### Rate of Return

1.   You are considering buying a new car, and you plan to keep it for ten years. Consumer's Report (a magazine) has published data that estimates the repair costs you should expect for the next ten years. The car dealer offers to sell you an insurance policy that will pay all of these costs. The cost of the policy is \$2,500. If you view the 2,500 as an investment to save future maintenance costs, what is the rate of return on that investment? Use the end of year assumption for costs. Give the answer to the nearest number in the table.

 Year 1 2 3 4 5 Cost 100 150 200 250 300

 Year 6 7 8 9 10 Cost 350 400 450 500 550

2. A businessman is considering purchasing a delivery truck. He does not now provide delivery service. He feels that the service will bring in an additional revenue of \$7,000 per year. The truck costs \$11,000. It will last for five years. Its resale value at that time is zero. A part-time driver for the truck will be hired for \$2,000 a year. Gas, oil and repairs for the truck will be \$1,000 in the first year, \$1,500 the second year, and continue to increase by \$500 per year thereafter. What is the rate of return of this proposed investment? Give the answer to the nearest number in the table.

3.  You have just graduated from high school and are considering the economics of a college education. For the next four years you will make tuition payments of \$10,000 per year. You will make no income during these years. After four years you hope to get a job. The college education will give you an added income of \$5000 for the fifth year. This is the income above what you would expect without the college education. You guess that the added income will increase by \$500 in each year after the fifth (\$5500 in year 6, \$6000 in year 7, and so on). Because it is so difficult to predict, you stop your analyis after 20 years of employment. For convenience, assume all payments are at the end of each year. Based on these assumptions, what is the rate of return of the investment in college?

4.

a. You invest \$10,000 in stock. The stock returns no dividends. If you sell the stock after 4 years for \$20,000, what annual rate of return did your stock yield?

b. You invest \$\$8000 in bonds. The bonds return an interest of \$600 at the end of each of the next four years. You receive the face value of the bonds equal to \$10,000 at the end of the four years. What annual rate of return did you receive for the bond investment?

c. You are considering an investment opportunity. Using your MARR to bring all the cash flows associated with the investment to time zero, you discover that the net present value is zero. What rate of return does this investment yield?

5.  In the following assume the investment is made at time 0 and that savings are at the end of each year.

a. An investment in a labor savings device of \$1,000 results in a savings of \$200 per year for five years. The salvage value of the device is zero after five years. What is the rate of return for this investment?

b. An investment in a labor savings device of \$1,000 results in a savings of \$200 per year for five years. The device can be sold for \$1,000 at the end of the five year period. What is the rate of return for this investment?

c. An investment in a labor savings device of \$1,000 results in a savings of \$200 per year. The device lasts forever. What is the rate of return for this investment?

d. Find the ROR of the cash flow below.