Described an arrangement in which the city of Cincinnati gave up the right to collect parking fees over a 30-year period in exchange for a lump sum of $92 million plus a 30-year annuity of $3 million. Suppose that if the city had not entered into that arrangement, it would have collected parking fees the following year of $6 million (net of operating costs), and those fees would have grown at a steady 3% for the next 30 years. At an interest rate of 4%, what is the present value of the parking revenue that the city could have collected? Using the same 4% to value the payments that the city was set to receive in their privatization deal, do you think that the city made the correct decision? Why or why not?
5-1 Using A Time Line:
P 5-1 The financial manager at Starbuck Industries is considering an investment that requires an initial outlay of $25,000 and is expected to result in cash inflows of $3,000 at the end of year 1, $6,000 at the end of years 2 and 3, $10,000 at the end of year 4, $8,000 at the end of year 5, and $7,000 at the end of year 6.
a. Draw and label a time line depicting the cash flows associated with Starbuck Industries' proposed investment.
b. Use arrows to demonstrate, on the time line in part a, how compounding to find future value can be used to measure all cash flows at the end of year 6.
c. Use arrows to demonstrate, on the time line in part b, how discounting to find present value can be used to measure all cash flows at time zero.
d. Which of the approaches-future value or present value-do financial managers rely on most often for decision making? Why?
P5-19: Future value of an annuity:
For each case in the accompanying table, answer the questions that follow.
Case Amount of annuity Interest rate Deposit period (years)
A $2,500 8% 10
B 500 12 6
C 30,000 20 5
D 11,500 9 8
E 6,000 14 30
a. Calculate the future value of the annuity assuming that it is
(1) An ordinary annuity.
(2) An annuity due.
b. Compare your findings in parts a(1) and a(2). All else being identical, which type of annuity-ordinary or annuity due-is preferable? Explain why.
P5-35 Relationship between future value and present value-Mixed stream The table below shows a mixed cash flow stream, except that the cash flow for year 3 is missing.
Year 1 $10,000
Year 2 5,000
Year 3
Year 4 20,000
Year 5 3,000
Suppose that somehow you know that the present value of the entire stream is $32,911.03, and the discount rate is 4%. What is the amount of the missing cash flow in year 3?
P8-1
Douglas Keel, a financial analyst for Orange Industries, wishes to estimate the rate of return for two similar-risk investments, X and Y. Douglas's research indicates that the immediate past returns will serve as reasonable estimates of future returns. A year earlier, investment X had a market value of $20,000; investment Y had a market value of $55,000. During the year, investment X generated cash flow of $1,500 and investment Y generated cash flow of $6,800. The current market values of investments X and Y are $21,000 and $55,000, respectively.
a. Calculate the expected rate of return on investments X and Y using the most recent year's data.
b. Assuming that the two investments are equally risky, which one should Douglas recommend? Why?
P8-9 Rate of return, standard deviation, coefficient of variation Mike is searching for a stock to include in his current stock portfolio. He is interested in Hi-Tech Inc.; he has been impressed with the company's computer products and believes Hi-Tech is an innovative market player. However, Mike realizes that any time you consider a technology stock, risk is a major concern. The rule he follows is to include only securities with a coefficient of variation of returns below 0.90.
Mike has obtained the following price information for the period 2009 through 2012. Hi-Tech stock, being growth-oriented, did not pay any dividends during these 4 years.
Year Stock price
Beginning End
2009 $14.36 $21.55
2010 21.55 64.78
2011 64.78 72.38
2012 72.38 91.80
a. Calculate the rate of return for each year, 2009 through 2012, for Hi-Tech stock.
b. Assume that each year's return is equally probable, and calculate the average return over this time period.
c. Calculate the standard deviation of returns over the past 4 years. (Hint: Treat these data as a sample.)