Your probationary period at the Cosmo K Manufacturing Group continues. Your supervisor, Gerry, assigns you a project each week to test your competence in finance.
The company is considering the addition of a new office machine that will perform many of the tasks now performed manually. For this week's task, Gerry has given you the responsibility of evaluating the cash flows associated with the new machine. He has requested the report to be delivered within the week.
Evaluation of a New Office Machine
The Cosmo K Manufacturing Group currently has sales of $1,400,000 per year. It is considering the addition of a new office machine, which will not result in any new sales but will save the company $105,500 before taxes per year over its 5-year useful life. The machine will cost $300,000 plus another $12,000 for installation. The new asset will be depreciated using a modified accelerated cost recovery system (MACRS) 5-year class life. It will be sold for $25,000 at the end of 5 years. Additional inventory of $11,000 will be required for parts and maintenance of the new machine. The company evaluates all projects at this risk level using an 11.99% required rate of return. The tax rate is expected to be 35% for the next decade.
Tasks:
Answer the following questions:
What is the total investment in the new machine at time = 0 (T = 0)?
What are the net cash flows in each of the 5 years of operation?
What are the terminal cash flows from the sale of the asset at the end of 5 years?
What is the NPV of the investment?
What is the IRR of the investment?
What is the payback period for the investment?
What is the profitability index for the investment?
According to the decision rules for the NPV and those for the IRR, is the project acceptable?
Is there a conflict between the two decision methods? If so, what would you use to make a recommendation?
What are the pros and cons of the NPV and the IRR? Explain your answers.
Full Answer Section
o calculate the net cash flows, we need to consider the before-tax savings, depreciation tax shield, and the change in net working capital (specifically the inventory). We'll use the MACRS 5-year class life depreciation percentages. The MACRS percentages for a 5-year class life are:
The depreciable base is the cost of the machine plus installation: $300,000 + $12,000 = 312,000.
Now, let's calculate the depreciation expense for each year:
Next, we calculate the net cash flow for each year:
3. What are the terminal cash flows from the sale of the asset at the end of 5 years?
At the end of year 5, the machine is sold for $25,000. We need to calculate the book value of the asset at that time to determine any gain or loss on the sale.
Total depreciation over 5 years = $62,400 + $99,840 + $59,904 + $35,966.40 + $35,966.40 = $294,116.80
Book Value at the end of Year 5 = Initial Cost + Installation - Total Depreciation Book Value = $312,000 - $294,116.80 = $17,883.20
Since the sale price ($25,000) is greater than the book value ($17,883.20), there is a gain on the sale:
Gain on Sale = $25,000 - $17,883.20 = $7,116.80
This gain is taxable, so the after-tax cash flow from the sale is:
After-Tax Cash Flow from Sale = Sale Price - (Gain on Sale x Tax Rate) After-Tax Cash Flow from Sale = $25,000 - (7,116.80×0.35) After-Tax Cash Flow from Sale = $25,000 - $2,490.88 = 22,509.12
Additionally, the initial investment in inventory of $11,000 will be recovered at the end of the project.
Total Terminal Cash Flow (Year 5) = Net Cash Flow from Operations (Year 5) + After-Tax Cash Flow from Sale + Recovery of Inventory Total Terminal Cash Flow = $57,785.08 + $22,509.12 + $11,000 = 91,294.20
4. What is the NPV of the investment?
To calculate the Net Present Value (NPV), we discount all the cash flows back to the present using the required rate of return of 11.99%.
The Net Present Value (NPV) of the investment is approximately -$123,155.22.
5. What is the IRR of the investment?
The Internal Rate of Return (IRR) is the discount rate that makes the NPV of the project equal to zero. We need to solve for the discount rate that satisfies the following equation:
0=−323,000+(1+IRR)149,855+(1+IRR)238,623+(1+IRR)350,603.80+(1+IRR)457,785.08+(1+IRR)591,294.20
Solving for IRR typically requires an iterative process or the use of a financial calculator or spreadsheet software. Using these tools, the approximate IRR of this investment is -1.86%.
6. What is the payback period for the investment?
The payback period is the time it takes for the cumulative cash inflows to equal the initial investment.
It appears there's an error in my calculation or understanding, as the cumulative cash flow never turns positive within the 5-year period. Let me re-examine the cash flows.
