- 20 Marks
FM – L2 – Q79 – Discounted Cash Flow
Question
The Board of Zenith Solutions Ltd is considering the company’s capital investment options for the coming year, and also evaluating the following potential investments:
Investment A
This investment is similar to its current investments and requires an investment of GH₵60,000 now, GH₵40,000 for new capital equipment and GH₵20,000 for increases in working capital. This will be financed from Shareholders Funds. Sales next year would be 10,000 units, variable costs would be GH₵6 and the product would be sold for GH₵10. But due to entry of new competitors and technological improvements, the sales price would decline by 20% per annum thereafter, sales volume would fall by 10% and variable costs would fall by 20% per annum. Overheads attributed to the project would be GH₵15,000 per annum.
In year three the project would be wound up, working capital investment would be recovered and capital equipment sold off for 25% of its purchase costs the following year. Fixed costs include an annual charge of GH₵4,000 for depreciation.
Investment B
This is a long-term project in a totally new area, involving an immediate outlay of GH₵90,000, which they intend to borrow from their lenders at 6%. They expect net profits of GH₵12,000 next year, rising thereafter by 3% per annum in perpetuity.
Investment C
This is another long-term investment in a totally new area, involving an immediate outlay of GH₵25,000 which they intend financing by retained earnings. Expected annual net cash profits are as follows:
Years 1 to 4: GH₵3,000
Years 5 to 7: GH₵5,000
Year 8 onwards forever: GH₵7,000
The company discounts all projects lasting ten years duration or less at a cost of capital of 10% and all other projects at a cost of 13%. You may ignore taxation.
Required:
(a) Calculate the NPV of each project.
(b) Calculate the IRR of investments A and B (you may use 25% as the upper limit if you wish) and comment accordingly.
Answer
(A). INVESTMENT A
| Year | Sales (units) | Selling Price (GH₵) | Variable Cost (GH₵) | Total Sales (GH₵) | Variable Cost (GH₵) | Contribution (GH₵) | Overheads (GH₵) | Net Cash Flow (GH₵) | DF (10%) | PV (GH₵) |
|---|---|---|---|---|---|---|---|---|---|---|
| 0 | (60,000) | 1.000 | (60,000) | |||||||
| 1 | 10,000 | 10.00 | 6.00 | 100,000 | 60,000 | 40,000 | 15,000 | 29,000 | 0.909 | 26,361 |
| 2 | 9,000 | 8.00 | 4.80 | 72,000 | 43,200 | 28,800 | 15,000 | 17,800 | 0.826 | 14,703 |
| 3 | 8,100 | 6.40 | 3.84 | 51,840 | 31,104 | 20,736 | 15,000 | 29,736* | 0.751 | 22,312 |
| 4 | 10,000** | 0.683 | 6,830 |
*Includes recovery of working capital (GH₵20,000)
**Sale of capital equipment (25% of GH₵40,000 = GH₵10,000)
NPV = GH₵10,226
INVESTMENT B
r = 13%
g = 3%
Costs = GH₵90,000
Yr 1 = GH₵12,000
NPV = PV benefits – PV of costs =
PV Benefits = CF1 / (r – g) = 12,000 / (0.13 – 0.03) = GH₵120,000
NPV = GH₵120,000 – GH₵90,000 = GH₵30,000
INVESTMENT C
NPV = PV benefits – PV of costs =
PV of GH₵7,000 per annum in perpetuity = CFt / r = 7,000 / 0.13 = GH₵53,846.15
Less PV of GH₵7,000 a years 1 to 7 × discount factor = GH₵7,000 × 4.423 = GH₵30,961
Thus PV of GH₵7,000 a year from year 8 in perpetuity = GH₵53,846.15 – GH₵30,961 = GH₵22,885.15
| Year | Net Cash Flow (GH₵) | Discount Factor (13%) | Present Value (GH₵) |
|---|---|---|---|
| 0 | (25,000) | 1.000 | (25,000) |
| 1-4 | 3,000 | 2.974 | 8,922 |
| 5-7 | 5,000 | 1.448 | 7,240 |
| 8+ | 7,000 | 22,888 | |
| NPV | 14,050 |
As all projects have positive NPVs, they should all be undertaken. On the basis of the NPV criteria, project B has the greatest positive net present value, followed by A then C and all should be undertaken.
Since the NPV values depend crucially on the discount rate used, students should outline to the board of Zenith Solutions Ltd. the appropriateness of their choice of discount rates.
(B).
From the calculations below, the IRR of Investment A is approximately 23% while the IRR of Investment B is approximately 18.5%. Thus both meet the required return of projects as given by the board of Zenith Solutions Ltd. i.e. 10% for all projects lasting ten years duration or less and 13% for all other projects.
INVESTMENT A
| Year | Net Cash Flow (GH₵) | DF (25%) | PV (GH₵) |
|---|---|---|---|
| 0 | (60,000) | 1.000 | (60,000) |
| 1 | 29,000 | 0.800 | 23,200 |
| 2 | 17,800 | 0.640 | 11,392 |
| 3 | 29,736 | 0.512 | 15,225 |
| 4 | 10,000 | 0.410 | 4,100 |
NPV = -6,083
IRR = A + {(a / (a – b)) × (B – A)}
i.e. at r = 10%, NPV = GH₵10,226
i.e. at r = 25%, NPV = GH₵-2,426.72
IRR = 10% + {(10,226 / (10,226 – (-6,083)) × (25% – 10%)}
10% + {(10,226 / 16,309) × (15%)}
10% + {(0.627) × (15%)}
10% + {0.094}
10% + 9.4%
19.4% approximately
INVESTMENT B
r = 13%
g = 3%
Costs = GH₵90,000
Year 1 = GH₵12,000
NPV = PV Benefits – PV of Costs =
PV Benefits = CF1 / (r – g) = 12,000 / (0.13 – 0.03) = GH₵120,000
NPV = GH₵120,000 – 90,000 = GH₵30,000
r = 25%
g = 3%
Costs = GH₵90,000
Year 1 = GH₵12,000
NPV = PV Benefits – PV of Costs =
PV Benefits = CF1 / (r – g) = 12,000 / (0.25 – 0.03) = GH₵54,545.45
NPV = GH₵54,545.45 – 90,000.00 = -35,454.55
i.e. at r = 13%, NPV = GH₵30,000
i.e. at r = 25%, NPV = GH₵-35,454.55
IRR = 13% + ((30,000 / (30,000 – (-35,454.55)) × (25% – 13%)))
= 13% + ((30,000 / 65,454.55) × 12%)
= 13% + (0.458 × 12%)
= 13% + 5.50%
= 18.50% approximately
- Tags: Capital Budgeting, Discounted cash flow, investment appraisal, IRR, Perpetuity
- Level: Level 2
- Topic: Discounted cash flow
- Uploader: Samuel Duah