Question

A company is considering two mutually exclusive projects requiring an initial cash outlay of $100 each and with a useful life of 5 years. The company required rate of return is 10% and the appropriate corporate tax rate is 40%. The projects will be depreciated on a straight line basis. The before depreciation and taxes cash flows expected to b generated by the projects are as follows.

Year	1	2	3	4	5
Project A ($)	4,000	4,000	10,000	2,000	1,000
Project B ($)	6,000	3,000	2,000	5,000	5,000

Required
a) Determine the cashflow associated with the projects?

b) Which project should be accepted by using the appraisal method below;

1. Payback period
2. Net present value

Answer 1

a)

Depreciation = Initial cost/Useful life = $ 100/5 = $ 20

Computation of cash flow for Project A:

Project A
Year	0	1	2	3	4	5
Gross profit		$4,000	$4,000	$10,000	$2,000	$1,000
Less: Depreciation		$20	$20	$20	$20	$20
PBT		$3,980	$3,980	$9,980	$1,980	$980
Less: Tax @ 40 %		$1,592	$1,592	$3,992	$792	$392
Net income		$2,388	$2,388	$5,988	$1,188	$588
Add: Depreciation		$20	$20	$20	$20	$20
Annual cash flow	($100)	$2,408	$2,408	$6,008	$1,208	$608

Computation of cash flow for Project B:

Project B
Year	0	1	2	3	4	5
Gross profit		$6,000	$3,000	$2,000	$5,000	$5,000
Less: Depreciation		$20	$20	$20	$20	$20
PBT		$5,980	$2,980	$1,980	$4,980	$4,980
Less: Tax @ 40 %		$2,392	$1,192	$792	$1,992	$1,992
Net income		$3,588	$1,788	$1,188	$2,988	$2,988
Add: Depreciation		$20	$20	$20	$20	$20
Annual cash flow	($100)	$3,608	$1,808	$1,208	$3,008	$3,008

b)

I.

Payback Period = A +B/C

Where,

A = Last period with a negative cumulative cash flow

B = Absolute value of cumulative cash flow at the end of the period A

C = Total cash flow during the period after A

Computation of Payback Period for Project A:

Year	Cash Flow	‘Cum Cash Flow
0	($100)	($100)
1	$4,000	$3,900
2	$4,000	$7,900
3	$10,000	$17,900
4	$2,000	$19,900
5	$1,000	$20,900

     Payback Period = 0 + $ 100/$4,000

                                  = 0 + 0.025 = 0.025 years

Computation of Payback Period for Project B:

Year	Cash Flow	‘Cum Cash Flow
0	($100)	($100)
1	$6,000	$5,900
2	$3,000	$8,900
3	$2,000	$10,900
4	$5,000	$15,900
5	$5,000	$20,900

     Payback Period = 0 + $ 100/$6,000

                                 = 0 + 0.0166666667= 0.017 years

Based on payback period decision, Project B should be accepted as it has lower payback period than Project A.

II.

Computation of NPV for both projects:

NPV = Sum of FV of cash inflows – Initial investment

			Project A		Project B
Year	PV Factor computation	PV factor @ 10 % (F)	Cash Flow (CA)	PV (=CA x F)	Cash Flow (CB)	PV (=CB x F)
0	1/(1+0.1)^0	1	($100)	($100.00)	($100)	($100.00)
1	1/(1+0.1)^1	0.909090909090909	$2,408	$2,189.09	$3,608	$3,280.00
2	1/(1+0.1)^2	0.826446280991735	$2,408	$1,990.08	$1,808	$1,494.21
3	1/(1+0.1)^3	0.751314800901578	$6,008	$4,513.90	$1,208	$907.59
4	1/(1+0.1)^4	0.683013455365071	$1,208	$825.08	$3,008	$2,054.50
5	1/(1+0.1)^5	0.620921323059155	$608	$377.52	$3,008	$1,867.73
			NPV	$9,795.67	NPV	$9,504.04

Based on NPV decision, Project A should be accepted as it has higher NPV than Project B.