Strategic Maneuvering for the Exam
High-Priority Concepts & Difficulty Levels
Based on the provided past questions, the ICMAB exam heavily focuses on Net Present Value (NPV) and related concepts. The difficulty level is typically intermediate to advanced, requiring careful attention to detail and a solid grasp of cash flow adjustments. You must be able to perform multi-step calculations that involve:
- Calculating Incremental Cash Flows: This is a core skill. You should know how to find the difference between cash flows with and without the project, including changes in revenue, costs, and depreciation.
- Adjusting for Non-Standard Information: Questions often include elements like inflation, changes in working capital, or different tax treatments for assets, which are designed to test your attention to detail.
- Handling Mutually Exclusive Projects and Capital Rationing: You must understand when to use NPV vs. other criteria like the Profitability Index (PI). The exam tests your ability to apply the correct decision rule based on the constraints of the problem.
What to Mention for Maximum Marks
For computational problems, don't just provide a final number. To get full marks, you must show your work clearly. A professional presentation would include:
- A clear table outlining all cash flow components for each year.
- Explicitly state all formulas used for each step of the calculation.
- Provide a clear and concise conclusion at the end, advising on whether to accept or reject the project, and a brief justification based on your findings (e.g., "Since NPV > 0, the project should be accepted.").
- Highlight key assumptions you've made, especially regarding inflation or tax treatment, if not explicitly stated in the question.
Past Questions & Solutions
Problem Statement: International Foods Corporation (IFC) currently processes seafood with a unit it purchased several years ago. The unit, which originally cost Tk. 500,000, currently has a book value of Tk. 250,000. IFC is considering replacing the existing unit with a newer, more efficient one. The new unit will cost Tk. 700,000 and will require an additional Tk. 50,000 for delivery and installation. The new unit will also require IFC to increase its investment in initial net working capital by Tk. 40,000. The new unit will be depreciated on a straight-line basis over five years to a zero balance. IFC expects to sell the existing unit for Tk. 275,000. IFC's marginal tax rate is 40 percent.
If IFC purchases the new unit, annual revenues are expected to increase by Tk. 100,000 (due to increased processing capacity), and annual operating costs (exclusive of depreciation) are expected to decrease by Tk. 20,000. Annual revenues and operating costs are expected to remain constant at this new level over the 5-year life of the project. IFC estimates that its net working capital investment will increase by Tk. 10,000 per year over the life of the project. At the end of the project's life (5 years), all working capital investments will be recovered. After five years, the new unit will be completely depreciated and is expected to be sold for Tk. 70,000. (Assume that the existing unit is being depreciated at a rate of Tk. 50,000 per year.)
Required:
(i) Calculate the project's net investment.
(ii) Calculate the annual net cash flows for the project.
Solution:
i. Net Investment (Initial Outlay):
Tricky Area:
Remember that the sale of the old asset has a tax implication. You must account for the taxable gain or loss to find the true after-tax cash flow from the sale.
- Cost of New Unit: Tk. 700,000 (unit) + Tk. 50,000 (installation) = Tk. 750,000
- Initial Working Capital Increase: Tk. 40,000
- Cash Flow from Sale of Old Unit:
Sale Price = Tk. 275,000
Book Value = Tk. 250,000
Taxable Gain = Sale Price - Book Value = $275,000 - 250,000 = \text{Tk. } 25,000$
Tax on Gain = $25,000 \times 0.40 = \text{Tk. } 10,000$
Net Cash from Sale = Sale Price - Tax on Gain = $275,000 - 10,000 = \text{Tk. } 265,000$
Net Investment = Cost of New Unit + Initial NWC - Net Cash from Sale of Old Unit
= $750,000 + 40,000 - 265,000 = \textbf{Tk. 525,000}$
ii. Annual Net Cash Flows:
Tricky Area:
This problem requires calculating **incremental** cash flows, which is the difference between the new project's cash flows and the old one's. You must also remember to account for changes in working capital and the after-tax salvage value at the end of the project.
The annual net cash flow is the sum of the incremental after-tax operating income, the incremental tax shield from depreciation, and the changes in working capital.
- Incremental Revenues: Tk. 100,000
- Incremental Cost Savings: Tk. 20,000
- Incremental Depreciation:
New Dep. = $\frac{750,000}{5} = \text{Tk. } 150,000$
Old Dep. = Tk. 50,000
Incremental Dep. = $150,000 - 50,000 = \text{Tk. } 100,000$
| Particulars | Amount (Tk.) |
|---|---|
| Incremental Revenues | 100,000 |
| Incremental Cost Savings | 20,000 |
| Incremental Depreciation | (100,000) |
| Incremental EBIT | 20,000 |
| Tax (40%) | (8,000) |
| Incremental EAT | 12,000 |
| Add back Incremental Dep. | 100,000 |
| Annual Cash Flow from Operations | 112,000 |
We must also account for the change in net working capital (NWC).
- Annual NWC Increase (Years 1-4): Tk. 10,000
Annual net cash flow (Y1-4) = $112,000 - 10,000 = \textbf{Tk. 102,000}$
- Terminal Cash Flow (Year 5):
Annual Cash Flow from Operations = Tk. 112,000
Salvage Value (after-tax) = Salvage Value - Tax on Gain
Book Value = Tk. 0. Taxable Gain = $70,000 - 0 = \text{Tk. } 70,000$.
Tax on Gain = $70,000 \times 0.40 = \text{Tk. } 28,000$
After-tax Salvage Value = $70,000 - 28,000 = \text{Tk. } 42,000$
Recovery of Total NWC = Initial NWC + Total Annual Increases = $40,000 + (4 \times 10,000) = \text{Tk. } 80,000$
Terminal Cash Flow (Y5) = Annual CF + After-tax Salvage + NWC Recovery
= $112,000 + 42,000 + 80,000 = \textbf{Tk. 234,000}$
Problem Statement: The Acme Blivet Company is evaluating three investment situations: (1) produce a newline of aluminum blivets, (2) expand its existing blivet line to include several new sizes, and (3) develop a new, higher-quality line of blivet. If only the project in question is undertaken, the expected present values and the amounts of investment required are as follows:
| Project | Investment required | Present value of future cash flows |
|---|---|---|
| 1 | 200,000 | 290,000 |
| 2 | 115,000 | 185,000 |
| 3 | 270,000 | 400,000 |
If projects 1 and 2 are jointly undertaken, there will be no economies; the investment required and present values will simply be the sum of the parts. With projects 1 and 3, economies are possible in investment because one of the machines acquired can be used in both production processes. The total investment required for projects 1 and 3 combined is Tk. 440,000. If projects 2 and 3 are undertaken, there are economies to be achieved in marketing and producing the products but not in investment. The expected present value of future cash flows for projects 2 and 3 combined is Tk. 620,000. If all three projects are undertaken simultaneously, the economies noted above will still hold. However, a Tk. 125,000 extension on the plant will be necessary, as space is not available for all three projects.
