- 21 Marks
FM – L2 – Q62 – Discounted cash flow
Question
DOME FABRICATION LIMITED
(a) Contribution
Strategy 1
| Year | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Demand (units) | 10,000 | 12,000 | 15,000 | 18,000 | 20,000 |
| Selling price (unit) | GH¢25 | GH¢25 | GH¢25 | GH¢25 | GH¢25 |
| Variable cost (unit) | GH¢15 | GH¢15 | GH¢15 | GH¢15 | GH¢15 |
| Contribution (unit) | |||||
| Inflated contribution | |||||
| Total contribution (GH¢) |
| 10% discount factors | |||||
|---|---|---|---|---|---|
| PV of contribution (GH¢) |
Total PV of Strategy 1 contributions =
Strategy 2
| Year | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Demand (units) | 12,000 | 14,000daf | 16,000 | 18,000 | 20,000 |
| Selling price (unit) | GH¢22 | GH¢22 | GH¢22 | GH¢22 | GH¢22 |
| Variable cost (unit) | GH¢12 | GH¢12 | GH¢12 | GH¢12 | GH¢12 |
| Contribution (unit) | |||||
| Inflated contribution | |||||
| Total contribution | |||||
| Total contribution | |||||
| PV of contribution (GH¢) |
Total PV of strategy 2 contributions =
Strategy 2 is preferred as it has the higher present value of contributions.
(b) Evaluating the investment in the new machine using internal rate of return
| Year | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Total contribution | |||||
| Fixed costs | |||||
| Profit | |||||
| 10% discount factors | |||||
| Present value | |||||
| 20% discount factors | |||||
| Present value of profits |
Answer
(a) Contribution
Strategy 1
| Year | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Demand (units) | 10,000 | 12,000 | 15,000 | 18,000 | 20,000 |
| Selling price (unit) | GH¢25 | GH¢25 | GH¢25 | GH¢25 | GH¢25 |
| Variable cost (unit) | GH¢15 | GH¢15 | GH¢15 | GH¢15 | GH¢15 |
| Contribution (unit) | GH¢10 | GH¢10 | GH¢10 | GH¢10 | GH¢10 |
| Inflated contribution | GH¢10 | GH¢10 | GH¢10 | GH¢10 | GH¢10 |
| Total contribution (GH¢) | 100,000 | 120,000 | 150,000 | 180,000 | 200,000 |
| 10% discount factors | 0.909 | 0.826 | 0.751 | 0.683 | 0.621 |
| PV of contribution (GH¢) | 90,900 | 99,120 | 112,650 | 122,940 | 124,200 |
Total PV of Strategy 1 contributions = GH¢2,280,045.
Strategy 2
| Year | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Demand (units) | 12,000 | 14,000 | 16,000 | 18,000 | 20,000 |
| Selling price (unit) | GH¢22 | GH¢22 | GH¢22 | GH¢22 | GH¢22 |
| Variable cost (unit) | GH¢12 | GH¢12 | GH¢12 | GH¢12 | GH¢12 |
| Contribution (unit) | GH¢10 | GH¢10 | GH¢10 | GH¢10 | GH¢10 |
| Inflated contribution | GH¢10 | GH¢10 | GH¢10 | GH¢10 | GH¢10 |
| Total contribution | 120,000 | 140,000 | 160,000 | 180,000 | 200,000 |
| 10% discount factors | 0.909 | 0.826 | 0.751 | 0.683 | 0.621 |
| PV of contribution (GH¢) | 109,080 | 115,640 | 120,160 | 122,940 | 124,200 |
Total PV of Strategy 2 contributions = GH¢2,542,474.
Strategy 2 is preferred as it has the higher present value of contributions.
(b) Evaluating the investment in the new machine using internal rate of return
| Year | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Total contribution | 458,700 | 550,275 | 667,730 | 809,713 | 952,737 |
| Fixed costs | (114,400) | (118,976) | (123,735) | (128,684) | (133,800) |
| Profit | 344,300 | 431,299 | 543,995 | 681,029 | 818,937 |
| 10% discount factors | 0.909 | 0.826 | 0.751 | 0.683 | 0.621 |
| Present value | 312,969 | 356,253 | 408,540 | 465,143 | 508,380 |
| 20% discount factors | 0.833 | 0.694 | 0.579 | 0.482 | 0.402 |
| Present value of profits | 286,802 | 299,322 | 314,973 | 328,256 | 329,213 |
Including the cost of the initial investment to give the present values at two discount rates:
| 10% discount rate | 20% discount rate | |
|---|---|---|
| GH¢ | GH¢ | |
| Sum of present values of profits | 2,076,285 | 1,574,633 |
| Initial investment | (1,600,000) | (1,600,000) |
| Net present value | 476,265 | (25,367) |
IRR = 10% + [476,285 / (476,285 + 25,367)] × (20 – 10)% = 19.5%
Since the internal rate of return is greater than the company’s cost of capital of 10%, the investment is financially acceptable.
- Tags: Cash Flows, Contribution, Cost of Capital, Discounted cash flow, Financial analysis, Inflation, investment appraisal, IRR, NPV
- Level: Level 2
- Topic: Discounted cash flow
- Uploader: Samuel Duah