Posted: March 29th, 2022

# Module 1 – case present value and the risk/return trade-off

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## Module 1 – Case

### Present Value and the Risk/Return Trade-Off

#### Assignment Overview

For this assignment, make sure to first carefully review all of the required readings about present value, future value, risk and return, and the CAPM. Once you are relatively comfortable with these concepts, try working through some of the examples in the background readings and try computing the answers on your own. Once you are confident you both understand the concepts and the computational steps, complete the assignment below.

#### Case Assignment

Present your answers to the problem below in a Word document, and also upload an Excel file with your computations. Excel is required for Questions 2 and 3. Excel is optional for Questions 1 and 4, but you are required to show your steps for all quantitative problems. Even if you get the answer wrong, you can still get partial credit if you show your work.

1. Calculate the following:
1. Suppose you wish to raise some money for your favorite local charity. This charity needs \$50,000 a year to run its operation and you want to make sure that it is ensured an annual payment of this amount from now on for every year in the foreseeable future. Given an interest rate of 5%, how much would you have to fund this perpetuity to guarantee the charity a payment of \$50,000 per year?
2. You decide to put \$1,000 in a new bank account and don’t plan to withdraw the money for 10 years. If your bank does continuous compounding and the interest rate is 1%, what will be the value of this bank account in 10 years?
2. Suppose you won the lottery but not all of your winnings will come in one year. Instead, you will get a series of annual payments over the next five years. The table below tells you what your payment will be every year for the next five years. Use the information in the table to make the following computations:
1. The present and future value of your lottery ticket if the interest rate is 8%
2. The present and future value of your lottery ticket if the interest rate is 10%

Year

Payment

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1

5000

2

6000

3

7000

4

8000

5

9000

1. The table below gives the probability of different returns for three different assets. Using this table, calculate the following:
1. The expected return of each asset
2. The standard deviation of returns of each asset
3. The coefficient of variation of each asset
4. Based on your answers to B) and C) above, which asset has the highest total risk and highest relative risk?

Asset A

Asset B

Asset C

Probability

Return

Probability

Return

Probability

Return

0.3

5

0.1

25

0.1

4

0.4

8

0.3

20

0.8

5

0.3

9

0.5

15

0.1

6

0.1

14

1. Suppose the market return is 8%, the risk-free rate is 1% and the beta for a given stock is 1.2. Answer the following questions based on this information:
1. What is the required return for this stock?
2. If the beta increases by 50% (but beta remains at 1.2), what will be the new required return for the stock? What is the percentage-wise change in required return compared to your answer to A) above?
3. If the market return increases by 50% (but beta remains at 1.2), what will be the new required return for the stock? What is the percentage-wise change in required return compared to your answer to A) above?
2. Suppose there are three different companies. The first one, Trendy Tech Inc., has investors who are “fair-weather friends.” When the stock market is going up, everybody wants to invest in Trendy Tech, but as soon as the market goes down everyone jumps ships and sells their shares. The second company is Oily Oil Inc. Oily’s stock price seems to depend only on the price of oil and nothing else. Finally, there is Conglomerated Conglomerate Inc. Conglomerated is a giant company with holdings in almost every industry imaginable—from cell phones to grocery stores and even amusement parks. Based on this information, which company would you think has the highest beta? The lowest beta? Which one do you think has a beta closest to 1?

#### Assignment Expectations

• Answer the assignment questions directly.
• Stay focused on the precise assignment questions. Do not go off on tangents or devote a lot of space to summarizing general background materials.
• For computational problems, make sure to show your work and explain your steps.
• For short answer/short essay questions, make sure to reference your sources of information with both a bibliography and in-text citations. See the Student Guide to Writing a High-Quality Academic Paper, including pages 11-14 on in-text citations. Another resource is the “Writing Style Guide,” which is found under “My Resources” in the TLC Portal.

### Present Value and the Risk/Return Trade-Off

#### Assignment Overview

For this assignment, make sure to first carefully review all of the required readings about present value, future value, risk and return, and the CAPM. Once you are relatively comfortable with these concepts, try working through some of the examples in the background readings and try computing the answers on your own. Once you are confident you both understand the concepts and the computational steps, complete the assignment below.

#### Case Assignment

Present your answers to the problem below in a Word document, and also upload an Excel file with your computations. Excel is required for Questions 2 and 3. Excel is optional for Questions 1 and 4, but you are required to show your steps for all quantitative problems. Even if you get the answer wrong, you can still get partial credit if you show your work.

1. Calculate the following:
1. Suppose you wish to raise some money for your favorite local charity. This charity needs \$50,000 a year to run its operation and you want to make sure that it is ensured an annual payment of this amount from now on for every year in the foreseeable future. Given an interest rate of 5%, how much would you have to fund this perpetuity to guarantee the charity a payment of \$50,000 per year?
2. You decide to put \$1,000 in a new bank account and don’t plan to withdraw the money for 10 years. If your bank does continuous compounding and the interest rate is 1%, what will be the value of this bank account in 10 years?
2. Suppose you won the lottery but not all of your winnings will come in one year. Instead, you will get a series of annual payments over the next five years. The table below tells you what your payment will be every year for the next five years. Use the information in the table to make the following computations:
1. The present and future value of your lottery ticket if the interest rate is 8%
2. The present and future value of your lottery ticket if the interest rate is 10%

Year

Payment

1

5000

2

6000

3

7000

4

8000

5

9000

1. The table below gives the probability of different returns for three different assets. Using this table, calculate the following:
1. The expected return of each asset
2. The standard deviation of returns of each asset
3. The coefficient of variation of each asset
4. Based on your answers to B) and C) above, which asset has the highest total risk and highest relative risk?

Asset A

Asset B

Asset C

Probability

Return

Probability

Return

Probability

Return

0.3

5

0.1

25

0.1

4

0.4

8

0.3

20

0.8

5

0.3

9

0.5

15

0.1

6

0.1

14

1. Suppose the market return is 8%, the risk-free rate is 1% and the beta for a given stock is 1.2. Answer the following questions based on this information:
1. What is the required return for this stock?
2. If the beta increases by 50% (but beta remains at 1.2), what will be the new required return for the stock? What is the percentage-wise change in required return compared to your answer to A) above?
3. If the market return increases by 50% (but beta remains at 1.2), what will be the new required return for the stock? What is the percentage-wise change in required return compared to your answer to A) above?
2. Suppose there are three different companies. The first one, Trendy Tech Inc., has investors who are “fair-weather friends.” When the stock market is going up, everybody wants to invest in Trendy Tech, but as soon as the market goes down everyone jumps ships and sells their shares. The second company is Oily Oil Inc. Oily’s stock price seems to depend only on the price of oil and nothing else. Finally, there is Conglomerated Conglomerate Inc. Conglomerated is a giant company with holdings in almost every industry imaginable—from cell phones to grocery stores and even amusement parks. Based on this information, which company would you think has the highest beta? The lowest beta? Which one do you think has a beta closest to 1?

#### Assignment Expectations

• Answer the assignment questions directly.
• Stay focused on the precise assignment questions. Do not go off on tangents or devote a lot of space to summarizing general background materials.
• For computational problems, make sure to show your work and explain your steps.
• For short answer/short essay questions, make sure to reference your sources of information with both a bibliography and in-text citations. See the Student Guide to Writing a High-Quality Academic Paper, including pages 11-14 on in-text citations. Another resource is the “Writing Style Guide,” which is found under “My Resources” in the TLC Portal.

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