Required: Which project or projects should be chosen?
Solution:
Tricky Area:
This is a complex mutually exclusive project problem. You must evaluate every possible combination of projects, including the synergies and costs associated with combining them, to find the one with the highest total NPV.
We need to evaluate the net present value (NPV) of each possible combination of projects and select the combination with the highest positive NPV. The NPV is calculated as the present value of future cash flows minus the investment required.
- Project 1 Only: $NPV_1 = 290,000 - 200,000 = \text{Tk. } 90,000$
- Project 2 Only: $NPV_2 = 185,000 - 115,000 = \text{Tk. } 70,000$
- Project 3 Only: $NPV_3 = 400,000 - 270,000 = \text{Tk. } 130,000$
- Projects 1 & 2 Combined:
Investment = $200,000 + 115,000 = \text{Tk. } 315,000$
PV of CF = $290,000 + 185,000 = \text{Tk. } 475,000$
$NPV_{1+2} = 475,000 - 315,000 = \text{Tk. } 160,000$
- Projects 1 & 3 Combined:
Investment = Tk. 440,000
PV of CF = $290,000 + 400,000 = \text{Tk. } 690,000$
$NPV_{1+3} = 690,000 - 440,000 = \textbf{Tk. 250,000}$
- Projects 2 & 3 Combined:
Investment = $115,000 + 270,000 = \text{Tk. } 385,000$
PV of CF = Tk. 620,000
$NPV_{2+3} = 620,000 - 385,000 = \text{Tk. } 235,000$
- Projects 1, 2, & 3 Combined:
Investment = (Inv 1 + Inv 2 + Inv 3) - Inv savings from 1&3 + cost of plant extension
= $(200,000+115,000+270,000) - ((200,000+270,000) - 440,000) + 125,000$
= $585,000 - 30,000 + 125,000 = \text{Tk. } 680,000$
PV of CF = (PV of 1+PV of 2+PV of 3) + PV gains from 2&3
= $(290,000+185,000+400,000) + (620,000 - (185,000+400,000))$
= $875,000 + 35,000 = \text{Tk. } 910,000$
$NPV_{1+2+3} = 910,000 - 680,000 = \text{Tk. } 230,000$
Comparing the NPVs of all possible combinations, the highest is **Tk. 250,000** from undertaking **Projects 1 and 3**. Therefore, this is the optimal choice.
Problem Statement: PRAN Candy Limited is evaluating three mutually exclusive projects (A, B and C) with a discount rate of 12%. The initial investment and cash inflows are as follows:
Cash inflows (Tk.)
| Project | Initial Outlay | Year 1 | Year 2 |
|---|---|---|---|
| A | (225,000) | 165,000 | 165,000 |
| B | (450,000) | 300,000 | 300,000 |
| C | (225,000) | 181,000 | 135,000 |
i. Compute the Profitability Index (PI) for each project.
ii. Compute the NPV for each project.
iii. Which project(s) should PRAN accept based on the PI rule if they are mutually exclusive?
iv. Which project(s) should PRAN accept if the budget is Tk. 450,000 and projects are not divisible?
Solution:
Tricky Area:
This is a classic capital rationing problem. You must be careful to distinguish between the **PI rule for mutually exclusive projects** (choose the one with the highest PI) and the **PI rule for capital rationing** (choose the combination of projects that maximizes total NPV within the budget).
First, we calculate the NPV for each project, which is required for the profitability index calculation.
| Project | PV of Future Cash Flows | Initial Outlay | NPV | PI |
|---|---|---|---|---|
| A | 278,867 | 225,000 | 53,867 | 1.24 |
| B | 507,030 | 450,000 | 57,030 | 1.13 |
| C | 269,244 | 225,000 | 44,244 | 1.20 |
i. Compute the Profitability Index (PI) for each project.
Formula: $PI = \frac{\text{PV of Future Cash Flows}}{\text{Initial Investment}}$
$PI_A = \frac{278,867}{225,000} = \textbf{1.24}$
$PI_B = \frac{507,030}{450,000} = \textbf{1.13}$
$PI_C = \frac{269,244}{225,000} = \textbf{1.20}$
ii. Compute the NPV for each project.
Formula: $NPV = \text{PV of Inflows} - \text{Initial Outlay}$
$NPV_A = 278,867 - 225,000 = \textbf{Tk. 53,867}$
$NPV_B = 507,030 - 450,000 = \textbf{Tk. 57,030}$
$NPV_C = 269,244 - 225,000 = \textbf{Tk. 44,244}$
iii. Which project(s) should PRAN accept based on the PI rule if they are mutually exclusive?
When projects are mutually exclusive, you should accept the project with the highest PI, as long as its PI is greater than 1. In this case, Project A has the highest PI of 1.24. Therefore, PRAN should accept **Project A**.
iv. Which project(s) should PRAN accept if the budget is Tk. 450,000 and projects are not divisible?
With a capital budget constraint, we must rank the projects by their PI and then select the combination that fits within the budget while maximizing total NPV.
- Project A requires Tk. 225,000. Budget remaining: Tk. 225,000. Total NPV: Tk. 53,867.
- Project C requires Tk. 225,000. Budget remaining: Tk. 225,000. Total NPV: Tk. 44,244.
- Project B requires Tk. 450,000. Budget remaining: Tk. 0. Total NPV: Tk. 57,030.
The combination of Projects A and C has a combined cost of $225,000 + 225,000 = 450,000$, and a combined NPV of $53,867 + 44,244 = \textbf{98,111}$.
Project B alone costs Tk. 450,000 and has an NPV of Tk. 57,030.
Since the combination of Projects A and C yields a higher total NPV than Project B, PRAN should accept **Projects A and C**.
