remember, the geometric average return will always be less than the arithmetic average return if thereturns have any variation.

Problem 10-22 Calculating Returns [LO 2,3]Consider the following table for an eight-year period:

Year T-bill return Inflation Year 1 7.45% 8.55% Year 2 8.84 12.18 Year 3 6.03 6.78 Year 4 5.87 5.02 Year 5 5.61 6.54 Year 6 8.44 8.86 Year 7 10.72 13.13 Year 8 12.90 12.36

Requirement 1:Calculate the average return for Treasury bills and the average annual inflation rate (consumer price index)

for this period. (Do not round intermediate calculations. Enter your answers as a percentage roundedto 2 decimal places (e.g., 32.16).)

Average return for Treasury bills 8.23 % Average annual inflation rate 9.18 %

Requirement 2:Calculate the standard deviation of Treasury bill returns and inflation over this time period. (Do not roundintermediate calculations. Enter your answers as a percentage rounded to 2 decimal places (e.g.,32.16).)

Standard deviation of Treasury bills 2.57 % Standard deviation of inflation 3.05 %

Requirement 3:(a) Calculate the real return for each year. (Negative amounts should be indicated by a minus

sign. Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediatecalculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

Year Real returnYear 1 -1.01 % Year 2 -2.98 % Year 3 -0.70 % Year 4 0.81 % Year 5 -0.87 % Year 6 -0.39 % Year 7 -2.13 % Year 8 0.48 %

(b) What is the average real return for Treasury bills? (Negative amount should be indicated by a minussign. Do not round intermediate calculations. Enter your answer as a percentagerounded to 2 decimal places (e.g., 32.16).)

Average real return for Treasury bills -0.85 %

WorksheetLearning Objective: 10-02 Discuss thehistorical returns on various important typesof investments.

Problem 10-22 Calculating Returns [LO 2,3]Learning Objective: 10-03 Explain thehistorical risks on various important types ofinvestments.

Problem 10-22 Calculating Returns [LO 2,3]Consider the following table for an eight-year period:

Year T-bill return Inflation Year 1 7.45% 8.55% Year 2 8.84 12.18 Year 3 6.03 6.78 Year 4 5.87 5.02 Year 5 5.61 6.54 Year 6 8.44 8.86 Year 7 10.72 13.13 Year 8 12.90 12.36

Requirement 1:Calculate the average return for Treasury bills and the average annual inflation rate (consumer price index)for this period. (Do not round intermediate calculations. Enter your answers as a percentage roundedto 2 decimal places (e.g., 32.16).)

Average return for Treasury bills 8.23 1% % Average annual inflation rate 9.18 1% %

Requirement 2:Calculate the standard deviation of Treasury bill returns and inflation over this time period. (Do not roundintermediate calculations. Enter your answers as a percentage rounded to 2 decimal places (e.g.,32.16).)

Standard deviation of Treasury bills 2.57 1% %

Standard deviation of inflation 3.05 1% %

Requirement 3:(a) Calculate the real return for each year. (Negative amounts should be indicated by a minus

sign. Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediatecalculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

Year Real returnYear 1 -1.01 0.01 % Year 2 -2.98 0.01 % Year 3 -0.70 0.01 % Year 4 0.81 0.01 % Year 5 -0.87 0.01 % Year 6 -0.39 0.01 % Year 7 -2.13 0.01 % Year 8 0.48 0.01 %

(b) What is the average real return for Treasury bills? (Negative amount should be indicated by a minussign. Do not round intermediate calculations. Enter your answer as a percentagerounded to 2 decimal places (e.g., 32.16).)

Average real return for Treasury bills -0.85 0.01 %

Explanation:

To find the real return we need to use the Fisher equation. Re-writing the Fisher equation to solve for thereal return, we get:

r = [(1 + R)/(1 + h)] 1

So, the real return each year was:Year T-bill return Inflation Real return

Year 1 .0745 .0855 .0101 Year 2 .0884 .1218 .0298 Year 3 .0603 .0678 .0070 Year 4 .0587 .0502 .0081 Year 5 .0561 .0654 .0087 Year 6 .0844 .0886 .0039 Year 7 .1072 .1313 .0213 Year 8 .1290 .1236 .0048

.6586 .7342 .0679

1:

The average return for T-bills over this period was:

Average return = .6586 / 8Average return = .0823, or 8.23%

And the average inflation rate was:

Average inflation = .7342 / 8Average inflation = .0918, or 9.18%

2:

Using the equation for variance, we find the variance for T-bills over this period was:

Variance = 1/7[(.0745 .0823)2 + (.0884 .0823)2 + (.0603 .0823)2 + (.0587 .0823)2 + (.0561 .0823)2+ (.0844 .0823)2 + (.1072 .0823)2 + (.1290 .0823)2]Variance = .000662

And the standard deviation for T-bills was:


The variance of inflation over this period was:





Variance = 1/7[(.0855 .0918)2 + (.1218 .0918)2 + (.0678 .0918)2 + (.0502 .0918)2 + (.0654 .0918)2 + (.0886 .0918)2 + (.1313 .0918)2 + (.1236 .0918)2]Variance = .000932

And the standard deviation of inflation was:


3:

The average observed real return over this period was:Average observed real return = .0679 / 8Average observed real return = .0085, or .85%

Problem 10-3 Calculating Dollar Returns [LO 1]You purchased 330 shares of a particular stock at the beginning of the year at a price of $75.93. The stockpaid a dividend of $1.25 per share, and the stock price at the end of the year was $82.44.

