- 16 Marks
FM – L2 – Q68 – Discounted Cash Flow
Question
Accra Nova Cosmetics Limited has designed a new product that it would like to introduce to the market. It has spent GH¢250,000 on the design work so far. A market research report has indicated that the product will have a life of four years, and at a selling price of GH¢35 per unit, annual sales would be as follows:
| Year | Sales (units) |
|---|---|
| 1 | 40,000 |
| 2 | 60,000 |
| 3 | 60,000 |
| 4 | 20,000 |
It has been estimated that to produce the new product, annual fixed production costs (all cash flows) will increase by GH¢200,000, and the variable cost per unit will be GH¢10.
Other cash flows for the project will be:
- Capital expenditure of GH¢1,400,000 at the beginning of the project. There will be a residual value of GH¢600,000 from this investment at the end of Year 4.
- An investment of GH¢400,000 will be required in working capital. This will be recovered at the end of Year 4.
- Expenditure on advertising will be required, as follows:
| Year | Advertising costs |
|---|---|
| 0 | 800,000 |
| 1 | 600,000 |
| 2 | 400,000 |
| 3 | 200,000 |
Required
(a) Calculate the expected NPV of the project to launch the new product, if the company’s cost of capital is 12%.
(b) Calculate the target cost for the product that is needed to achieve a return of 12% on investment and calculate the size of the current cost gap.
Answer
(A). NPV of the project
| Year | Working capital | Cost/residual value | Sales revenue | Advertising costs | Fixed production (cash) costs | Net cash flows, excluding variable costs | Discount factor at 12% | Present va
lue |
|---|---|---|---|---|---|---|---|---|
| 0 | (400) | (1,400) | (800) | (2,600) | 1.000 | (2,600) | ||
| 1 | 1,400 | (600) | (200) | 600 | 0.893 | 536 | ||
| 2 | 2,100 | (400) | (200) | 1,500 | 0.797 | 1,196 | ||
| 3 | 2,100 | (200) | (200) | 1,700 | 0.712 | 1,210 | ||
| 4 | 400 | 600 | 700 | (200) | 1,500 | 0.636 | 954 | |
| NPV | 1,296 |
(B).
The target cost per unit is the maximum variable cost per unit that would result in an NPV of zero.
From the answer to part (a), the NPV of the project, ignoring variable costs, is GH¢1,296,000.
The variable cost per unit is GH¢10.
| Year | Sales | Variable cost per unit | Total variable cost | Discount factor at 12% | Present value |
|---|---|---|---|---|---|
| 1 | 40,000 | 10 | 400 | 0.893 | 357 |
| 2 | 60,000 | 10 | 600 | 0.797 | 478 |
| 3 | 60,000 | 10 | 600 | 0.712 | 427 |
| 4 | 20,000 | 10 | 200 | 0.636 | 127 |
| 1,389 |
The NPV of the project, allowing for variable costs, is therefore 1,296 – 1,389 = GH¢(93,000).
To achieve a return of 12%, the NPV should be zero, so the PV of the variable costs should be reduced by GH¢93,000, to GH¢1,296,000.
Total sales are 40,000 + 60,000 + 60,000 + 20,000 = 180,000 units.
The target cost per unit is therefore:
PV of variable costs = 1,296,000 / (357 + 478 + 427 + 127) = 1,296,000 / 1,389 = 0.933 × 10 = GH¢9.33.
The current cost gap per unit is therefore GH¢10 – GH¢9.33 = GH¢0.67 per unit.
The total cost gap is GH¢0.67 × 180,000 = GH¢120,600.
- Tags: Cost Gap, investment appraisal, NPV, Target Cost, variable costs
- Level: Level 2
- Topic: Discounted cash flow
- Uploader: Samuel Duah