Top hedge fund manager Sally Buffit believes that a stock with the same market risk as the S&P 500 will sell at year-end at a price of $47. The stock will pay a dividend at year-end of $2.00. Assume that risk-free Treasury securities currently offer an interest rate of 2.3%.

Average rates of return on Treasury bills, government bonds, and common stocks, 19002017 (figures in percent per year) are as follows.

Portfolio

Average Annual Rate of Return (%)

Average Premium (Extra return versus Treasury bills) (%)

Treasury bills

3.8

Treasury bonds

5.3

1.5

Common stocks

11.5

7.7

a. What is the discount rate on the stock? (Enter your answer as a percent rounded to 2 decimal places.)

b. What price should she be willing to pay for the stock today? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Assume these are the stock market and Treasury bill returns for a 5-year period:

Year

Stock Market Return (%)

T-Bill Return (%)

2013

35.90

0.21

2014

15.20

0.21

2015

5.10

0.21

2016

16.90

0.08

2017

25.90

0.10

Required:

a. What was the risk premium on common stock in each year?

b. What was the average risk premium?

c. What was the standard deviation of the risk premium? (Ignore that the estimation is from a sample of data.)

A stock is selling today for $25 per share. At the end of the year, it pays a dividend of $2 per share and sells for $28.

Required:

a. What is the total rate of return on the stock?

b. What are the dividend yield and percentage capital gain?

c. Now suppose the year-end stock price after the dividend is paid is $21. What are the dividend yield and percentage capital gain in this case?

You purchase 100 shares of stock for $50 a share. The stock pays a $2 per share dividend at year-end.

a. What is the rate of return on your investment if the end-of-year stock price is (i) $48; (ii) $50; (iii) $55? (Leave no cells blank - be certain to enter "0" wherever required. Enter your answers as a whole percent.)

b. What is your real (inflation-adjusted) rate of return if the inflation rate is 3%? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Negative amounts should be indicated by a minus sign.)

Consider the following scenario analysis:

Rate of Return

Scenario

Probability

Stocks

Bonds

Recession

0.20

6

%

18

%

Normal economy

0.50

19

%

11

%

Boom

0.30

26

%

8

%

a. Is it reasonable to assume that Treasury bonds will provide higher returns in recessions than in booms?

multiple choice

No

Yes

b. Calculate the expected rate of return and standard deviation for each investment. (Do not round intermediate calculations. Enter your answers as a percent rounded to 1 decimal place.)

c. Which investment would you prefer?

In a recent 5-year period, mutual fund manager Diana Sauros produced the following percentage rates of return for the Mesozoic Fund. Rates of return on the market index are given for comparison.

1

2

3

4

5

Fund

1.2

+23.8

+41.7

+10.7

+0.3

Market index

0.8

+14.0

+31.2

+9.7

0.6

a. Calculate (a) the average return on both the Fund and the index, and (b) the standard deviation of the returns on each. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

b. Did Ms. Sauros do better or worse than the market index on these measures?

Consider the following scenario analysis:

Rate of Return

Scenario

Probability

Stocks

Bonds

Recession

0.2

-5

%

17

%

Normal economy

0.5

18

11

Boom

0.3

23

4

Assume a portfolio with weights of 0.60 in stocks and 0.40 in bonds.

a. What is the rate of return on the portfolio in each scenario? (Enter your answer as a percent rounded to 1 decimal place.)

b. What are the expected rate of return and standard deviation of the portfolio? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Here are the returns on two stocks.

Digital Cheese

Executive Fruit

January

+17

+7

February

3

+2

March

+5

+4

April

+7

+15

May

4

+3

June

+3

+5

July

2

3

August

8

2

Required:

a-1. Calculate the variance and standard deviation of each stock.

a-2. Which stock is riskier if held on its own?

b. Now calculate the returns in each month of a portfolio that invests an equal amount each month in the two stocks.

c. Is the variance more or less than halfway between the variance of the two individual stocks?

rev: 05_06_2020_QC_CS-211110

A stock with a beta of 1.1 has an expected rate of return of 12%. If the market return this year turns out to be 9 percentage points below expectations, what is your best guess as to the rate of return on the stock? (Do not round intermediate calculations. Enter your answer as a percent rounded to 1 decimal place.)

