Question

A four-year financial project is forecast to have net cash inflows of $10,000; $25,000; $60,000; and $50,000 in the next four years. It will cost $125,000 to implement the project payable at the beginning of the project. The discount rate is 11%. What is the NPV of this project? What is the BCR of this project? Based on the NPV and BCR, would you do this project? What is the NPV of the project if the cost is due in even installments in year 2 and year 3 ($62,500 due each year)

Answer 1

The Cash flows and the discounted cash flows of the firm are as given below:

PV of Benefits of the project (PV of cash inflows)   

= 10000 / (1+11%)^1 + 25000 / (1+11%)^2 + 60000 / (1+11%)^3 + 50000 / (1+11%)^4

= 9009 + 20291 + 43871 + 32937

= $106108

PV of costs of the project = $125000

BCR = Benefits/ Costs

= 106108 / 125000

= 0.849

PV of cash flows = CFt/ (1+k)^t

where CFt is cash flow in year t, k = Cost of capital or Discount Rate & t is the year of Cash flow

Alternatively, PV of cash flows = CFt X Discount Factor

where Discount Factor = 1 / (1+k)^t

NPV = Sum of PV of all future cash flows - PV of Investment

= 106108 - 125000

= - $18,892.40

Since BCR is less than 1 and NPV is < 0, Project should not be accepted

Year	Cash Flows (CF)	Discount Factor @ 11% (DF)	Discounted Cash Flows = CF X DF
0	-125000.00	1.000	-125000
1	10000.00	0.901	9009
2	25000.00	0.812	20291
3	60000.00	0.731	43871
4	50000.00	0.659	32937

Part 2 : If the cost is due in even installments in Year 2 & Year 3 ($62,500 each), the cash flows and PV of cash flows will look like this

Year 2 Cash flow = 25000 - 62500 = - $37500

Year 3 Cash flow = 60000 - 62500 = - $2500

Year	Cash Flows	Discount Factor	Discounted Cash Flows
0	0.00	1.000	0
1	10000.00	0.901	9009
2	-37500.00	0.812	-30436
3	-2500.00	0.731	-1828
4	50000.00	0.659	32937

NPV = Sum of PV of all future cash flows (including netted investments)

= 10000 / (1+11%)^1 - 37500 / (1+11%)^2 - 2500 / (1+11%)^3 + 50000 / (1+11%)^4

= 9009 - 30436 - 1828 + 32937

= $9682