Problem Statement: Metro Limited manufactures household utensils in Bangladesh and is considering investing in a new aluminum smelting and molding plant. This plant will have a useful life of 5 years but will cost Tk. 400,000 to acquire and install with a residual value of Tk. 20,000. The plant will produce 100,000 units per year. Other estimates are given below: Selling price: Tk. 30 per unit, Direct cost: Tk. 20 per unit. Fixed cost (including depreciation) is Tk. 160,000 per annum. Marketing and promotion cost not included in the above will be Tk. 20,000 and Tk. 32,000 for years 1 and 2, respectively. Additionally, investment in debtors and stocks will increase in year 1 by Tk. 30,000 and Tk. 40,000, respectively. Creditors will also increase by Tk. 20,000 in year 1. Thus, debtors, stocks, and creditors will be recouped at the end of the machine life. The cost of capital is 18%. Corporate tax is 25% and is paid in the year in which profits are made. Depreciation is tax deductible. Required: Compute the Net Present Value of this project and advise Metro Limited whether the plant should be acquired.
Solution:
Tricky Area:
This problem requires you to meticulously track cash flows over five years, accounting for initial and final working capital investments and project-specific costs like marketing. NPV calculation is a key part of the question.
Net Present Value (NPV) Calculation:
First, we calculate the initial investment and the change in working capital.
Initial Outlay (Year 0): Tk. (400,000)
Change in Working Capital (Year 1): Tk. (30,000 + 40,000 - 20,000) = Tk. (50,000)
Depreciation (Straight-line) = $\frac{\text{Cost} - \text{Salvage Value}}{\text{Life}} = \frac{400,000 - 20,000}{5} = \text{Tk. } 76,000$ per year.
Annual Cash Flows (Years 1-5):
| Particulars | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
|---|---|---|---|---|---|
| Sales Revenue | 3,000,000 | 3,000,000 | 3,000,000 | 3,000,000 | 3,000,000 |
| Direct Cost | (2,000,000) | (2,000,000) | (2,000,000) | (2,000,000) | (2,000,000) |
| Fixed Cost (excl. dep) | (84,000) | (84,000) | (84,000) | (84,000) | (84,000) |
| Marketing Cost | (20,000) | (32,000) | 0 | 0 | 0 |
| Depreciation | (76,000) | (76,000) | (76,000) | (76,000) | (76,000) |
| EBIT | 820,000 | 808,000 | 840,000 | 840,000 | 840,000 |
| Tax (25%) | (205,000) | (202,000) | (210,000) | (210,000) | (210,000) |
| EBIT(1-T) | 615,000 | 606,000 | 630,000 | 630,000 | 630,000 |
| Add back Depreciation | 76,000 | 76,000 | 76,000 | 76,000 | 76,000 |
| Working Capital Recovery | 50,000 | ||||
| Salvage Value | 20,000 | ||||
| Tax on Salvage (assuming no gain/loss) | (0) | ||||
| Total Cash Flow | 691,000 | 682,000 | 706,000 | 706,000 | 776,000 |
Note: Fixed cost without depreciation is $160,000 - 76,000 = \text{Tk. } 84,000$.
Now, we calculate the NPV by discounting all cash flows at 18%.
$NPV = -400,000 + \frac{691,000}{1.18^1} + \frac{682,000}{1.18^2} + \frac{706,000}{1.18^3} + \frac{706,000}{1.18^4} + \frac{776,000}{1.18^5} - 50,000$
We adjust for the initial working capital investment in year 0. So, initial investment is Tk. (450,000). The recovery is at year 5.
$NPV = -450,000 + 585,593 + 489,510 + 430,978 + 364,547 + 338,367 = \textbf{Tk. 1,358,995}$
The NPV of the project is approximately **Tk. 1,358,995**. Since the NPV is positive, Metro Limited should **acquire** the plant.
Problem Statement: PRAN Candy Limited is evaluating three mutually exclusive projects (A, B and C) with a discount rate of 12%. The initial investment and cash inflows are as follows:
Cash inflows (Tk.)
| Project | Initial Outlay | Year 1 | Year 2 |
|---|---|---|---|
| A | (225,000) | 165,000 | 165,000 |
| B | (450,000) | 300,000 | 300,000 |
| C | (225,000) | 181,000 | 135,000 |
i. Compute the Profitability Index (PI) for each project.
ii. Compute the NPV for each project.
iii. Which project(s) should PRAN accept based on the PI rule if they are mutually exclusive?
iv. Which project(s) should PRAN accept if the budget is Tk. 450,000 and projects are not divisible?
Solution:
Tricky Area:
This is a classic capital rationing problem. You must be careful to distinguish between the **PI rule for mutually exclusive projects** (choose the one with the highest PI) and the **PI rule for capital rationing** (choose the combination of projects that maximizes total NPV within the budget).
First, we calculate the NPV for each project, which is required for the profitability index calculation.
| Project | PV of Future Cash Flows | Initial Outlay | NPV | PI |
|---|---|---|---|---|
| A | 278,867 | 225,000 | 53,867 | 1.24 |
| B | 507,030 | 450,000 | 57,030 | 1.13 |
| C | 269,244 | 225,000 | 44,244 | 1.20 |
i. Compute the Profitability Index (PI) for each project.
Formula: $PI = \frac{\text{PV of Future Cash Flows}}{\text{Initial Investment}}$
$PI_A = \frac{278,867}{225,000} = \textbf{1.24}$
$PI_B = \frac{507,030}{450,000} = \textbf{1.13}$
$PI_C = \frac{269,244}{225,000} = \textbf{1.20}$
ii. Compute the NPV for each project.
Formula: $NPV = \text{PV of Inflows} - \text{Initial Outlay}$
$NPV_A = 278,867 - 225,000 = \textbf{Tk. 53,867}$
$NPV_B = 507,030 - 450,000 = \textbf{Tk. 57,030}$
$NPV_C = 269,244 - 225,000 = \textbf{Tk. 44,244}$
iii. Which project(s) should PRAN accept based on the PI rule if they are mutually exclusive?
When projects are mutually exclusive, you should accept the project with the highest PI, as long as its PI is greater than 1. In this case, Project A has the highest PI of 1.24. Therefore, PRAN should accept **Project A**.
iv. Which project(s) should PRAN accept if the budget is Tk. 450,000 and projects are not divisible?
With a capital budget constraint, we must rank the projects by their PI and then select the combination that fits within the budget while maximizing total NPV.
- Project A requires Tk. 225,000. Budget remaining: Tk. 225,000. Total NPV: Tk. 53,867.
