Question

You are considering the following two mutually exclusive projects. Project A Project B Year 0 -$10,000 -$20,000 Year 1 $ 3,000 $ 5,000 Year 2 $ 8,000 $ 7,000 Year 3 $ 4,000 $12,000 Year 4 $ 2,000 $10,000 The required return on each project is 12 percent. Which project should you accept and what is the best reason for that decision? a. Project B; because it has the higher net present value b. Project A; because it pays back faster c. Project A; because it has the higher net present value d. Project B; because it has the higher profitability index e. Project A; because it has the higher profitability index

Answer 1

Year	Project A	Project B
0	-10000	-20000
1	3000	5000
2	8000	7000
3	4000	12000
4	2000	10000

Cash Flow for Year n = CFn

Required Return = r = 12%

NPV = Σ CFn/(1+r)ⁿ

NPV_A = -10000 + 3000/(1+0.12) + 8000/(1+0.12)² + 4000/(1+0.12)³ + 2000/(1+0.12)⁴ = $3174.28

NPV_B = -20000 + 5000/(1+0.12) + 7000/(1+0.12)² + 12000/(1+0.12)³ + 10000/(1+0.12)⁴ = $4941.19

Profitability Index PI = PV of future cash flows / Initial investment = (NPV + Initial investment) / Initial Investment

PI_A = (3174.28 + 10000)/10000 = 1.32

PI_B = (4941.19 + 20000)/20000 = 1.25

To find payback period, let us find the cumulative cash flows -

Year	Project A	Cumulative A	Project B	Cumulative B
0	-10000	-10000	-20000	-20000
1	3000	-7000	5000	-15000
2	8000	1000	7000	-8000
3	4000	5000	12000	4000
4	2000	7000	10000	14000

Payback period is the period when the cumulative cash flow becomes positive

Payback for Project A = 1 + 7000/8000 = 1.88 years

Payback for Project B = 2 + 8000/12000 = 2.67 years

Of all the rules, NPV rule should be considered first

Hence, "a. Project B; because it has the higher net present value" is the correct answer option