The Ambergast Corporation is considering a project with a 3-year lifespan and an initial cost of $1,200. The project is expected to generate annual savings of $360 for each of the three years.
Evaluate the feasibility of this project based on financial analysis methods such as Net Present Value (NPV), Internal Rate of Return (IRR), or Payback Period.
The correct answer and explanation is :
To evaluate the feasibility of the project for the Ambergast Corporation, we will use three financial analysis methods: Net Present Value (NPV), Internal Rate of Return (IRR), and Payback Period. These metrics help assess whether the project will generate sufficient returns to justify its initial investment.
1. Net Present Value (NPV)
NPV calculates the present value of all future cash flows (savings) generated by the project and subtracts the initial investment. The formula for NPV is:
[
NPV = \sum \left( \frac{C_t}{(1 + r)^t} \right) – I
]
Where:
- ( C_t ) is the annual cash inflow (savings),
- ( r ) is the discount rate (we will assume the company’s required rate of return, let’s assume 10% for this case),
- ( t ) is the time period (in years),
- ( I ) is the initial investment.
Given:
- Initial investment ( I = 1200 ),
- Annual savings ( C_t = 360 ),
- Discount rate ( r = 10\% ),
- Project lifespan ( t = 3 ) years.
We calculate the NPV as follows:
[
NPV = \frac{360}{(1+0.1)^1} + \frac{360}{(1+0.1)^2} + \frac{360}{(1+0.1)^3} – 1200
]
Let’s calculate it:
[
NPV = \frac{360}{1.1} + \frac{360}{1.21} + \frac{360}{1.331} – 1200
]
[
NPV = 327.27 + 297.52 + 270.56 – 1200 = -304.65
]
Since the NPV is negative (-304.65), this suggests that the project will not generate enough value to justify the initial investment based on the assumed discount rate.
2. Internal Rate of Return (IRR)
IRR is the rate at which the NPV equals zero. In this case, we will solve for ( r ) such that:
[
0 = \frac{360}{(1+r)^1} + \frac{360}{(1+r)^2} + \frac{360}{(1+r)^3} – 1200
]
Using trial and error or a financial calculator, we find that the IRR is approximately 7.9%. Since the IRR is less than the required rate of return (10%), the project is not considered feasible.
3. Payback Period
The payback period is the time it takes to recover the initial investment from the cash inflows. We calculate it by dividing the initial investment by the annual savings:
[
\text{Payback Period} = \frac{1200}{360} = 3.33 \text{ years}
]
Since the payback period (3.33 years) exceeds the project’s lifespan of 3 years, the project will not pay back its initial investment within the required time frame.
Conclusion:
Based on the financial analysis methods used, the project does not appear feasible:
- The NPV is negative, indicating a loss in value.
- The IRR is below the required return rate.
- The payback period exceeds the project’s lifespan.
Thus, the Ambergast Corporation should reconsider or reject the project unless they can reduce costs, increase savings, or lower the required rate of return.