- Project C requires Tk. 225,000. Budget remaining: Tk. 225,000. Total NPV: Tk. 44,244.
- Project B requires Tk. 450,000. Budget remaining: Tk. 0. Total NPV: Tk. 57,030.
The combination of Projects A and C has a combined cost of $225,000 + 225,000 = 450,000$, and a combined NPV of $53,867 + 44,244 = \textbf{98,111}$.
Project B alone costs Tk. 450,000 and has an NPV of Tk. 57,030.
Since the combination of Projects A and C yields a higher total NPV than Project B, PRAN should accept **Projects A and C**.
Problem Statement: Metro Limited manufactures household utensils in Bangladesh and is considering investing in a new aluminum smelting and molding plant. This plant will have a useful life of 5 years but will cost Tk. 400,000 to acquire and install with a residual value of Tk. 20,000. The plant will produce 100,000 units per year. Other estimates are given below: Selling price: Tk. 30 per unit, Direct cost: Tk. 20 per unit. Fixed cost (including depreciation) is Tk. 160,000 per annum. Marketing and promotion cost not included in the above will be Tk. 20,000 and Tk. 32,000 for years 1 and 2, respectively. Additionally, investment in debtors and stocks will increase in year 1 by Tk. 30,000 and Tk. 40,000, respectively. Creditors will also increase by Tk. 20,000 in year 1. Thus, debtors, stocks, and creditors will be recouped at the end of the machine life. The cost of capital is 18%. Corporate tax is 25% and is paid in the year in which profits are made. Depreciation is tax deductible. Required: Compute the Net Present Value of this project and advise Metro Limited whether the plant should be acquired.
Solution:
Tricky Area:
This problem requires you to meticulously track cash flows over five years, accounting for initial and final working capital investments and project-specific costs like marketing. NPV calculation is a key part of the question.
Net Present Value (NPV) Calculation:
First, we calculate the initial investment and the change in working capital.
Initial Outlay (Year 0): Tk. (400,000)
Change in Working Capital (Year 1): Tk. (30,000 + 40,000 - 20,000) = Tk. (50,000)
Depreciation (Straight-line) = $\frac{\text{Cost} - \text{Salvage Value}}{\text{Life}} = \frac{400,000 - 20,000}{5} = \text{Tk. } 76,000$ per year.
Annual Cash Flows (Years 1-5):
| Particulars | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
|---|---|---|---|---|---|
| Sales Revenue | 3,000,000 | 3,000,000 | 3,000,000 | 3,000,000 | 3,000,000 |
| Direct Cost | (2,000,000) | (2,000,000) | (2,000,000) | (2,000,000) | (2,000,000) |
| Fixed Cost (excl. dep) | (84,000) | (84,000) | (84,000) | (84,000) | (84,000) |
| Marketing Cost | (20,000) | (32,000) | 0 | 0 | 0 |
| Depreciation | (76,000) | (76,000) | (76,000) | (76,000) | (76,000) |
| EBIT | 820,000 | 808,000 | 840,000 | 840,000 | 840,000 |
| Tax (25%) | (205,000) | (202,000) | (210,000) | (210,000) | (210,000) |
| EBIT(1-T) | 615,000 | 606,000 | 630,000 | 630,000 | 630,000 |
| Add back Depreciation | 76,000 | 76,000 | 76,000 | 76,000 | 76,000 |
| Working Capital Recovery | 50,000 | ||||
| Salvage Value | 20,000 | ||||
| Tax on Salvage (assuming no gain/loss) | (0) | ||||
| Total Cash Flow | 691,000 | 682,000 | 706,000 | 706,000 | 776,000 |
Note: Fixed cost without depreciation is $160,000 - 76,000 = \text{Tk. } 84,000$.
Now, we calculate the NPV by discounting all cash flows at 18%.
$NPV = -400,000 + \frac{691,000}{1.18^1} + \frac{682,000}{1.18^2} + \frac{706,000}{1.18^3} + \frac{706,000}{1.18^4} + \frac{776,000}{1.18^5} - 50,000$
We adjust for the initial working capital investment in year 0. So, initial investment is Tk. (450,000). The recovery is at year 5.
$NPV = -450,000 + 585,593 + 489,510 + 430,978 + 364,547 + 338,367 = \textbf{Tk. 1,358,995}$
The NPV of the project is approximately **Tk. 1,358,995**. Since the NPV is positive, Metro Limited should **acquire** the plant.
Problem Statement: PRAN Candy Limited is evaluating three mutually exclusive projects (A, B and C) with a discount rate of 12%. The initial investment and cash inflows are as follows:
Cash inflows (Tk.)
| Project | Initial Outlay | Year 1 | Year 2 |
|---|---|---|---|
| A | (225,000) | 165,000 | 165,000 |
| B | (450,000) | 300,000 | 300,000 |
| C | (225,000) | 181,000 | 135,000 |
i. Compute the Profitability Index (PI) for each project.
ii. Compute the NPV for each project.
iii. Which project(s) should PRAN accept based on the PI rule if they are mutually exclusive?
iv. Which project(s) should PRAN accept if the budget is Tk. 450,000 and projects are not divisible?
Solution:
Tricky Area:
This is a classic capital rationing problem. You must be careful to distinguish between the **PI rule for mutually exclusive projects** (choose the one with the highest PI) and the **PI rule for capital rationing** (choose the combination of projects that maximizes total NPV within the budget).
First, we calculate the NPV for each project, which is required for the profitability index calculation.
| Project | PV of Future Cash Flows | Initial Outlay | NPV | PI |
|---|---|---|---|---|
| A | 278,867 | 225,000 | 53,867 | 1.24 |
| B | 507,030 | 450,000 | 57,030 | 1.13 |
| C | 269,244 | 225,000 | 44,244 | 1.20 |
i. Compute the Profitability Index (PI) for each project.
Formula: $PI = \frac{\text{PV of Future Cash Flows}}{\text{Initial Investment}}$
$PI_A = \frac{278,867}{225,000} = \textbf{1.24}$
$PI_B = \frac{507,030}{450,000} = \textbf{1.13}$
$PI_C = \frac{269,244}{225,000} = \textbf{1.20}$
ii. Compute the NPV for each project.
