Professional Custom Accounting Papers: Do the SD, CV, and beta produce the same risk ranking? Why or why not?
John Adams is the CEO of a nursing home in San Jose. He is now 50 years old and plans to retire in ten years. He expects to live for 25 years after he retires—that is, until he is 85. He wants a fixed retirement income that has the same purchasing power at the time he retires as $40,000 has today (he realizes that the real value of his retirement income will decline year by year after he retires). His retirement income will begin the day he retires, ten years from today, and he will then get 24 additional annual payments. Inflation is expected to be 5 percent per year for ten years (ignore inflation after John retires); he currently has $100,000 saved up; and he expects to earn a return on his savings of 8 percent per year, annual compounding. To the nearest dollar, how much must he save during each of the next ten years (with deposits being made at the end of each year) to meet his retirement goal? (Hint: The inflation rate 5 percent per year is used only to calculate desired retirement income.)
Assume that you recently graduated and you just landed a job as a financial planner with the Cleveland Clinic. Your first assignment is to invest $100,000. Because the funds are to be invested at the end of one year, you have been instructed to plan for a one-year holding period. Further, your boss has restricted you to the following investment alternatives, shown with their probabilities and associated outcomes.
| State of Economy | Probability | T-Bills | Alta Inds. | Repo Men | American Foam | Market Port. |
| Recession | 0.1 | 8.00% | -22.0% | 28.0% | 10.0% | -13.0% |
| Below Average | 0.2 | 8.00% | -2.0% | 14.7% | -10.0% | 1.0% |
| Average | 0.4 | 8.00% | 20.0% | 0.0% | 7.0% | 15.0% |
| Above Average | 0.2 | 8.00% | 35.0% | -10.0% | 45.0% | 29.0% |
| Boom | 0.1 | 8.00% | 50.0% | -20.0% | 30.0% | 43.0% |
Barney Smith Investment Advisors recently issued estimates for the state of the economy and the rate of return on each state of the economy. Alta Industries, Inc. is an electronics firm; Repo Men Inc. collects past due debts; and American Foam manufactures mattresses and various other foam products. Barney Smith also maintains an “index fund” which owns a market-weighted fraction of all publicly traded stocks; you can invest in that fund and thus obtain average stock market results. Given the situation as described, answer the following questions.
a. Calculate the expected rate of return on each alternative.
b. Calculate the standard deviation of returns on each alternative.
c. Calculate the coefficient of variation on each alternative.
d. Calculate the beta on each alternative.
e. Do the SD, CV, and beta produce the same risk ranking? Why or why not?
f. Suppose you create a two-stock portfolio by investing $50,000 in Alta Industries and $50,000 in Repo Men. Calculate the expected return, standard deviation, coefficient of variation, and beta for this portfolio. How does the risk of this two-stock portfolio compare with the risk of the individual stocks if they were held in isolation?
Mini Case Chapter 6
Sam Strother and Shawna Tibbs are vice presidents of Mutual of Seattle Group Health Cooperative and codirectors of the organization’s pension fund management division. The unions that represent the GHC hospital staff have requested an investment seminar so that they better understand the decisions being made on behalf of their members. Strother and Tibbs, who will make the actual presentation, have asked you to help them by answering the following questions.
a. What is the value of a ten-year, $1,000 par value bond with a 10 percent annual coupon if its required rate of return is 10 percent?
b. What would be the value of the bond described in question a. if, just after it had been issued, the expected inflation rate rose by 3 percentage points, causing investors to require a 13 percent return? Would we now have a discount or a premium bond?
c. What would be the value of the bond described in question a. if, just after it had been issued, the expected inflation rate fell by 3 percentage points, causing investors to require a 7 percent return? Would we now have a discount or a premium bond?
d. What would happen to the value of the ten-year bond over time if the required rate of return remained at 13 percent, remained at 7 percent, or remained at 10 percent? Graph your results using the table below:
| Value of Bond in Given Year: | |||
| N | 7% | 10% | 13% |
| 0 | |||
| 1 | |||
| 2 | |||
| 3 | |||
| 4 | |||
| 5 | |||
| 6 | |||
| 7 | |||
| 8 | |||
| 9 | |||
| 10 |
e. What is the yield to maturity on a ten-year, 9 percent annual coupon, $1,000 par value bond that sells for $887.00?
f. What are the total return, the current yield, and the capital gains yield for the bond in question e.? (Assume the bond is held to maturity and the company does not default on the bond.)
