ASSIGNMENT #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 (provided on page 3) 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.

Sample Questions and Solutions

Sample Question # 1: A company has an issue of 12-year bonds that pay 5% interest, annually. Further assume that today's required rate of return on these bonds is 7%. How much would these bonds sell for today? Round off to the nearest $1.

Solution

(i) The problem assumes that the face value of the bond is $1000. The bond will pay an annual coupon of 5% i.e., coupon or interest amount of $50 is assumed to paid every year. It also assumes that investors currently required a return of 7% on investments with similar risk characteristics. The use of bond valuation concept is appropriate to calculate the true value of these bonds. The accuracy of the solution depends on the correctness of the assumptions on face value, coupon payments and required rate of return assumption.

(ii) The use of bond valuation concept which suggests that the true value of a bond is the present value of its future coupon and face value discounted at investors required rate of return is appropriate to calculate the true value of these bonds. We are required to compute the present value (PV) which represents the true value of the bond.

(iii) FV= $1000; PMT=$50; Rate = 7%; N=12 years; Compute PV = ? $841.15 Value of the Bond = $841.15 2

Sample Question # 2: 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 companys 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 periods 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.

Assignment Problems

1. ABC Corporation issues a bond which has a coupon rate of 10.20%, a yield to maturity of 9.75%, a face value of $1,000, and a market price of $1,150. What is the annual interest payment? Round to two decimal places.

2. A shipping company sold an issue of 16-year $1,000 par bonds to build new ships. The bonds pay 8.25% interest, compounded semiannually. Today's required rate of return is 6.80%. How much should these bonds sell for today? Round to two decimal places.

3. Assume a company has an issue of 19-year $1,000 par value bonds that pay 4.5% interest, compounded annually. Further assume that today's required rate of return on these bonds is 6%. How much would these bonds sell for today? Round to two decimal places.

4. ABC Company issued bonds on January 1, 2006. The bonds had a coupon rate of 5.0%, with interest paid semiannually. The face value of the bonds is $1,000 and the bonds mature on January 1, 2024. What is the yield to maturity for these bonds on January 1, 2016 if the market price of the bond on that date is $1,100?

5. A $1,000 par value 12-year bond with a 14 percent coupon rate recently sold for $925. What is the yield to maturity? Assume semiannual payments and submit your answer as a percentage rounded to two decimal places.

6. Consider a 10 year bond with face value $1,000 that pays a 6.8% coupon semi-annually and has a yield-to-maturity of 8.4%. What is the approximate percentage change in the price of bond if interest rates in the economy are expected to decrease by 0.60% per year? Submit your answer as a percentage and round to two decimal places. (Hint: What is the expected price of the bond before and after the change in interest rates?)

7. ACME, Inc. expects its current annual $3.25 per share common stock dividend to remain the same for the foreseeable future. What is the intrinsic value of the stock to an investor with a required return of 65%? Round to two decimal places.

8. ABC Company's common stock is expected to pay a $9.50 dividend in the coming year. If investors require a 17% return and the growth rate in dividends is expected to be 7%, what should the market price of the stock be? Round to two decimal places.

9. ABC Corporation stock is currently selling for $64.00. The stock is expected to pay a dividendof $5.75 at the end of the year. Dividends are expected to grow at a constant rate of 8.5% indefinitely. Compute the expected rate of return on ABC Corporation stock. Submit your answer as a percentage and round to two decimal places.

10. XYZ Corp. just paid a dividend today of $8.60 per share. The dividend is expected to grow at a constant rate of 2.8% per year. If XYZ Corp. stock is selling for $22.00 per share, what is the stockholders' expected rate of return? Submit your answer as a percentage and round to two decimal places.