Ah, I see the mistake. The terminal cash flow in year 5 includes the operational cash flow for that year. Let's recalculate the cumulative cash flow:
The cumulative cash flow still doesn't turn positive within the 5-year period. This indicates that the payback period is longer than the project's useful life. Therefore, the payback period is greater than 5 years.
To be more precise, we can estimate where the payback would occur if the project continued. After 4 years, -$126,133.12 is still outstanding. In year 5, the operational cash flow is $57,785.08.
Payback Period = 4 years + ($126,133.12 / $57,785.08) years Payback Period ≈ 4 + 2.18 years ≈ 6.18 years
7. What is the profitability index for the investment?
The Profitability Index (PI) is the present value of the future cash flows divided by the initial investment.
PI=InitialInvestmentPresentValueofFutureCashFlows
From our NPV calculation, the present value of the future cash flows is:
$PV_{Future} = $44,515.51 + $30,793.05 + $36,025.91 + $36,739.13 + $51,771.18 = 199,844.80
PI=323,000199,844.80 PI≈0.6187
The Profitability Index (PI) for the investment is approximately 0.6187.
8. According to the decision rules for the NPV and those for the IRR, is the project acceptable?
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NPV Decision Rule: Accept the project if the NPV is positive, reject if it is negative.
- Based on our calculation, the NPV is -$123,155.22, which is negative. Therefore, according to the NPV rule, the project is not acceptable.
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IRR Decision Rule: Accept the project if the IRR is greater than the required rate of return, reject if it is lower.
- Based on our calculation, the IRR is -1.86%, which is lower than the required rate of return of 11.99%. Therefore, according to the IRR rule, the project is not acceptable.
9. Is there a conflict between the two decision methods? If so, what would you use to make a recommendation?
In this case, there is no conflict between the NPV and IRR decision methods. Both methods indicate that the project is not acceptable, as the NPV is negative and the IRR is lower than the required rate of return.
If there were a conflict (e.g., positive NPV but IRR lower than the required return, or vice versa), I would primarily rely on the Net Present Value (NPV) to make a recommendation.
Reasoning for prioritizing NPV:
- Direct Measure of Value: NPV directly measures the dollar amount by which the project is expected to increase or decrease the value of the company. A positive NPV directly translates to an increase in shareholder wealth.
- Handles Scale and Timing of Cash Flows: NPV correctly accounts for the absolute size of the project and the timing of cash flows, especially important for mutually exclusive projects or projects with different scales.
- Consistent with Shareholder Wealth Maximization: The primary goal of financial management is to maximize shareholder wealth, and NPV is directly aligned with this goal.
While IRR is a useful metric for understanding the rate of return on an investment, it can sometimes lead to incorrect decisions in situations involving:
- Non-conventional cash flows: Projects with cash outflows after the initial investment can have multiple IRRs or no real IRR.
- Mutually exclusive projects: The project with the higher IRR may not always have the higher NPV, especially if the projects differ in scale or timing of cash flows.
- Reinvestment rate assumption: IRR implicitly assumes that cash flows can be reinvested at the IRR, which may not be realistic. NPV uses the more realistic required rate of return for discounting.
10. What are the pros and cons of the NPV and the IRR? Explain your answers.
Net Present Value (NPV)
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Pros:
- Direct measure of value: As mentioned above, NPV directly indicates the change in shareholder wealth.
- Handles scale and timing correctly: It accounts for the absolute dollar value of cash flows and the time value of money using the appropriate discount rate.
- Consistent with financial theory: NPV is widely accepted as the most theoretically sound capital budgeting technique.
- Clear decision rule: A positive NPV indicates an acceptable project that will increase shareholder wealth.
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Cons:
- Requires estimating the discount rate: The accuracy of the NPV depends on the accuracy of the required rate of return, which can be subjective and difficult to estimate precisely.
- Less intuitive for non-financial managers: The concept of discounting cash flows to present value might be less easily understood by those without a strong financial background compared to a percentage return like IRR.
Internal Rate of Return (IRR)
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Pros:
- Intuitively appealing: Expressing the return as a percentage is often easier for non-financial managers to understand and compare to other rates of return.
- Does not require a discount rate for calculation: The IRR is calculated directly from the project's cash flows.
- Can provide a quick "hurdle rate" comparison: It shows the project's profitability relative to a benchmark.
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