Required:What was your dollar return on this investment? (Do not round intermediate calculations. Round youranswer to 2 decimal places (e.g., 32.16).)

Dollar return $ 2,560.80

Worksheet Problem 10-3 Calculating Dollar Returns [LO1]Learning Objective: 10-01 Calculate thereturn on an investment.

Problem 10-3 Calculating Dollar Returns [LO 1]You purchased 330 shares of a particular stock at the beginning of the year at a price of $75.93. The stockpaid a dividend of $1.25 per share, and the stock price at the end of the year was $82.44.

Required:What was your dollar return on this investment? (Do not round intermediate calculations. Round youranswer to 2 decimal places (e.g., 32.16).)

Dollar return $ 2,560.80 .1%

Explanation:

To calculate the dollar return, we multiply the number of shares owned by the change in price per shareand the dividend per share received. The total dollar return is:

Dollar return = 330($82.44 75.93 + 1.25)Dollar return = $2,560.80

Problem 10-5 Nominal versus Real Returns [LO 2]Consider the following information on large-company stocks for a period of years.

Series Arithmetic Mean Large-company stocks 12.7% Small-company stocks 16.4 Long-term corporate bonds 6.2 Long-term government bonds 6.1



Intermediate-term governmentbonds 5.6 U.S. Treasury bills 3.8 Inflation 3.3

Required:(a) What was the arithmetic average annual return on large-company stocks in nominal terms? (Do not

round intermediate calculations. Enter your answer as a percentage rounded to 2decimal places (e.g., 32.16).)

Nominal return 12.70 %

(b) What was the arithmetic average annual return on large-company stocks in real terms? (Do not roundintermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g.,32.16).)

Real return 9.10 %

Worksheet Problem 10-5 Nominal versus Real Returns[LO 2]Learning Objective: 10-02 Discuss thehistorical returns on various important typesof investments.

Problem 10-5 Nominal versus Real Returns [LO 2]Consider the following information on large-company stocks for a period of years.

Series Arithmetic Mean Large-company stocks 12.7% Small-company stocks 16.4 Long-term corporate bonds 6.2 Long-term government bonds 6.1 Intermediate-term governmentbonds 5.6 U.S. Treasury bills 3.8 Inflation 3.3

Required:(a) What was the arithmetic average annual return on large-company stocks in nominal terms? (Do not

round intermediate calculations. Enter your answer as a percentage rounded to 2decimal places (e.g., 32.16).)

Nominal return 12.70 1% %

(b) What was the arithmetic average annual return on large-company stocks in real terms? (Do not roundintermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g.,32.16).)

Real return 9.10 1% %

Explanation:

(a)The nominal return is the stated return, which is 12.7 percent.

(b)Using the Fisher equation, the real return was:

(1 + R) = (1 + r)(1 + h)

r = (1.1270) / (1.033) 1r = .0910, or 9.10%

Problem 10-6 Bond Returns [LO 2]Consider the following information for a period of years.

Series Arithmetic Mean Large-company stocks 11.7 % Small-company stocks 16.4 Long-term corporate bonds 6.7 Long-term government bonds 6.6 Intermediate-term government bonds 5.6 U.S. Treasury bills 3.8 Inflation 3.3

Requirement 1:What is the real return on long-term government bonds? (Do not round intermediate calculations. Enteryour answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Real return 3.20 %

Requirement 2:What is the real return on long-term corporate bonds? (Do not round intermediate calculations. Enteryour answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Real return 3.29 %

Worksheet Problem 10-6 Bond Returns [LO 2]Learning Objective: 10-02 Discuss thehistorical returns on various important typesof investments.

Problem 10-6 Bond Returns [LO 2]Consider the following information for a period of years.

Series Arithmetic Mean Large-company stocks 11.7 % Small-company stocks 16.4 Long-term corporate bonds 6.7 Long-term government bonds 6.6 Intermediate-term government bonds 5.6 U.S. Treasury bills 3.8 Inflation 3.3

Requirement 1:What is the real return on long-term government bonds? (Do not round intermediate calculations. Enteryour answer as a percentage rounded to 2 decimal places (e.g., 32.16).)


Requirement 2:What is the real return on long-term corporate bonds? (Do not round intermediate calculations. Enteryour answer as a percentage rounded to 2 decimal places (e.g., 32.16).)