10

1.76points

Item 10

The risk-free rate is 7% and the expected rate of return on the market portfolio is 11%.

a. Calculate the required rate of return on a security with a beta of 1.92. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

b. If the security is expected to return 15%, is it overpriced or underpriced?

multiple choice

Overpriced

Underpriced

11

1.76points

Item 11

Consider the following two scenarios for the economy and the expected returns in each scenario for the market portfolio, an aggressive stock A, and a defensive stock D.

Rate of Return

Scenario

Market

Aggressive Stock A

Defensive Stock D

Bust

8

%

10

%

6

%

Boom

27

41

20

Required: a. Find the beta of each stock. b. If each scenario is equally likely, find the expected rate of return on the market portfolio and on each stock. c. If the T-bill rate is 5%, what does the CAPM say about the fair expected rate of return on the two stocks? d. Which stock seems to be a better buy on the basis of your answers to (a) through (c)?

12

1.76points

Item 12

A share of stock with a beta of 0.81 now sells for $56. Investors expect the stock to pay a year-end dividend of $4. The T-bill rate is 4%, and the market risk premium is 7%. If the stock is perceived to be fairly priced today, what must be investors expectation of the price of the stock at the end of the year? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Suppose that the S&P 500, with a beta of 1.0, has an expected return of 15% and T-bills provide a risk-free return of 6%.

a. What would be the expected return and beta of portfolios constructed from these two assets with weights in the S&P 500 of (i) 0; (ii) 0.25; (iii) 0.50; (iv) 0.75; (v) 1.0? (Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations. Enter the value of Expected return as a percentage rounded to 2 decimal places and value of Beta rounded to 2 decimal places.)

b. How does expected return vary with beta? (Do not round intermediate calculations.)

The Treasury bill rate is 7%, and the expected return on the market portfolio is 11%. According to the capital asset pricing model:

a. What is the risk premium on the market? b. What is the required return on an investment with a beta of 1.6? (Do not round intermediate calculations. Enter your answer as a percent rounded to 1 decimal place.) c. If an investment with a beta of 0.9 offers an expected return of 9.2%, does it have a positive or negative NPV? d. If the market expects a return of 11.8% from stock X, what is its beta? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

15

1.76points

Item 15

A project under consideration has an internal rate of return of 13% and a beta of 0.4. The risk-free rate is 3%, and the expected rate of return on the market portfolio is 13%.

a. What is the required rate of return on the project? (Do not round intermediate calculations. Enter your answer as a whole percent.)

b. Should the project be accepted?

c. What is the required rate of return on the project if its beta is 1.50? (Do not round intermediate calculations. Enter your answer as a whole percent.)

d. If project's beta is 1.50, should the project be accepted?

16

1.76points

Item 16

The Treasury bill rate is 4% and the market risk premium is 8%.

Project

Beta

Internal Rate of Return, %

P

0.65

10

Q

0.00

10

R

1.00

12

S

0.05

11

T

0.60

14

a. What are the project costs of capital for new ventures with betas of 0.40 and 1.78? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

b. Which of the capital investments shown above have positive (non-zero) NPV's? (You may select more than one answer. Single click the box with the question mark to produce a check mark for a correct answer and double click the box with the question mark to empty the box for a wrong answer.)

check all that apply

Project Punanswered

Project Qunanswered

Project Sunanswered

Project Tunanswered

Project Runanswered

17

1.84points

Item 17

You are considering the purchase of real estate that will provide perpetual income that should average $66,000 per year. How much will you pay for the property if you believe its market risk is the same as the market portfolios? The T-bill rate is 4%, and the expected market return is 11.0%.