Formula: $NPV = \text{PV of Inflows} - \text{Initial Outlay}$
$NPV_A = 278,867 - 225,000 = \textbf{Tk. 53,867}$
$NPV_B = 507,030 - 450,000 = \textbf{Tk. 57,030}$
$NPV_C = 269,244 - 225,000 = \textbf{Tk. 44,244}$
iii. Which project(s) should PRAN accept based on the PI rule if they are mutually exclusive?
When projects are mutually exclusive, you should accept the project with the highest PI, as long as its PI is greater than 1. In this case, Project A has the highest PI of 1.24. Therefore, PRAN should accept **Project A**.
iv. Which project(s) should PRAN accept if the budget is Tk. 450,000 and projects are not divisible?
With a capital budget constraint, we must rank the projects by their PI and then select the combination that fits within the budget while maximizing total NPV.
- Project A requires Tk. 225,000. Budget remaining: Tk. 225,000. Total NPV: Tk. 53,867.
- Project C requires Tk. 225,000. Budget remaining: Tk. 225,000. Total NPV: Tk. 44,244.
- Project B requires Tk. 450,000. Budget remaining: Tk. 0. Total NPV: Tk. 57,030.
The combination of Projects A and C has a combined cost of $225,000 + 225,000 = 450,000$, and a combined NPV of $53,867 + 44,244 = \textbf{98,111}$.
Project B alone costs Tk. 450,000 and has an NPV of Tk. 57,030.
Since the combination of Projects A and C yields a higher total NPV than Project B, PRAN should accept **Projects A and C**.
Problem Statement: DeltaPic is considering investing in a machine to produce computer keyboards. The price of the machine will be Tk. 1.2 million, and its economic life is five years. The machine will be fully depreciated by the straight-line method. The machine will produce 25,000 keyboards each year. The price of each keyboard will be Tk. 47 in the first year and will increase by 3 percent per year. The production cost per keyboard will be Tk. 17 in the first year and will increase by 4 percent per year. The project will have an annual fixed cost of Tk. 235,000 and require an immediate investment of Tk. 200,000 in net working capital. The corporate tax rate for the company is 21 percent. If the appropriate discount rate is 11 percent, what is the NPV of the investment?
Solution:
Tricky Area:
This problem requires you to meticulously track cash flows over five years, accounting for initial and final working capital investments and project-specific costs like marketing. NPV calculation is a key part of the question.
Net Present Value (NPV) Calculation:
First, we calculate the initial investment and the change in working capital.
Initial Outlay (Year 0): Tk. (1,200,000 + 200,000) = Tk. (1,400,000)
Depreciation (Straight-line) = $\frac{\text{Cost} - \text{Salvage Value}}{\text{Life}} = \frac{1,200,000}{5} = \text{Tk. } 240,000$ per year.
Annual Cash Flows (Years 1-5):
| Year | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Initial Outlay | (1,400,000) | |||||
| Revenues (25,000 units) | 1,175,000 | 1,210,250 | 1,246,558 | 1,283,955 | 1,322,474 | |
| Variable Costs (25,000 units) | (425,000) | (442,000) | (459,680) | (478,067) | (497,190) | |
| Fixed Costs | (235,000) | (235,000) | (235,000) | (235,000) | (235,000) | |
| Depreciation | (240,000) | (240,000) | (240,000) | (240,000) | (240,000) | |
| EBIT | 275,000 | 293,250 | 311,878 | 330,888 | 350,284 | |
| Tax (21%) | (57,750) | (61,583) | (65,494) | (69,486) | (73,559) | |
| Net Income | 217,250 | 231,667 | 246,384 | 261,402 | 276,725 | |
| Add Back Depreciation | 240,000 | 240,000 | 240,000 | 240,000 | 240,000 | |
| Annual NWC Change | 200,000 | |||||
| Terminal Value | ||||||
| Total Cash Flow | (1,400,000) | 457,250 | 471,667 | 486,384 | 501,402 | 716,725 |
Note: The NWC of Tk. 200,000 is recovered in year 5. We calculate the PV of all cash flows at the 11% discount rate.
$NPV = -1,400,000 + \frac{457,250}{1.11^1} + \frac{471,667}{1.11^2} + \frac{486,384}{1.11^3} + \frac{501,402}{1.11^4} + \frac{716,725}{1.11^5}$
$NPV = -1,400,000 + 411,937 + 381,644 + 355,510 + 330,899 + 425,142 = \textbf{Tk. 505,132}$
The NPV of the investment is approximately **Tk. 505,132**. Since the NPV is positive, Metro Limited should **acquire** the plant.
Problem Statement: A project requires an initial investment of Tk. 1,000,000, and is expected to generate cash inflows of Tk. 300,000, Tk. 400,000, Tk. 500,000, and Tk. 600,000 for years 1, 2, 3, and 4 respectively. The required rate of return is 15%. Required: (i) Calculate the NPV of the project. (ii) Calculate the IRR of the project. (iii) Should the project be accepted?
Solution:
i. NPV Calculation:
We calculate the NPV by discounting all cash flows at the required rate of return of 15%.
$NPV = -1,000,000 + \frac{300,000}{(1.15)^1} + \frac{400,000}{(1.15)^2} + \frac{500,000}{(1.15)^3} + \frac{600,000}{(1.15)^4}$
$NPV = -1,000,000 + 260,870 + 302,468 + 328,756 + 343,059 = \textbf{Tk. 235,153}$
ii. IRR Calculation:
The IRR is the discount rate that makes the NPV equal to zero. We find this by trial and error.
$0 = -1,000,000 + \frac{300,000}{(1+IRR)^1} + \frac{400,000}{(1+IRR)^2} + \frac{500,000}{(1+IRR)^3} + \frac{600,000}{(1+IRR)^4}$
Using a financial calculator or a spreadsheet function, we find that the IRR is approximately **24.5%**.
iii. Project Acceptance Decision:
Tricky Area:
The decision rule is the same for both NPV and IRR for conventional projects. The IRR rule states you should accept if the IRR is greater than the required return. The NPV rule states you should accept if the NPV is positive.
Based on the NPV rule, since the NPV is positive (Tk. 235,153), the project should be accepted. Based on the IRR rule, since the IRR (24.5%) is greater than the required rate of return (15%), the project should also be accepted.
Therefore, the project should be **accepted**.
Problem Statement: An investment project involves a cost of Tk. 100,000 at year zero. The project is expected to generate cash inflows of Tk. 30,000 in year one, Tk. 40,000 in year two, Tk. 50,000 in year three, and Tk. 60,000 in year four. The company's required rate of return is 10%. Required: (i) Compute the NPV, IRR, and PI. (ii) Advise management whether to accept or reject the project.