Explanation:

Using the Fisher equation, the real returns for government and corporate bonds were:

(1 + R) = (1 + r)(1 + h)

1:rG = 1.066 / 1.033 1rG = .0319, or 3.19%

2:rC = 1.067 / 1.033 1rC = .0329, or 3.29%



Problem 10-17 Return Distributions [LO 3]Consider the following table for the total annual returns for a given period of time.

Series Average return Standard Deviation Large-company stocks 11.7 % 20.6% Small-company stocks 16.4 33.0 Long-term corporate bonds 6.3 9.6 Long-term government bonds 6.1 9.4 Intermediate-term government bonds 5.6 5.7 U.S. Treasury bills 3.8 3.1 Inflation 3.1 4.2

Requirement 1:What range of returns would you expect to see 95 percent of the time for long-term corporate bonds?(Negative amount should be indicated by a minus sign. Input your answers from lowest to highestto receive credit for your answers. Do not round intermediate calculations. Enter your answers as apercentage rounded to 2 decimal places (e.g., 32.16).)

Expected range of returns -12.90 % to 25.30 %

Requirement 2:What about 99 percent of the time? (Negative amount should be indicated by a minus sign. Inputyour answers from lowest to highest to receive credit for your answers. Do not round intermediatecalculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

Expected range of returns -22.50 % to 35.10 %

Worksheet Problem 10-17 Return Distributions [LO 3]Learning Objective: 10-03 Explain thehistorical risks on various important types ofinvestments.

Problem 10-17 Return Distributions [LO 3]Consider the following table for the total annual returns for a given period of time.

Series Average return Standard Deviation Large-company stocks 11.7 % 20.6% Small-company stocks 16.4 33.0 Long-term corporate bonds 6.3 9.6 Long-term government bonds 6.1 9.4 Intermediate-term government bonds 5.6 5.7 U.S. Treasury bills 3.8 3.1 Inflation 3.1 4.2

Requirement 1:What range of returns would you expect to see 95 percent of the time for long-term corporate bonds?(Negative amount should be indicated by a minus sign. Input your answers from lowest to highestto receive credit for your answers. Do not round intermediate calculations. Enter your answers as apercentage rounded to 2 decimal places (e.g., 32.16).)

Expected range ofreturns -12.90 1% % to 25.50 1% %

Requirement 2:What about 99 percent of the time? (Negative amount should be indicated by a minus sign. Inputyour answers from lowest to highest to receive credit for your answers. Do not round intermediatecalculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

Expected range ofreturns -22.50 1% % to 35.10 1% %

Explanation:

Looking at the long-term corporate bond return history, we see that the mean return was 6.3 percent, witha standard deviation of 9.6 percent. The range of returns you would expect to see 95 percent of the time is


You did not receive credit for this question in a previous attempt

the mean plus or minus 2 standard deviations, or:

R 2 = 6.3% 2(9.6%) = 12.90% to 25.50%

The range of returns you would expect to see 99 percent of the time is the mean plus or minus 3 standarddeviations, or:

R 3 = 6.3% 3(9.6%) = 22.50% to 35.10%

Problem 10-23 Calculating Investment Returns [LO 1]You bought one of Rocky Mountain Manufacturing Co.s 8.25 percent coupon bonds one year ago for$1,045.80. These bonds make annual payments and mature ten years from now. Suppose that you decideto sell your bonds today, when the required return on the bonds is 7.75 percent.

Required:If the inflation rate was 3.6 percent over the past year, what would be your total real return on investment?(Do not round intermediate calculations. Enter your answer as a percentage rounded to 2decimal places (e.g., 32.16).)

Total real return on investment n/r %

Worksheet Problem 10-23 Calculating InvestmentReturns [LO 1]Learning Objective: 10-01 Calculate thereturn on an investment.

Problem 10-23 Calculating Investment Returns [LO 1]You bought one of Rocky Mountain Manufacturing Co.s 8.25 percent coupon bonds one year ago for$1,045.80. These bonds make annual payments and mature ten years from now. Suppose that you decideto sell your bonds today, when the required return on the bonds is 7.75 percent.

Required:If the inflation rate was 3.6 percent over the past year, what would be your total real return on investment?(Do not round intermediate calculations. Enter your answer as a percentage rounded to 2decimal places (e.g., 32.16).)

Total real return on investment 3.04 1% %

Explanation:

To find the return on the coupon bond, we first need to find the price of the bond today. Since the bond has10 years to maturity, the price today is:

P1 = $82.50(PVIFA7.75%,10) + $1,000 / 1.077510P1 = $1,033.93

You received the coupon payments on the bond, so the nominal return was:

R = ($1,033.93 1,045.80 + 82.50) / $1,045.80R = .0675, or 6.75%

And using the Fisher equation to find the real return, we get:

r = (1.0675 / 1.036) 1r = 0.0304, or 3.04%

Chapter 10 - Connect Plus

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