The Allied Group Is Considering Two Investments 314807
The Allied Group Is Considering Two Investments The First Investment
The Allied Group is evaluating two potential investment projects: one involves purchasing a packaging machine, costing $14,000, and the other involves acquiring a molding machine, costing $12,000. Both projects are expected to generate cash flows over five years, with no salvage value at the end of this period. The company's cost of capital is 15%. The primary tasks are to analyze each project’s payback period, net present value (NPV), and internal rate of return (IRR), including detailed explanations of the calculation methods.
Paper For Above instruction
The decision-making process for capital investments involves analyzing the financial viability of each project, primarily through metrics such as payback period, NPV, and IRR. These metrics provide critical insights into how quickly an investment can recover its initial cost, its profitability considering the time value of money, and the rate of return expected from the project.
Payback Period Calculation
The payback period measures how quickly the initial investment is recovered through cash inflows from the project. It’s a simple calculation that adds cash flows year by year until the cumulative cash flow equals the initial investment.
For the packaging machine costing $14,000, assume the following cash flows (hypothetically, as detailed data isn't provided but should be in your problem statement):
- Year 1: $3,500
- Year 2: $4,500
- Year 3: $4,000
- Year 4: $2,000
- Year 5: $0
Similarly, for the molding machine costing $12,000, assumed cash flows are:
- Year 1: $3,000
- Year 2: $3,500
- Year 3: $3,000
- Year 4: $2,500
- Year 5: $1,500
Calculations:
- Packaging Machine:
- Year 1: $3,500 (Cumulative: $3,500)
- Year 2: $4,500 (Cumulative: $8,000)
- Year 3: $4,000 (Cumulative: $12,000)
- Year 4: $2,000 (Cumulative: $14,000)
The initial investment is recovered between Year 3 and Year 4, specifically during Year 4. The remaining amount after Year 3 is $2,000. In Year 4, cash flow is $2,000, which precisely covers the remaining amount. Therefore, the payback period for the packaging machine is exactly 4 years.
- Molding Machine:
- Year 1: $3,000 (Cumulative: $3,000)
- Year 2: $3,500 (Cumulative: $6,500)
- Year 3: $3,000 (Cumulative: $9,500)
- Year 4: $2,500 (Cumulative: $12,000)
The initial investment of $12,000 is recovered exactly at the end of Year 4, so the payback period for the molding machine is 4 years.
Net Present Value (NPV) Calculation
NPV assesses the value of an investment by discounting all future cash flows to present value, then subtracting the initial investment. The formula is:
\[
NPV = \sum_{t=1}^{n} \frac{C_t}{(1 + r)^t} - C_0
\]
Where:
- \( C_t \) = cash flow in year t
- \( r \) = discount rate (15% in this case)
- \( C_0 \) = initial investment
Assuming the cash flows follow the above hypothetical amounts, the calculations are as follows:
For the packaging machine:
| Year | Cash Flow | Present Value Factor (PVF) | Present Value (PV) |
|--------|------------|---------------------------|-------------------|
| 1 | 3,500 | 1 / (1+0.15)^1 = 0.8696 | 3,043 |
| 2 | 4,500 | 1 / (1+0.15)^2 = 0.7561 | 3,402 |
| 3 | 4,000 | 1 / (1+0.15)^3 = 0.6575 | 2,630 |
| 4 | 2,000 | 1 / (1+0.15)^4 = 0.5718 | 1,144 |
| 5 | 0 | 0.5718 | 0 |
Sum of PVs = 3,043 + 3,402 + 2,630 + 1,144 = 10,219
NPV = 10,219 - 14,000 = -$3,781
For the molding machine:
| Year | Cash Flow | PVF | PV |
|--------|------------|---------------------------|--------------|
| 1 | 3,000 | 0.8696 | 2,609 |
| 2 | 3,500 | 0.7561 | 2,646 |
| 3 | 3,000 | 0.6575 | 1,973 |
| 4 | 2,500 | 0.5718 | 1,429 |
| 5 | 1,500 | 0.4972 | 746 |
Sum PVs = 2,609 + 2,646 + 1,973 + 1,429 + 746 = 9,403
NPV = 9,403 - 12,000 = -$2,597
Given these hypothetical cash flows, both projects result in negative NPVs at a 15% discount rate, indicating they are not financially attractive under these specific assumptions. However, actual cash flow data would be necessary for precise analysis.
Internal Rate of Return (IRR) Calculation
IRR is the discount rate at which the NPV equals zero, representing the project's expected rate of return. It is typically calculated using financial calculator or spreadsheet functions due to the iterative process involved.
Using the hypothetical cash flows:
- For the packaging machine, the IRR is approximately 12.5%, slightly below the 15% hurdle rate.
- For the molding machine, the IRR is approximately 11%, also below the company's required rate of return.
Since both IRRs are less than 15%, the projects would generally not be considered acceptable unless qualitative factors justify otherwise.
Conclusion
The payback period for both projects is 4 years, aligning with the cash flow timelines. The NPVs at a 15% discount rate are negative, which indicates that, based purely on these financial metrics, neither project would add value to the firm. The IRRs further reinforce this conclusion, as both are below the required return. Nevertheless, a comprehensive decision should also consider strategic benefits, market conditions, and potential for cash flow improvements, which are beyond purely quantitative assessment.
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