Solution:
i. NPV, IRR, and PI Calculation:
Tricky Area:
For this problem, it is best to first set up a cash flow table to organize the data, which will make the subsequent calculations for NPV, IRR, and PI more straightforward.
NPV Calculation:
| Year | Cash Flow (Tk.) | PV Factor (10%) | PV of Cash Flow (Tk.) |
|---|---|---|---|
| 0 | (100,000) | 1.000 | (100,000) |
| 1 | 30,000 | 0.9091 | 27,273 |
| 2 | 40,000 | 0.8264 | 33,056 |
| 3 | 50,000 | 0.7513 | 37,565 |
| 4 | 60,000 | 0.6830 | 40,980 |
| Total NPV | 38,874 |
The NPV of the project is approximately **Tk. 38,874**.
IRR Calculation:
$0 = -100,000 + \frac{30,000}{(1+IRR)^1} + \frac{40,000}{(1+IRR)^2} + \frac{50,000}{(1+IRR)^3} + \frac{60,000}{(1+IRR)^4}$
Using a financial calculator or spreadsheet, the IRR is approximately **25.7%**.
PI Calculation:
Formula: $PI = \frac{\text{PV of Future Cash Flows}}{\text{Initial Investment}}$
PV of future cash flows = $27,273 + 33,056 + 37,565 + 40,980 = 138,874$
$PI = \frac{138,874}{100,000} = \textbf{1.39}$
ii. Project Acceptance Decision:
Since the NPV is positive (Tk. 38,874), the project should be **accepted**. This is consistent with the IRR (25.7%), which is greater than the required rate of return (10%), and the PI (1.39), which is greater than 1. All three criteria indicate the project is a good investment.
Problem Statement: BTRL is considering a project that will have an initial cost of Tk. 1,500,000. It is expected to generate cash inflows of Tk. 600,000, Tk. 700,000, and Tk. 800,000 over the next three years. The required rate of return for the project is 12%. Required: (i) Calculate the project's NPV. (ii) Calculate the project's IRR. (iii) Advise BTRL on whether to accept or reject the project.
Solution:
i. NPV Calculation:
$NPV = -1,500,000 + \frac{600,000}{(1.12)^1} + \frac{700,000}{(1.12)^2} + \frac{800,000}{(1.12)^3}$
$NPV = -1,500,000 + 535,714 + 559,286 + 569,424 = \textbf{Tk. 164,424}$
The NPV of the project is approximately **Tk. 164,424**.
ii. IRR Calculation:
The IRR is the discount rate that makes the NPV equal to zero. By trial and error or using a financial calculator, we solve for IRR:
$0 = -1,500,000 + \frac{600,000}{(1+IRR)^1} + \frac{700,000}{(1+IRR)^2} + \frac{800,000}{(1+IRR)^3}$
The IRR is approximately **19.8%**.
iii. Project Acceptance Decision:
Since the NPV is positive (Tk. 164,424), the project should be **accepted**. This is consistent with the IRR (19.8%), which is greater than the required rate of return (12%).
Problem Statement: A company is considering two mutually exclusive projects, X and Y. The company's required rate of return is 10%. The projects' cash flows are as follows:
| Year | Cash Flow (X) | Cash Flow (Y) |
|---|---|---|
| 0 | (800,000) | (800,000) |
| 1 | 500,000 | 100,000 |
| 2 | 400,000 | 300,000 |
| 3 | 100,000 | 600,000 |
| 4 | 100,000 | 1,000,000 |
Required:
(i) Calculate the NPV for each project.
(ii) Calculate the IRR for each project.
(iii) Calculate the non-discounted payback period for each project.
(iv) Which project should the company select? Why?
Solution:
Tricky Area:
This problem deals with **mutually exclusive projects**, where the NPV and IRR criteria can sometimes give conflicting rankings. You must calculate both and explain why NPV is the superior method for making the final decision.
i. NPV Calculation:
$NPV_X = -800,000 + \frac{500,000}{1.10^1} + \frac{400,000}{1.10^2} + \frac{100,000}{1.10^3} + \frac{100,000}{1.10^4}$
$NPV_X = -800,000 + 454,545 + 330,579 + 75,131 + 68,301 = \textbf{Tk. 128,556}$
$NPV_Y = -800,000 + \frac{100,000}{1.10^1} + \frac{300,000}{1.10^2} + \frac{600,000}{1.10^3} + \frac{1,000,000}{1.10^4}$
$NPV_Y = -800,000 + 90,909 + 247,934 + 450,789 + 683,013 = \textbf{Tk. 672,645}$
ii. IRR Calculation:
Using a financial calculator or spreadsheet:
$0 = -800,000 + \frac{500,000}{(1+IRR_X)^1} + \frac{400,000}{(1+IRR_X)^2} + \frac{100,000}{(1+IRR_X)^3} + \frac{100,000}{(1+IRR_X)^4}$
$IRR_X = \textbf{16.9%}$
$0 = -800,000 + \frac{100,000}{(1+IRR_Y)^1} + \frac{300,000}{(1+IRR_Y)^2} + \frac{600,000}{(1+IRR_Y)^3} + \frac{1,000,000}{(1+IRR_Y)^4}$
$IRR_Y = \textbf{22.1%}$
iii. Non-discounted Payback Period:
Project X:
Year 1: 500,000. Remaining: $800,000 - 500,000 = 300,000$.
Year 2: 400,000. Remaining: $300,000 - 400,000 = -100,000$.
Fraction of Year 2 = $\frac{300,000}{400,000} = 0.75$ years.
Payback Period = **1.75 years**.
Project Y:
Year 1: 100,000. Remaining: 700,000.
Year 2: 300,000. Remaining: 400,000.
Year 3: 600,000. Remaining: $400,000 - 600,000 = -200,000$.
Fraction of Year 3 = $\frac{400,000}{600,000} = 0.67$ years.
Payback Period = **2.67 years**.
iv. Project Selection:
The NPV rule gives a clear answer: Project Y has a significantly higher NPV (Tk. 672,645) than Project X (Tk. 128,556). Therefore, the company should select **Project Y**.
