- 20 Marks
FM – L2 – Q69 – Discounted cash flow
Question
A well-established company in the region of the Volta River manufactures engines. One of its current products is Product X, for which sales will be 150,000 units in the year just ending (Year 1). However, after four more years, at the end of Year 5, Product X will no longer be permitted, when new government environmental regulations come into force. On or before that time, the company needs to introduce a new product to replace Product X.
A replacement product has already been developed. This is Product Y. A market research report has estimated that, if Product Y is introduced to the market now to replace Product X, annual sales of Product Y at a unit price of GH₵350 would be:
| Annual sales (units) | Probability |
|---|---|
| 100,000 | 0.2 |
| 80,000 | 0.5 |
| 50,000 | 0.3 |
The current selling price of Product X is GH₵250 per unit, and its variable cost of sales is GH₵180. There is no possibility of increasing the selling price.
The annual sales demand for Product X is expected to fall each year if it is kept on the market. The best estimate is that annual sales in Year 2 will be 10,000 units less than in Year 1, with a further fall in sales by 10,000 units each year until Year 5.
To prepare a production facility for manufacturing Product Y instead of Product X, an initial capital outlay of GH₵2,000,000 would be required. Annual fixed costs would increase by GH₵160,000. The variable cost of making and selling Product Y would be GH₵230 per unit.
The company’s cost of capital is 8%. Ignore inflation and taxation.
Required:
(a) Using DCF analysis, calculate the NPV of a proposal to replace Product X with Product Y from Year 2 onwards.
(b) Estimate the minimum annual sales for Product Y that would be required to justify the immediate replacement of Product X with Product Y. Assume that the estimates of annual sales of Product X are correct.
(c) Calculate the minimum reduction in the annual sales of Product X, in Year 2 and in each subsequent year that would be necessary before you recommended the immediate replacement of Product X with Product Y. Assume that the estimates of annual sales of Product Y are correct.
(d) List briefly the weaknesses or limitations in the financial analysis in part (a) to (c) above.
Answer
(a) Workings
If Product X is kept on the market for four more years:
| Year | Unit sales | Unit contribution | Annual contribution |
|---|---|---|---|
| GH₵ | GH₵ | ||
| 1 | 140,000 | 70 | 9,800,000 |
| 2 | 130,000 | 70 | 9,100,000 |
| 3 | 120,000 | 70 | 8,400,000 |
| 4 | 110,000 | 70 | 7,700,000 |
If Product Y is introduced:
EV of annual sales = (0.2 × 100,000) + (0.5 × 80,000) + (0.3 × 50,000) = 75,000 units.
Unit contribution = GH₵350 − GH₵230 = GH₵120.
EV of annual contribution = 75,000 units × GH₵120 = GH₵9,000,000.
Solution
| Year | Extra costs | Lost contribution from X | Contribution from Y | Net cash flow | Discount factor 8% | PV |
|---|---|---|---|---|---|---|
| GH₵000 | GH₵000 | GH₵000 | GH₵000 | GH₵000 | ||
| 0 | (2,000) | (2,000) | 1.000 | (2,000) | ||
| 1 | (160) | (9,800) | 9,000 | (960) | 0.926 | (889) |
| 2 | (160) | (9,100) | 9,000 | (260) | 0.857 | (223) |
| 3 | (160) | (8,400) | 9,000 | 440 | 0.794 | 349 |
| 4 | (160) | (7,700) | 9,000 | 1,140 | 0.735 | 838 |
| NPV | (1,925) |
The NPV is -GH₵1,925,000, indicating that the immediate replacement of Product X with Product Y is not justified.
(b) The discount factor for Year 1-4 at a cost of capital of 8% = 3.312.
To justify the immediate replacement of Product X with Product Y, the annual contribution from Product Y would need to be higher by at least GH₵1,925,000 / 3.312 = GH₵581,220.
The annual contribution per unit from Product Y is currently estimated to be GH₵120.
Annual sales in units from Product Y would therefore need to be higher by at least: GH₵581,220 / GH₵120 per unit = 4,843.5 units – say 5,000 units.
(c) Tutorial note: Annual sales of Product X are expected to fall by an additional amount each year. It is therefore not possible to devise a simple computation for the minimum fall in annual sales that would be required to justify immediate replacement by Product Y. The method used in the solution below is therefore based on an interpolation method. The NPV is estimated assuming a fall of 15,000 units in sales each year, rather than 10,000 units. A net present value is calculated, and this is used together with the answer in (a) to obtain a ‘breakeven’ point.
Solution
If annual sales of Product X were to fall by 15,000 units in each subsequent year from Year 2 onwards, the contribution lost by replacing Product X with Product Y would be as follows:
| Year | Unit sales | Unit contribution | Annual contribution |
|---|---|---|---|
| GH₵ | GH₵ | ||
| 1 | 135,000 | 70 | 9,450,000 |
| 2 | 120,000 | 70 | 8,400,000 |
| 3 | 105,000 | 70 | 7,350,000 |
| 4 | 90,000 | 70 | 6,300,000 |
The NPV of a decision to introduce Product Y immediately would be:
| Year | Extra costs | Lost contribution from X | Contribution from Y | Net cash flow | Discount factor 8% | PV |
|---|---|---|---|---|---|---|
| GH₵000 | GH₵000 | GH₵000 | GH₵000 | GH₵000 | ||
| 0 | (2,000) | (2,000) | 1.000 | (2,000) | ||
| 1 | (160) | (9,450) | 9,000 | (610) | 0.926 | (565) |
| 2 | (160) | (8,400) | 9,000 | 440 | 0.857 | 377 |
| 3 | (160) | (7,350) | 9,000 | 1,490 | 0.794 | 1,183 |
| 4 | (160) | (6,300) | 9,000 | 2,540 | 0.735 | 1,867 |
| NPV | +862 |
If annual sales of Product X fall by 10,000 units each year, the NPV would be GH₵(1,925,000).
If annual sales of Product X fall by 15,000 units each year, the NPV would be GH₵862,000.
The minimum fall in annual sales of Product X needed to justify its immediate replacement by Product Y is therefore approximately:
(d) Limitations of analysis:
(1) Expected value used for sales of Product Y. Actual sales could be higher or lower than 75,000 each year.
(2) Estimates of falls in sales of Product X cannot be predicted accurately.
(3) The calculations have ignored taxation and inflation, which is inappropriate in practice.
(4) A cost of capital of 8% has been assumed. This may be inappropriate.
(5) There has been no consideration of the options to introduce Product Y at the beginning of Year 3, or Year 4 or Year 5.
(6) The option to reduce the selling price of Product X to increase annual sales has not been considered. Similarly, an option to sell Product Y at a lower price to increase annual sales has not been considered.
(7) Non-financial factors have been ignored: for example, the longer-term marketing advantage to be gained from introducing Y as soon as possible.
- Tags: DCF, Financial analysis, Limitations, NPV, product replacement
- Level: Level 2
- Topic: Discounted cash flow
- Uploader: Samuel Duah