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Present Value and the Risk/Return Trade-Off Case

Question Description

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 risk-free rate of 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?
    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.

Module 1 – Background

Present Value and the Risk/Return Trade-Off

To begin the module, start off with these two videos to give yourself an overview of the main concepts covered in this module. The first video is from Professor Holthausen of the Wharton School of Business at the University of Pennsylvania. He explains the concept of the time value of money and also goes through some calculations using Microsoft Excel. The second video is from Professor Pinder of the University of Melbourne and covers some basic concepts of risk and return.

University of PennsylvaniaHolthausen, R. (2015). Time value of money. Coursera. Retrieved from: https://www.coursera.org/learn/wharton-decision-ma…

Unversity of Melbourne

Pinder, S. (2017) Unsystematic versus systematic risk. Coursera. Retrieved from: https://www.coursera.org/learn/valuation/lecture/L…

A second video from Dr. Pinder on the capital asset pricing model is highly recommended but not required. A link to Dr. Pinder’s video is included under the optional reading list below.

Once you have finished viewing the videos, take a closer look at the concepts covered in the videos by reading through these book chapters. In addition to reading about the basic concepts, make sure to work through some of the numerical examples as these will help you with your assignments:

time and money scale

Vishwanath, S. (2007). Chapter 2: Time value of money. Corporate finance: Theory and practice. SAGE Publications India. Available in the Trident Online Library.

risk and reward tightwire

Vishwanath, S. (2007). Chapter 3: Risk and return. Corporate finance: Theory and practice. SAGE Publications India. Available in the Trident Online Library.

If you have any difficulty with the material above, it is highly recommended that you take a look at some of the optional readings below. The materials below cover the same material but sometimes concepts can be absorbed better if you see some explained in a different manner or see additional examples.

Finally, if you don’t have much experience with Microsoft Excel then please take a look at the following videos:

Davis, J. (2013). Present value of a single amount in Excel. Retrieved from:

Moy, R. (2014). Present value of multiple cash flows in Excel. Retrieved from:

Codible. (2012). Future value for a series of annual deposits. Retrieved from:

Optional Reading

Pinder, S. (2017). Capital asset pricing model (It’s all about the discount rate). Coursera. Retrieved from: https://www.coursera.org/learn/valuation/lecture/6…

Clifford, J. (2014). Time value of money. ACDC Leadership. Retrieved from:

Ross, S., Westerfield, R., & Jordan, B. (2007) Chapter 4: Introduction to valuation: The time value of money. Essentials of Corporate Finance. McGraw Hill. Retrieved from: http://novellaqalive2.mheducation.com/sites/dl/fre…

Ross, S., Westerfield, R., & Jordan, B. (2007) Chapter 11: Risk and return. Essentials of Corporate Finance. McGraw Hill. Retrieved from: http://novellaqalive2.mheducation.com/sites/dl/fre…

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