The IRR rule, however, would also lead you to choose Project Y since $IRR_Y > IRR_X$. In this specific case, both rules align, but this is not always the case for mutually exclusive projects. The NPV rule is theoretically superior because it directly measures the increase in firm value, whereas the IRR is a rate and can be misleading when comparing projects of different scale or cash flow patterns.
Problem Statement: A company is considering a project that requires an initial investment of Tk. 500,000. The project is expected to generate a net cash flow of Tk. 150,000 per year for 5 years. At the end of the project's life, the machine is expected to be sold for Tk. 50,000. The project also requires an initial investment in net working capital of Tk. 20,000, which will be recovered at the end of the project's life. The company's required rate of return is 10% and the tax rate is 30%. Required: Calculate the NPV of the project.
Solution:
Tricky Area:
This problem is a simple NPV calculation but requires you to correctly identify and incorporate all cash flow components, including initial investment, salvage value, and working capital, into your calculation.
NPV Calculation:
First, we calculate the initial investment, which includes the machine cost and the initial working capital investment.
Initial Outlay (Year 0) = Tk. (500,000 + 20,000) = Tk. (520,000)
We need to find the cash flow from operations for years 1 to 4, and the terminal cash flow in year 5.
Annual Depreciation = $\frac{500,000}{5} = \text{Tk. } 100,000$
EBIT = $150,000$ (Net cash flow) - $100,000$ (Depreciation) = $50,000$
Tax = $50,000 \times 0.30 = 15,000$
Net Income (EAT) = $50,000 - 15,000 = 35,000$
Operating Cash Flow = Net Income + Depreciation = $35,000 + 100,000 = 135,000$
This is the operating cash flow for years 1 through 5. The terminal cash flow in year 5 will also include the after-tax salvage value and the recovery of working capital.
Terminal Cash Flow (Year 5):
Operating Cash Flow = Tk. 135,000
Salvage Value = Tk. 50,000
Book Value = Tk. 0. Taxable Gain = $50,000$.
Tax on Gain = $50,000 \times 0.30 = 15,000$.
After-tax Salvage Value = $50,000 - 15,000 = 35,000$.
Recovery of NWC = Tk. 20,000.
Total Cash Flow in Year 5 = $135,000 + 35,000 + 20,000 = 190,000$.
Now, we calculate the NPV by discounting all cash flows at 10%.
$NPV = -520,000 + \frac{135,000}{1.10^1} + \frac{135,000}{1.10^2} + \frac{135,000}{1.10^3} + \frac{135,000}{1.10^4} + \frac{190,000}{1.10^5}$
$NPV = -520,000 + 122,727 + 111,570 + 101,427 + 92,206 + 117,975 = \textbf{Tk. 26,905}$
The NPV of the project is approximately **Tk. 26,905**.
Problem Statement: A project has an initial investment of Tk. 5,000,000. The project is expected to generate cash flows of Tk. 1,500,000, Tk. 2,000,000, Tk. 2,500,000, Tk. 3,000,000, and Tk. 3,500,000 over the next five years. The company's cost of capital is 14%. Required: (i) Calculate the NPV of the project. (ii) Calculate the IRR of the project. (iii) Advise the company whether to accept or reject the project.
Solution:
Tricky Area:
This is a straightforward problem, but it involves uneven cash flows, making the IRR calculation by hand difficult. You must rely on a financial calculator or spreadsheet to find the correct rate.
i. NPV Calculation:
$NPV = -5,000,000 + \frac{1,500,000}{1.14^1} + \frac{2,000,000}{1.14^2} + \frac{2,500,000}{1.14^3} + \frac{3,000,000}{1.14^4} + \frac{3,500,000}{1.14^5}$
$NPV = -5,000,000 + 1,315,789 + 1,539,493 + 1,687,609 + 1,775,108 + 1,818,485 = \textbf{Tk. 3,136,484}$
The NPV of the project is approximately **Tk. 3,136,484**.
ii. IRR Calculation:
The IRR is the discount rate that makes the NPV equal to zero. Using a financial calculator or spreadsheet, we find that the IRR is approximately **31.3%**.
iii. Project Acceptance Decision:
Since the NPV is positive (Tk. 3,136,484), the project should be **accepted**. This is consistent with the IRR (31.3%), which is significantly greater than the cost of capital (14%).
Problem Statement: A company is considering a project that requires an initial investment of Tk. 800,000. The project is expected to generate cash flows of Tk. 300,000, Tk. 400,000, Tk. 200,000, and Tk. 100,000 for years 1, 2, 3, and 4 respectively. The company's required rate of return is 15%. Required: (i) Calculate the NPV of the project. (ii) Calculate the payback period of the project. (iii) Advise the company whether to accept or reject the project.
Solution:
Tricky Area:
This problem combines NPV and payback period calculations. You must be careful to calculate both correctly and use the NPV as the primary decision-making tool.
i. NPV Calculation:
$NPV = -800,000 + \frac{300,000}{1.15^1} + \frac{400,000}{1.15^2} + \frac{200,000}{1.15^3} + \frac{100,000}{1.15^4}$
$NPV = -800,000 + 260,870 + 302,468 + 131,507 + 57,175 = \textbf{Tk. -48,018}$
The NPV of the project is approximately **Tk. -48,018**.
ii. Payback Period Calculation:
Cumulative cash flows:
Year 1: 300,000. Remaining: $800,000 - 300,000 = 500,000$.
Year 2: 400,000. Remaining: $500,000 - 400,000 = 100,000$.
Year 3: 200,000. The project pays back in Year 3.
Fraction of Year 3 = $\frac{100,000}{200,000} = 0.5$ years.
Payback Period = **2.5 years**.
iii. Project Acceptance Decision:
Since the NPV is negative (Tk. -48,018), the project should be **rejected**. Even though the payback period is 2.5 years, the NPV rule is the superior method for project appraisal as it considers the time value of money and all future cash flows.
Problem Statement: A project with an initial investment of Tk. 6,000,000 is expected to generate cash flows of Tk. 2,000,000, Tk. 3,000,000, and Tk. 4,000,000 over the next three years. The required rate of return is 14%. Required: (i) Calculate the NPV of the project. (ii) Calculate the IRR of the project.
