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NAME: PROBLEM SET 2 Chapter 4 -- Time Value Analysis Assigned Problem 1 Epitome Healthcare has just borrowed $1,500,000 on a five-year, annual payment term loan at a 15 percent rate. The first payment is due one year from now. Construct the amortization schedule for this loan. ANSWER First, the annual payment is found as follows: Annual payment = $447,473.33 (You may also use a financial calculator to find the annual payment.) Then, the amortization schedule can be constructed: Year Payment Interest 1 $1,500,000.00 $447,473.33 $225,000.00 $222,473.33 $1,277,526.67 2 $1,277,526.67 $447,473.33 $191,629.00 $255,844.33 $1,021,682.34 3 $1,021,682.34 $447,473.33 $153,252.35 $294,220.98 $727,461.37 4 $727,461.37 $447,473.33 $109,119.20 $338,354.12 $389,107.24 5 $389,107.24 $447,473.33 $58,366.09 $389,107.24 $0.00 Beginning amount Repayment of principal Remaining balance A B C D E F G H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
NAME: PROBLEM SET 2 Chapter 4 -- Time Value Analysis Assigned Problem 2 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.) ANSWER Annual inflation rate 5% Annual interest rate 8% Years until retirement 10 Years of life after retirement 25 Desired retirement income in today's dollars $40,000 Desired retirement income 10 years from today 65,155.79 751,165.30 Current savings $100,000 215,892.50 Amount needed 10 years from today 535,272.80 Annual amount to be saved 36,949.61 PV of desired retirement income (annuity due) 10 years from today FV of current savings 10 years from today
NAME: PROBLEM SET 2 Chapter 5 -- Financial Risk and Required Return Assigned Problem 3 Consider the following probability distribution of returns estimated for a proposed project that involves a new ultrasound machine: State of the Probability Rate of economy P*r P*(r-R')^2 Very poor 0.1 -10% -0.01 0.40% Poor 0.2 0% 0 0.20% Average 0.4 10% 0.04 0.00% Good 0.2 20% 0.04 0.20% Very good 0.1 30% 0.03 0.40% Expected Return (R') : 10.00% 0.01200 a. What is the expected rate of return on the project? b. What is the project's standard deviation of returns? c. What is the project's coefficient of variation (CV) of returns? d. What type of risk does the standard deviation and CV measure? e. In what situation is this risk relevant? ANSWER a. Expected rate of return: E(R) = 10% b. The standard deviation is found as follows: Variance = 0.012 Standard Deviation = 10.95% c. CV = 1.095 d. e. Investment is held in isolation. of occurrence (P) return (r) Standard Deviation and coefficient of variation measures total risk.
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NAME: PROBLEM SET 2 Chapter 5 -- Financial Risk and Required Return Assigned Problem 4 stocks of selected healthcare providers: Company Beta Quorum Health Group 0.90 Beverly Enterprises 1.20 HEALTHSOUTH Corporation 1.45 United Healthcare 1.70 At the time these betas were developed, reasonable estimates for the risk-free rate, RF, and the required rate of return on the market, R(Rm), were 6.5 percent and 13.5 percent, respectively. a. What are the required rates of return on the four stocks? b. Why do their required rates of return differ? c. Suppose that a person is planning to invest in only one stock rather than hold a well-diversified stock portfolio. Are the required rates of return calculated above applicable to the investment? Explain your answer. ANSWER a. Spreadsheet solution: RF 6.50% R(Rm) 13.50% Required Rate of Return on Each Stock Quorum Health Group 12.80% Beverly Enterprises 14.90% HEALTHSOUTH Corporation 16.65% United Healthcare 18.40% b. The rates of return differ due to the different beta factor. c. Yes, the calculations above allows the investors to gazen the return against the risk. A few years ago, the Value Line Investment Survey reported the following market betas for the