This Question 1 pt 20 of 31 0 complete This Test 31 pts pos

This Question: 1 pt 20 of 31 (0 complete) ? This Test: 31 pts possi Question Help e the (a) net present value (NPV), (b) profitability index (PI), and (e) internal rate of return (IRR) for Projects 1 and 2 (cash flows shown below), assuming a required return of 10%. Project 2 Project 1 $410 $110 $170 $110 $360 Year $400 $150 $120 $110 $360 a. What is the NPV of Project 1? (Round to the nearest cent) What is the NPV of Project 2? (Round to the nearest cent.) b. What is the PI of Project 1? ? (Round to two decimal places.)

Solution

Project 1

Calculation of NPV of project 1

NPV (at 10%) = Present value of cash inflows - Present value of cash outflows

= 568.91 - 410

= $158.91

P.I. of project 1 = Present value of cash inflows/Present value of cash outflows

= 568.91/410

= 1.39

Calculation of IRR of project 1

To find out IRR, two discount rates are needed. Let us discount cash flows at 22%

NPV(at 22%) = 427.41 - 410

= $17.41

At IRR, NPV is zero. Since even at 22% discount rate, NPV is positive, hence IRR must be above 22%. Let us take another discount rate 23%

NPV(at 23%) = 418.19 - 410

= $8.19

Since NPV is still positive at 23%, hence IRR must be slight above 23%. Exact IRR can be calculated as under:

IRR = lower rate + [NPV at lower rate/(NPV at lower rate - NPV at higher rate)] x (Higher rate - lower rate)

= 22% + [17.41/(17.41-8.19)] x (23 - 22)

= 22% + (17.41/9.22) x 1

= 22% + 1.89%

= 23.89%

Project 2

Calculation of NPV of project 2

NPV (at 10%) = Present value of cash inflows - Present value of cash outflows

= 563.96 - 400

= $163.96

P.I. of project 2 = Present value of cash inflows/Present value of cash outflows

= 563.96/400

= 1.41

Calculation of IRR of project 2

To find out IRR, two discount rates are needed. Let us discount cash flows at 22%

NPV(at 22%) = 426.61 - 400

= $26.61

At IRR, NPV is zero. Since even at 22% discount rate, NPV is positive, hence IRR must be above 22%. Let us take another discount rate 23%

NPV(at 23%) = 417.66 - 400

= $17.66

Since NPV is still positive at 23%, hence IRR must be slight above 23%. Exact IRR can be calculated as under:

IRR = lower rate + [NPV at lower rate/(NPV at lower rate - NPV at higher rate)] x (Higher rate - lower rate)

= 22% + [26.61/(26.61-17.66)] x (23 - 22)

= 22% + (26.61/8.95) x 1

= 22% + 2.97%

= 24.97%

Year	Cash flow	PVF(10%, 4)	Present value of cash flows
1	110	0.909	110 x 0.909 = 100
2	170	0.826	170 x 0.826 = 140.42
3	110	0.751	110 x 0.751 = 82.61
4	360	0.683	360 x 0.683 = 245.88
		Total	$568.91