Question

The following data are given for two mutually exclusive project proposals:

(PhP)	Project A	Project B
Initial Investment	50,000.00	60,000.00
Annual Net Cash Inflows:
Year 1	15,000.00	30,000.00
Year 2	14,000.00	14,000.00
Year 3	12,000.00	10,000.00
Year 4	12,000.00	10,000.00
Year 5	12,000.00	10,000.00

Assuming that the firm’s required rate of return is 20%, compute the following:

a) Net Present Value

b) Payback Period

Which project would you undertake? Justify

Answer 1

a) NPV of project = Present Values of Cash Inflows - Initial Investment where the discount rate is 20 % (Given)

Therefore

Project A
	Year 1	Year 2	Year 3	Year 4	Year 5
Cash Flows (A)	15000	14000	12000	12000	12000
Discount Factors (B)	=1/(1.20)^1	=1/(1.20)^2	=1/(1.20)^3	=1/(1.20)^4	=1/(1.20)^5
Discount Factors (B)	0.83333333	0.69444444	0.5787037	0.48225309	0.40187757
Present Values (A x B)	12,500.00	9,722.22	6,944.44	5,787.04	4,822.53
Total of All the present Values of Cash Inflows (D)	39,776.23
Initial Investment ('E)	50000
NPV (D-E)	-10,223.77
Project B
	Year 1	Year 2	Year 3	Year 4	Year 5
Cash Flows (A)	30000	14000	10000	10000	10000
Discount Factors (B)	=1/(1.20)^1	=1/(1.20)^2	=1/(1.20)^3	=1/(1.20)^4	=1/(1.20)^5
Discount Factors (B)	0.83333333	0.69444444	0.5787037	0.48225309	0.40187757
Present Values (A x B)	25,000.00	9,722.22	5,787.04	4,822.53	4,018.78
Total of All the present Values of Cash Inflows (D)	49,350.57
Initial Investment ('E)	60000
NPV (D-E)	-10,649.43

NPV of both the projects is negative. Based on NPV none of the projects is viable at the discount rate ofn 20%. Therefore both the projects needs to be not accepted.

b) Payback Period

We need to first compute the Cumalative Cash Flows of the project

Project A
	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5
Cash Flows (A)	-50000	15000	14000	12000	12000	12000
Cumalative Cash Flows	-50000	-35,000.00	-21,000.00	-9,000.00	3,000.00	15,000.00
1) last period number with a negative cumulative cash flow is Year 3
2) value without negative sign of cumulative net cash flow at the end of the period with a cumalative negative Cash Flow is 9000
3) Total cash inflow during the period following period with the last negative cumlative Cash flow is 12000
Payback Period = (1)+[(2)/(3)]
Payback Period	=3+9000/12000
Payback Period	3.75 years
Project A
	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5
Cash Flows (A)	-60000	30000	14000	10000	10000	10000
Cumalative Cash Flows	-60000	-30,000.00	-16,000.00	-6,000.00	4,000.00	14,000.00
1) last period number with a negative cumulative cash flow is Year 3
2) value without negative sign of cumulative net cash flow at the end of the period with a cumalative negative Cash Flow is 6000
3) Total cash inflow during the period following period with the last negative cumlative Cash flow is 10000
Payback Period = (1)+[(2)/(3)]
Payback Period	=3+6000/10000
Payback Period	3.6	Years

Considering only payback period as the criteria for selection of projects Project B having lesser payback period would be accepted. This means that the initial amount invested of the project would be received back in 3.6 years for project B.