Question

Consider the following two mutually exclusive projects:

  

Year	Cash Flow (A)	Cash Flow (B)
0	–$316,951	–$15,457
1	27,400	4,426
2	58,000	8,829
3	54,000	13,079
4	425,000	9,565

  

Whichever project you choose, if any, you require a 6 percent return on your investment.

a. What is the payback period for Project A?

   

b. What is the payback period for Project B?

c. What is the discounted payback period for Project A?

d. What is the discounted payback period for Project B?

e. What is the NPV for Project A?

f. What is the NPV for Project B ?

  

g. What is the IRR for Project A?

h. What is the IRR for Project B?

i. What is the profitability index for Project A?

j. What is the profitability index for Project B?

Answer 1

Answer a & b
Calculation of Payback period for Project A and Project B
	Project A		Project B
Year	Cash flow	Cumulative Cash Flow	Cash flow	Cumulative Cash Flow
0	-$316,951.00	-$316,951.00	-$15,457.00	-$15,457.00
1	$27,400.00	-$289,551.00	$4,426.00	-$11,031.00
2	$58,000.00	-$231,551.00	$8,829.00	-$2,202.00
3	$54,000.00	-$177,551.00	$13,079.00	$10,877.00
4	$425,000.00	$247,449.00	$9,565.00	$20,442.00
Payback period for Project A = 3 Years + [$177551 / $425000] = 3.42 years
Payback period for Project B = 2 Years + [$2202 / $13079] = 2.17 years
Answer c & d
Calculation of Discounted payback period for Project A and Project B
		Project A			Project B
Year	Discount Factor @ 6%	Cash flow	Present Value	Cumulative Cash Flow	Cash flow	Present Value	Cumulative Cash Flow
0	1.00000	-$316,951.00	-$316,951.00	-$316,951.00	-$15,457.00	-$15,457.00	-$15,457.00
1	0.94340	$27,400.00	$25,849.06	-$291,101.94	$4,426.00	$4,175.47	-$11,281.53
2	0.89000	$58,000.00	$51,619.79	-$239,482.15	$8,829.00	$7,857.78	-$3,423.75
3	0.83962	$54,000.00	$45,339.44	-$194,142.71	$13,079.00	$10,981.38	$7,557.63
4	0.79209	$425,000.00	$336,639.81	$142,497.10	$9,565.00	$7,576.38	$15,134.01
Discounted Payback period for Project A = 3 Years + [$194142.71 / $$336639.81] = 3.58 years
Discounted Payback period for Project B = 2 Years + [$3423.75 / $10981.38] = 2.31 years
Answer e & f
Calculation of NPV for Project A and Project B
		Project A		Project B
Year	Discount Factor @ 6%	Cash flow	Present Value	Cash flow	Present Value
0	1.00000	-$316,951.00	-$316,951.00	-$15,457.00	-$15,457.00
1	0.94340	$27,400.00	$25,849.06	$4,426.00	$4,175.47
2	0.89000	$58,000.00	$51,619.79	$8,829.00	$7,857.78
3	0.83962	$54,000.00	$45,339.44	$13,079.00	$10,981.38
4	0.79209	$425,000.00	$336,639.81	$9,565.00	$7,576.38
NPV			$142,497.10		$15,134.01
NPV of project A		$142,497.10
NPV of project B		$15,134.01
Answer g & h
Calculation of IRR for Project A and Project B
Year	Project A Cash flow	Project B Cash flow
0	-$316,951.00	-$15,457.00
1	$27,400.00	$4,426.00
2	$58,000.00	$8,829.00
3	$54,000.00	$13,079.00
4	$425,000.00	$9,565.00
IRR =	18.00%	38.00%
IRR for Project A		18.00%
IRR for Project B		38.00%
Answer I & j
Calculation of profitability index for Project A and Project B
Profitability Index = Present Value of future cash inflows / Initial Investment
			Project A	Project B
Present Value of future cash inflows			$459,448.10	$30,591.01
/ Initial Investment			$316,951.00	$15,457.00
Profitability Index			1.45	1.98