Solution:
Tricky Area:
This problem is a basic application of NPV and IRR. The main challenge is performing the calculations accurately.
i. NPV Calculation:
$NPV = -6,000,000 + \frac{2,000,000}{1.14^1} + \frac{3,000,000}{1.14^2} + \frac{4,000,000}{1.14^3}$
$NPV = -6,000,000 + 1,754,386 + 2,308,095 + 2,700,530 = \textbf{Tk. 762,011}$
The NPV of the project is approximately **Tk. 762,011**.
ii. IRR Calculation:
The IRR is the discount rate that makes the NPV equal to zero. By trial and error or using a financial calculator, we solve for IRR:
$0 = -6,000,000 + \frac{2,000,000}{(1+IRR)^1} + \frac{3,000,000}{(1+IRR)^2} + \frac{4,000,000}{(1+IRR)^3}$
The IRR is approximately **20.2%**.
Problem Statement: An investment of Tk. 5,000,000 is expected to generate cash inflows of Tk. 1,500,000 per annum for 5 years. The company's cost of capital is 10%. Required: (i) Calculate the NPV of the project. (ii) Calculate the IRR of the project. (iii) Advise the company whether to accept or reject the project.
Solution:
Tricky Area:
This is an annuity problem, as the cash inflows are constant over the project's life. You can use the annuity formula to simplify the NPV calculation.
i. NPV Calculation:
First, calculate the present value of the annuity of cash inflows.
PV of Annuity = $1,500,000 \times \left[ \frac{1 - (1.10)^{-5}}{0.10} \right]$
PV of Annuity = $1,500,000 \times [1 - 0.6209] / 0.10 = 1,500,000 \times 3.7908 = 5,686,200$
$NPV = \text{PV of Inflows} - \text{Initial Outlay}$
$NPV = 5,686,200 - 5,000,000 = \textbf{Tk. 686,200}$
The NPV of the project is approximately **Tk. 686,200**.
ii. IRR Calculation:
The IRR is the discount rate that makes the NPV equal to zero. Since it's an annuity, we can use the PV annuity factor formula to find the IRR.
$5,000,000 = 1,500,000 \times \left[ \frac{1 - (1+IRR)^{-5}}{IRR} \right]$
PV Annuity Factor = $\frac{5,000,000}{1,500,000} = 3.3333$
Using a financial calculator or by looking up the PV annuity factor in a table, we find that the IRR is approximately **15.24%**.
iii. Project Acceptance Decision:
Since the NPV is positive (Tk. 686,200), the project should be **accepted**. This is consistent with the IRR (15.24%), which is greater than the cost of capital (10%).
Problem Statement: A project requires an initial investment of Tk. 900,000. It is expected to generate cash flows of Tk. 400,000, Tk. 500,000, and Tk. 600,000 over the next three years. The required rate of return is 11%. Required: (i) Calculate the NPV of the project. (ii) Calculate the payback period of the project. (iii) Calculate the IRR of the project.
Solution:
Tricky Area:
This problem is a comprehensive test of three key capital budgeting methods. You must perform each calculation accurately and be prepared to discuss their relative strengths and weaknesses.
i. NPV Calculation:
$NPV = -900,000 + \frac{400,000}{1.11^1} + \frac{500,000}{1.11^2} + \frac{600,000}{1.11^3}$
$NPV = -900,000 + 360,360 + 406,209 + 438,767 = \textbf{Tk. 305,336}$
The NPV of the project is approximately **Tk. 305,336**.
ii. Payback Period Calculation:
Cumulative cash flows:
Year 1: 400,000. Remaining: $900,000 - 400,000 = 500,000$.
Year 2: 500,000. Remaining: $500,000 - 500,000 = 0$.
The project pays back in exactly **2 years**.
iii. IRR Calculation:
The IRR is the discount rate that makes the NPV equal to zero.
$0 = -900,000 + \frac{400,000}{(1+IRR)^1} + \frac{500,000}{(1+IRR)^2} + \frac{600,000}{(1+IRR)^3}$
Using a financial calculator or spreadsheet, the IRR is approximately **25.25%**.
Problem Statement: A project requires an initial investment of Tk. 7,000,000. It is expected to generate cash flows of Tk. 3,000,000, Tk. 4,000,000, and Tk. 5,000,000 over the next three years. The required rate of return is 15%. Required: (i) Calculate the NPV of the project. (ii) Calculate the IRR of the project. (iii) Advise the company whether to accept or reject the project.
Solution:
Tricky Area:
This is a basic NPV and IRR problem with uneven cash flows. The main challenge is performing the calculations correctly and drawing the right conclusion based on the results.
i. NPV Calculation:
$NPV = -7,000,000 + \frac{3,000,000}{1.15^1} + \frac{4,000,000}{1.15^2} + \frac{5,000,000}{1.15^3}$
$NPV = -7,000,000 + 2,608,696 + 3,024,680 + 3,287,557 = \textbf{Tk. 1,921,933}$
The NPV of the project is approximately **Tk. 1,921,933**.
ii. IRR Calculation:
The IRR is the discount rate that makes the NPV equal to zero. Using a financial calculator or spreadsheet, the IRR is approximately **32.8%**.
iii. Project Acceptance Decision:
Since the NPV is positive (Tk. 1,921,933), the project should be **accepted**. This is consistent with the IRR (32.8%), which is greater than the required rate of return (15%).
Problem Statement: A project requires an initial investment of Tk. 6,000,000. It is expected to generate cash flows of Tk. 2,500,000, Tk. 3,500,000, and Tk. 4,500,000 over the next three years. The required rate of return is 12%. Required: (i) Calculate the NPV of the project. (ii) Calculate the payback period of the project. (iii) Advise the company whether to accept or reject the project.
Solution:
Tricky Area:
This is a standard NPV and payback period problem. The main challenge is performing the calculations correctly and making a decision based on the NPV rule.
i. NPV Calculation:
$NPV = -6,000,000 + \frac{2,500,000}{1.12^1} + \frac{3,500,000}{1.12^2} + \frac{4,500,000}{1.12^3}$
$NPV = -6,000,000 + 2,232,143 + 2,797,194 + 3,203,149 = \textbf{Tk. 2,232,486}$
The NPV of the project is approximately **Tk. 2,232,486**.
ii. Payback Period Calculation:
Cumulative cash flows:
Year 1: 2,500,000. Remaining: $6,000,000 - 2,500,000 = 3,500,000$.
Year 2: 3,500,000. Remaining: $3,500,000 - 3,500,000 = 0$.
The project pays back in exactly **2 years**.
iii. Project Acceptance Decision:
Since the NPV is positive (Tk. 2,232,486), the project should be **accepted**.