# solidify your understanding on the applications of the risk

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Homework #2

The purpose of this assignment is to solidify your understanding on the applications of the risk

and return concepts and their role in valuing financial assets. The scores of this assignment will

help in assessing the following learning goal of the course: “students successfully completing

this course will be able to Analyze risk return characteristics to assess valuation of financial

assets”.

Instructions:

You are required to use a financial calculator or spreadsheet (Excel) to solve 10 problems related

to the risk and return, stocks and bonds valuation. You are required to show the following 3 steps

for each problem (sample questions and solutions are provided for guidance):

(i) Describe and interpret the assumptions related to the problem.

(ii) Apply the appropriate mathematical model to solve the problem.

(iii) Calculate the correct solution to the problem.

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Grading Rubric

Learning Objective

Subcomponent Not Submitted

0

Does Not Meet

Expectations 1

Meets Expectations

2

Exceeds Expectations

3

LO#2: Analyze risk return characteristic s to assess valuation of financial assets.

The student will make and evaluate important assumptions in identification of appropriate asset valuation variables and risk and return measures

No attempt made

Attempts to describe assumptions

Explicitly describes assumptions

Explicitly describes assumptions and provides rationale for why each assumption is appropriate. Show awareness that confidence in final conclusions is limited by the accuracy of the assumptions (e.g., provides descriptions about the assumptions of the model and its limitations; lists and describes each variable within the model)

The student will convert relevant information into various mathematical forms (e.g., equations, graphs, words)

No attempt made

Completes conversion of information but resulting mathematical portrayal is inappropriate or inaccurate

Completes conversion of information into mathematic al portrayal

Relevant information is expressed in an insightful mathematical portrayal in a way that contributes to a further or deeper understandin g (e.g., correct variables are selected and the mathematical model is portrayed with the correct variables)

The student will calculate risk and return measures and asset values

No attempt made

Calculations are attempted but are both unsuccessful and not

Calculations are attempted to solve the problem but

Calculations attempted are essentially all successful and sufficiently

3

comprehensiv e

not comprehens ive

comprehensive to solve the problem. Calculations are also presented elegantly (e.g., provides insights on the interpretation of the calculated value of an asset such as the value of a stock is valid only within the context of the model and its limitations)

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Sample Questions and Solutions

Sample Question: A company just paid a dividend of $1, and the dividends are expected to grow at constant rate of 4% forever. If the required return of the stockholders is 12%, what is the price of this company’s stock?

Solution

(i) The problem assumes the stock will have a constant growth of 4% forever. The constant growth model is appropriate to use for this problem. The accuracy of the solution depends on the correctness of the constant growth assumption.

(ii) The constant growth model is given as: P0 = D1/ (R-g); where • P0 is the current price to be calculated, • D1 is the next period’s dividend, • R is the required return on this stock • g is the constant growth

D1 needs to be calculated in order to apply this model.

(iii) D1= 1x(1+0.04) = 1.04

P0 = 1.04 /(0.12-0.04) = $13; the stock price should be $13 based on the constant growth model.

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Homework Problems

1. You have $100,000 invested in a 2-stock portfolio. $30,000 is invested in stock A and the remainder is invested stock B. A’s beta is 1.60 and B’s beta is 0.60. What is the portfolio beta?

2. The market return, based on a broad market index, is estimated as 15%. Calculate a company’s required return if the risk free rate is 4% and the stock’s beta is 1.35.

3. A company’s stock had a required return of 11.50% last year, when the risk-free rate was 5.50% and the market risk premium was 4.75%. Now suppose there is a shift in investor risk aversion, and the market risk premium increases by 2%. The risk-free rate and the beta remain unchanged. What is this company’s new required return?

4. A firm has some bonds maturing in 7 years, with par value of $1,000. Those bonds make annual coupon payment of $70. The market interest rate on similar bonds is 8.5%. What is the bond’s price?

5. A company’s non-callable bonds currently sell for $1,165. They have a 15-year maturity, coupon rate of 8% with semi-annual payments and par value of $1,000. What is their yield to maturity?

6. Assume that you are considering the purchase of a 15-year bond with coupon rate of 9.5%. The bond has a face value of $1,000 and makes semi-annual interest payments. If you require an 11% nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond?

7. A share of common stock has just paid a dividend of $2.00. If the expected long-run growth rate for this stock is 5%, and if investors’ required rate of return is 10.5%, what is the stock price?

8. A company plans to issue perpetual preferred stock with an annual dividend of $6.50 per share. If the required return on this preferred stock is 8.5%, at what price should the stock sell?

9. The most recent dividend paid by a company was $1.25. The dividends are expected to maintain a constant growth rate of 6% forever. If the stock currently sells for $32.5 per share, what is the required rate of return?

10. A Company just paid a dividend of $0.80 per share, and that dividend is expected to grow at a constant rate of 6% per year in the future. The company’s beta is 1.25, the market risk premium is 5.00%, and the risk-free rate is 4.00%. What is the company’s current stock price?