FM – L2 – Q70 – DCF: Risk and uncertainty

Calculate the expected NPV of a project with uncertain cash inflows affected by multiple probabilistic factors, using a 10% cost of capital.

Question

A company is considering whether or not to invest in a project where the investment would be GH¢5,250,000. The project would have a five-year life, and estimated annual cash flows are as follows:

Year	Cash inflows	Cash outflows
	GH¢	GH¢
1	3,000,000	1,500,000
2	4,000,000	1,800,000
3	5,000,000	2,400,000
4	4,000,000	1,700,000
5	3,000,000	1,000,000

The cost of capital is 10%.
The estimates of cash outflows are considered fairly reliable. However, the estimates of cash inflows are much more uncertain. Several factors could make the annual cash flows higher or lower than expected.
Factor 1: There is a 20% probability that government measures to control the industry will reduce annual cash inflows by 20%.
Factor 2: There is a 30% probability that another competitor will also enter the market: this would reduce the estimated cash inflows by 10%.
Factor 3: There is a 40% probability that demand will be stronger than expected. The company would not be able to supply more products to the market, but it would be able to sell at higher prices and cash inflows would be 5% higher than estimated.
Required
Calculate the expected net present value of the project.

Answer

Cash inflows for the project can be calculated as an EV of expected annual inflows.
The first step is to establish a probability distribution of possible outcomes.

	Factor 1	Factor 2	Factor 3	Joint
Yes, No, No	0.2	0.7	0.6	0.084
Yes, Yes, Yes	0.2	0.3	0.4	0.024
Yes, No, Yes	0.2	0.7	0.4	0.056
Yes, Yes, No	0.2	0.3	0.6	0.036
No, No, No	0.8	0.7	0.6	0.336
No, Yes, Yes	0.8	0.3	0.4	0.096
No, No, Yes	0.8	0.7	0.4	0.224
No, Yes, No	0.8	0.3	0.6	0.144

Probability of outcome	Cash inflows as a proportion of expectation
0.084	(-25%) 0.75
0.024	(-25% – 10% + 5%) 0.70
0.056	(-25% + 5%) 0.80
0.036	(-25% – 10%) 0.65
0.336	(+5%) 0.95
0.096	(-10% + 5%) 0.95
0.224	(+5%) 1.05
0.144	(-10%) 0.90
1.000

The EV of cash inflows, allowing for the three additional factors, will be 94% of the original estimates.

Year	Cash inflows (0.94 of original estimate)	Cash outflows	Net cash flow	Discount factor at	PV
	GH¢m	GH¢m	GH¢m
0	(5.25)		(5.25)	1.000	(5.25)
1	2.82	1.50	1.32	0.909	1.20
2	3.76	1.80	1.96	0.826	1.62
3	4.70	2.40	2.30	0.751	1.73
4	3.76	1.70	2.06	0.683	1.41
5	2.82	1.00	1.82	0.621	1.13
				NPV	0.84

Tags: Cash Flows, Discounted cash flow, Expected value, investment appraisal, Net Present Value, Probability Analysis, Risk Assessment
Level: Level 2

Topic: DCF: Risk and uncertainty

Uploader: Samuel Duah