# 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?

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#### Solution Preview

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.

IRR can be calculated through interpolation

Find NPV at two rates and interpolate

The two rates selected are 10% and 15%

Year Cash flow Discount factor @ Discounted cash flow= Discount factor @ Discounted cash flow=

10.00% 15.00%

0 ($40,000) 1 ($40,000) 1 ($40,000)

1 $20,000 0.909091 $18,182 0.869565 $17,391

2 $18,000 0.826446 $14,876 0.756144 $13,611

3 $13,000 0.751315 $9,767 0.657516 $8,548

$2,825 ($450)

Discount rate NPV Using interpolation

10.00% $2,825 IRR = 10.% + { 2825 / ( 2825 + 450) } x (15.% - 10.%)= 14.31%

15.00% -$450

B. With a cost of capital of 12 percent, should the machine be purchased?

Yes it should be purchased as the cost of capital (12%) ...

#### Solution Summary

Answers to 3 Questions on IRR, NPV, Expected Value of Cash Flow:

1) IRR for the purchase of manufacturing equipment by Home Security Systems

2) NPV of 2 projects for Norton Corporation

3) Expected cash flow for the purchase of new sound equipment for Debby's dance studio , where the probability distribution of cash flows is given.

I need some help with these question

(See attached file for full problem description)

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Problem 7-9

NPV and IRR. A project that costs $3,000 to install will provide annual cash flows of $800 for each of the next 6 years.

Is this project worth pursuing if the discount rate is 10 percent?

Project NPV

How high can the discount rate be before you would reject the project?

Maximum Project Rate

Problem 7-10

Payback. A project that costs $2,500 to install will provide annual cash flows of $600 for the

next 6 years. The firm accepts projects with payback periods of less than 5 years.

Will the project be accepted?

Project payback period

Should this project be pursued if the discount rate is 2 percent?

NPV of Project at 2%

What if the discount rate is 12 percent?

NPV of Project at 12%

Will the firm's decision change as the discount rate changes?

Problem 7-19

Here are the cash flows for two mutually exclusive projects:

Project C0 C1 C2 C3

A ($20,000) $8,000 $8,000 $8,000

B ($20,000) 0 0 $25,000

Use the MS Excel NPV function to calculate the NPVs for both projects in the profile below. In part B use the IRR function.

a. At what interest rates would you prefer project A to B?

NPV Profile

Discount

Rate NPVA NPVB

0% FORMULA FORMULA

2% FORMULA FORMULA

4% FORMULA FORMULA

6% FORMULA FORMULA

8% FORMULA FORMULA

10% FORMULA FORMULA

12% FORMULA FORMULA

14% FORMULA FORMULA

16% FORMULA FORMULA

18% FORMULA FORMULA

20% FORMULA FORMULA

b. What is the IRR of each project?

Project A IRR

Project B IRR

Problem 7-23

Profitability Index. Consider the following projects:

Project C0 C1 C2

A (2,100.00) 2,000.00 1,200.00

B (2,100.00) 1,440.00 1,728.00

a. Calculate the profitability index for A and B assuming a 22 percent opportunity cost of capital.

Project A NPV

Project B NPV

Project A Profitability Index

Project B Profitability Index

b. Use the profitability index rule to determine which project(s) you should accept (i) if you

could undertake both and (ii) if you could undertake only one.

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