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# Calculating the Desired Parameters

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1. Investments in the stock market have increased at an average compound rate of about 5% since 1905. It is now 2012.

a. If you invested \$1,000 in the stock market in 1905, how much would that investment be worth today?

b. If your investment in 1905 has grown to \$1 million, how much did you invest in 1905?

2. If the interest rate this year is 8.4% and the interest rate next year will be 10.4%, what is the future value of \$1 after 2 years? What is the present value of a payment of \$1 to be received in 2 years?

3. In mid-2010 a pound of apples cost \$1.36, while oranges cost \$1.20. Ten years earlier the price of apples was only \$.97 a pound and that of oranges was \$.75 a pound.

a. What was the annual compound rate of growth in the price of the two fruits?

b. If the same rates of growth persist in the future, what will be the price of apples in 2030?

c. What about the price of oranges?

#### Solution Preview

1. Investments in the stock market have increased at an average compound rate of about 5% since 1905. It is now 2012.

a. If you invested \$1,000 in the stock market in 1905, how much would that investment be worth today?

Total number of periods=n=107 years
Average growth rate=r=5%
Amount invested in 1905=P=\$1000
Amount accumulated in 2012=F=P*(1+r)^n=1000*(1+5%)^107=185,035.48

b. If your investment in 1905 has grown to \$1 million, how much did ...

#### Solution Summary

Solutions describe the steps to calculate present/future values and growth rates in the given cases.

\$2.19
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## Capital Budgeting

1) Great Lakes Clinic has been asked to provide exclusive healthcare services for next year's World Exposition. Although flattered by the request, the clinic's managers want to conduct a financial analysis of the project. There will be an up-front cost of \$160,000 to get the clinic in operation. Then, a net cash inflow of \$1million is expected from operations in each of the two years of the exposition. However, the clinic has to pay the organizers of the exposition a fee for the marketing value of the opportunity. This fee, which must be paid at the end of the second year, is \$2million.

a)What are the cash flows associated with the project?
b)What is the project's Internal Rate of Return?
c)Assuming a project cost of capital of 10%, what is the project's Net Present Value?
d)What is the project's Modified Internal Rate of Return?

2) Assume that you are the chief financial officer at Porter Memorial Hospital. The CEO has asked you to analyze two proposed capital investments-Project X and Project Y. Each project requires a net investment outlay of \$10,000 and the cost of capital for each project is 12%. The projects' expected net cash flows are as follows:

Year Project X Project Y
0 (\$10,000) (\$10,000)
1 6,500 3,000
2 3,000 3,000
3 3,000 3,000
4 1,000 3,000

a)Calculate each projects payback period, net present value (NPV) and internal rate of return (IRR)

The director of capital budgeting for Big Sky Health Systems, Inc., has estimated the following cash flows in thousands of dollars for a proposed new service:

Year Expected Net Cash Flow
0 (\$100)
1 70
2 50
3 20
The projects cost of capital is 10%.

a) What is the project's payback period?
b) What is the projects NPV?
c) What is the projects IRR? Its MIRR?

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