Project Profitability Calculation Based on Discount Rate
Which project is more profitable at a discount rate of 5% and 10%?
Assuming 2 projects; the 1st will provide a benefit of 100,000 Rand for 3 years and has an initial cost of 200,000 Rand, The 2nd will provide a benefit of 200,000 Rand for 3 years with an initial cost of 300,000 Rand. Regardless of the discount rate (5% or 10%), the second project is more profitable than the first project. Compare the present value of each project's cash flows at different discount rates to determine which project is more profitable.
Project Profitability Analysis
To determine which project is more profitable at different discount rates, calculate the present value of each project's cash flows and compare them. Let's calculate the present value (PV) of each project using the formula:
PV = CF / (1 + r)^n
Where:
- PV is the present value
- CF is the cash flow
- r is the discount rate
- n is the number of years
Calculating Present Value
For the first project:
- Initial cost (CF): -200,000 Rand
- Benefit per year (CF): 100,000 Rand (for 3 years)
- Discount rate (r): i) 5% ii) 10%
For the second project:
- Initial cost (CF): -300,000 Rand
- Benefit per year (CF): 200,000 Rand (for 3 years)
- Discount rate (r): i) 5% ii) 10%
Present Value Calculation
i) Discount rate of 5%
For the first project:
PV = -200,000 / (1 + 0.05)^0 + 100,000 / (1 + 0.05)^1 + 100,000 / (1 + 0.05)^2 + 100,000 / (1 + 0.05)^3
PV ≈ -200,000 + 95,238 + 90,703 + 86,382 ≈ 72,323 Rand
For the second project:
PV = -300,000 / (1 + 0.05)^0 + 200,000 / (1 + 0.05)^1 + 200,000 / (1 + 0.05)^2 + 200,000 / (1 + 0.05)^3
PV ≈ -300,000 + 190,476 + 181,407 + 172,863 ≈ 244,746 Rand
ii) Discount rate of 10%
For the first project:
PV = -200,000 / (1 + 0.10)^0 + 100,000 / (1 + 0.10)^1 + 100,000 / (1 + 0.10)^2 + 100,000 / (1 + 0.10)^3
PV ≈ -200,000 + 90,909 + 82,644 + 75,131 ≈ 48,684 Rand
For the second project:
PV = -300,000 / (1 + 0.10)^0 + 200,000 / (1 + 0.10)^1 + 200,000 / (1 + 0.10)^2 + 200,000 / (1 + 0.10)^3
PV ≈ -300,000 + 181,818 + 165,289 + 150,263 ≈ 197,370 Rand
Comparison of Present Values
i) At a discount rate of 5%, the second project has a PV of 244,746 Rand, while the first project has a PV of 72,323 Rand. Therefore, the second project is more profitable.
ii) At a discount rate of 10%, the second project has a PV of 197,370 Rand, while the first project has a PV of 48,684 Rand. Therefore, the second project is more profitable.