Questions on IRR, NPV, Expected Value of Cash Flow

Please see attached document.
Question 1

Home Security Systems is analyzing the purchase of manufacturing equipment that will cost $40,000. The annual cash inflows for the next three years will be:

Year Cash Flow

1......................... $20,000
2..........................$18,000
3..........................$13,000

A. Determine the internal rate of return using interpolation.
B. With a cost of capital of 12 percent, should the machine be purchased?

Question 2

You are asked to evaluate the following two projects for the Norton Corporation. Using the net present value method, combined with profitability index approach described in footnote 2 on page 375, which project would you select? Use a discount rate of 10 percent.

Project X (Video tapes of weather report) Project Y (Slow-motion replays of commercials)
($10,000 Investment) ($30,000 investment)
Year cash flow Year cash flow
1 $5,000 1 15,000
2 3,000 2 8,000
3 4,000 3 9,000
4 3,600 4 7,000

Footnote*** A further possible refinement under the net present value method is to compute a profitability index

Question 3

Debby's dance studio is considering the purchase of new sound equipment that will enhance the popularity of its aerobics dancing. The equipment will cost $25,000. Debby's is not sure how many members the new equipment will attract, but she estimates that her increase annual cash flows for each of the next five years will have the following probability distribution. Debby's cost of capital is 11 percent.

P
(Probability) Cash Flow
.2 $3,000
.3 $5,000
.4 $7,400
.1 $9,800

A) What is the expected value of the cash flow? The value you compute will apply to each of the five years
B) What is the expected net present value?
C) Should Debby buy the new equipment?