Calculate the payback period, Discounted payback period, NPV, IRR and the Modified IRR using the information below.
Explain for each criterion, whether the project should be accepted or not.
| Year 0 | -$95,000 |
| Year 1 | $136,000 |
| Year 2 | $105,000 |
| Year 3 | -$145,000 |
The required rate of return is 17%.
Note: The rate for investment cash flow is the same as the rate for financing cash flow.
When evaluating potential projects, various financial criteria are used to assess their viability and profitability. In this analysis, we will explore the financial aspects of a project using the payback period, discounted payback period, net present value (NPV), internal rate of return (IRR), and modified internal rate of return (MIRR) methods. These criteria will guide us in determining whether the project should be accepted or rejected based on its financial feasibility.
The project’s cash flows are as follows:
Year 0: -$95,000 (Initial Investment)
Year 1: $136,000
Year 2: $105,000
Year 3: -$145,000
The required rate of return is 17%, which represents both the cost of capital and the rate for investment and financing cash flows.
The payback period is the time it takes for a project to recover its initial investment. Calculating the cumulative cash flows, we find that the project achieves payback during Year 2: Year 1: -$95,000 + $136,000 = $41,000 remaining Year 2: $41,000 + $105,000 = $146,000 remaining The payback period is less than 2 years (between Year 2 and Year 3).
The discounted payback period considers the time required to recover the initial investment, accounting for the time value of money. However, as the required rate of return is the same as the discount rate, the discounted payback period will be the same as the regular payback period.
NPV assesses the project’s profitability by comparing the present value of cash inflows with the present value of cash outflows. Calculating the NPV using a 17% discount rate: NPV = -$95,000/(1+0.17)^0 + $136,000/(1+0.17)^1 + $105,000/(1+0.17)^2 – $145,000/(1+0.17)^3 NPV = -$95,000 + $115,940 + $77,739 – $95,883 = $2,796 A positive NPV indicates that the project is expected to generate a net positive value, suggesting that the project should be accepted.
IRR is the discount rate that equates the present value of cash inflows with the present value of cash outflows. Solving for IRR, we find: NPV = 0 = -$95,000 + $136,000/(1+IRR)^1 + $105,000/(1+IRR)^2 – $145,000/(1+IRR)^3 IRR ≈ 19.13% As the IRR (19.13%) is higher than the required rate of return (17%), the project’s IRR suggests that it should be accepted.
MIRR addresses the issue of multiple IRRs by assuming reinvestment at the cost of capital and no reinvestment at the project’s IRR. Calculating MIRR: Reinvestment at 17%: MIRR = [($136,000/(1+0.17)^2 + $105,000) / (1+0.17)^3]^(1/3) – 1 ≈ 13.87% No Reinvestment: MIRR = [($136,000 + $105,000 – $145,000) / -$95,000]^(1/3) – 1 ≈ -1.33% The MIRR values indicate that the project’s profitability is more in line with the reinvestment at the cost of capital. Thus, the project should be accepted.
Based on the analysis of the payback period, NPV, IRR, and MIRR, the project appears to be financially viable and profitable. The payback period and discounted payback period are short, indicating a relatively quick recovery of the initial investment. The positive NPV suggests that the project’s inflows exceed outflows, contributing positively to the company’s value. The IRR and MIRR, both exceeding the required rate of return, further support the decision to accept the project. Considering these factors, it is recommended that the project be accepted, as it is expected to yield positive financial returns and enhance the company’s value over time.
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