FM – L2 – Q63 – DCF: Risk and uncertainty

Calculate NPV for two machines under different sales demand levels for Kofi Enterprises Ltd.

Question

Kofi Enterprises Ltd must purchase a new machine for making a new product. There is a choice between two machines, Machine A and Machine B. Each machine has an estimated life of three years with no expected scrap value.
Machine A costs N₦15,000 and Machine B costs N₦20,000.
The variable costs of manufacture would be N₦1 per unit if Machine A is used and N₦0.50 per unit if Machine B is used. The product will sell for N₦4 per unit.
The demand for the product is uncertain. Following some market research, the following estimates of annual sales demand have been made:

Annual demand (Units)	Probability
2,000	0.2
3,000	0.6
5,000	0.2

The sales demand in each year will be the same. For example, if the demand is 2,000 units in Year 1, it will be 2,000 units for every year of the project.
Taxation and fixed costs will be unaffected by any decision made.
Kofi Enterprises Ltd’s cost of capital is 6%.

Required:
(a) Calculate the NPV for each of investment options, Machine A and Machine B, for each of the possible levels of sales demand.

(b) Calculate the expected NPV for each of the investment options.

(i) Calculate the probability that the NPV of the project will be negative.

(ii) Calculate the minimum annual sales required for the NPV of the project to be positive.

Answer

(A).

Machine A

	2,000 demand	3,000 demand	5,000 demand
Year	N₦	N₦	N₦
0	(15,000)	(15,000)	(15,000)
1	6,000	9,000	15,000
2	6,000	9,000	15,000
3	6,000	9,000	15,000

Discounted Cash Flows	Discount factor at 6%	PV (2,000)	PV (3,000)	PV (5,000)
Year 0	1.000	(15,000)	(15,000)	(15,000)
1	0.943	5,658	8,487	14,145
2	0.890	5,340	8,010	13,350
3	0.840	5,040	7,560	12,600
NPV		1,038	9,057	25,095

Machine B

	2,000 demand	3,000 demand	5,000 demand
Year	N₦	N₦	N₦
0	(20,000)	(20,000)	(20,000)
1	7,000	10,500	17,500
2	7,000	10,500	17,500
3	7,000	10,500	17,500

Discounted Cash Flows	Discount factor at 6%	PV
Year 0	1.000	(20,000)
1	0.943	6,601
2	0.890	6,230
3	0.840	5,880
NPV		(1,289)

(B). Expected value of NPV for Machine A = (0.2 × 1,038) + (0.6 × 9,057) + (0.2 × 25,095) = N₦10,661

Expected value of NPV for Machine B = (0.2 × (1,289)) + (0.6 × 8,067) + (0.2 × 26,778) = N₦9,938

Note: A quicker way of calculating expected values is to:

Calculate the EV of annual sales (which is 3,200 units)
Calculate the cash flows and NPV for annual sales of 3,200 units.
However, this approach makes it more difficult to carry out risk and uncertainty analysis.

On the basis of the figures, it would seem that Machine A should be purchased.

It has a higher expected value of NPV.
It is also a lower risk option, because the NPV will be positive even when sales are only 2,000 units each year. With Machine B, the NPV would be negative if the annual sales are just 2,000 units.
Machine A also gives a higher NPV if sales are 3,000 units, which is the most likely outcome.

(i) The NPV is + N₦1,038 even when sales are 2,000 units each year. The probability of a negative NPV is 0%. (With Machine B, the risk of a negative NPV is 20%).

(ii) The project will achieve a 6% return if the NPV of annual cash profits is N₦15,000.

Discount factor at 6% for years 1–3 = 2.673

Annual cash profits to achieve a PV of N₦15,000 = N₦15,000 / 2.673 = N₦5,612.

The contribution per unit is N₦3.

Therefore, minimum annual sales to achieve an NPV of N₦0 = N₦5,612 / N₦3 per unit = 1,871 units.

If annual sales exceed 1,871 units, the NPV with Machine A will be positive at a discount rate of 6%.

Tags: break-even analysis, DCF, investment appraisal, NPV, Probability, Sensitivity Analysis
Level: Level 2

Topic: DCF: Risk and uncertainty

Uploader: Samuel Duah