Your probationary period at the Cosmo K Manufacturing Group continues

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.

Sample Solution

. What is the total investment in the new machine at time = 0 (T = 0)?

The total initial investment at T = 0 includes the cost of the machine, the installation costs, and the initial investment in additional inventory.

Total Investment = Cost of Machine + Installation Costs + Increase in Net Working Capital (Inventory) Total Investment = $300,000 + $12,000 + $11,000 Total Investment = $323,000

2. What are the net cash flows in each of the 5 years of operation?

To calculate the net cash flows for each year, we need to consider the before-tax savings, depreciation expense, taxes, and the change in net working capital.

Full Answer Section

First, let's determine the depreciation expense for each year using the MACRS 5-year class life percentages. The MACRS 5-year class percentages are:

Year 1: 20.00% Year 2: 32.00% Year 3: 19.20% Year 4: 11.52% Year 5: 11.52% Year 6: 5.76%

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:

Year 1 Depreciation = $312,000 * 0.2000 = $62,400 Year 2 Depreciation = $312,000 * 0.3200 = $99,840 Year 3 Depreciation = $312,000 * 0.1920 = $59,904 Year 4 Depreciation = $312,000 * 0.1152 = $35,966.40 Year 5 Depreciation = $312,000 * 0.1152 = $35,966.40

Next, we calculate the net cash flow for each year:

Year 1: Before-tax savings = $105,500 Depreciation = $62,400 Taxable income = $105,500 - $62,400 = $43,100 Taxes = $43,100 * 0.35 = $15,085 After-tax savings = $105,500 - $15,085 = $90,415 Net Cash Flow (Year 1) = After-tax savings + Depreciation = $90,415 + $62,400 = $152,815

Year 2: Before-tax savings = $105,500 Depreciation = $99,840 Taxable income = $105,500 - $99,840 = $5,660 Taxes = $5,660 * 0.35 = $1,981 After-tax savings = $105,500 - $1,981 = $103,519 Net Cash Flow (Year 2) = After-tax savings + Depreciation = $103,519 + $99,840 = $203,359

Year 3: Before-tax savings = $105,500 Depreciation = $59,904 Taxable income = $105,500 - $59,904 = $45,596 Taxes = $45,596 * 0.35 = $15,958.60 After-tax savings = $105,500 - $15,958.60 = $89,541.40 Net Cash Flow (Year 3) = After-tax savings + Depreciation = $89,541.40 + $59,904 = $149,445.40

Year 4: Before-tax savings = $105,500 Depreciation = $35,966.40 Taxable income = $105,500 - $35,966.40 = $69,533.60 Taxes = $69,533.60 * 0.35 = $24,336.76 After-tax savings = $105,500 - $24,336.76 = $81,163.24 Net Cash Flow (Year 4) = After-tax savings + Depreciation = $81,163.24 + $35,966.40 = $117,129.64

Year 5: Before-tax savings = $105,500 Depreciation = $35,966.40 Taxable income = $105,500 - $35,966.40 = $69,533.60 Taxes = $69,533.60 * 0.35 = $24,336.76 After-tax savings = $105,500 - $24,336.76 = $81,163.24 Net Cash Flow (Year 5) = After-tax savings + Depreciation = $81,163.24 + $35,966.40 = $117,129.64

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, which will affect the taxes.

Total depreciation over 5 years = $62,400 + $99,840 + $59,904 + $35,966.40 + $35,966.40 = $294,076.80 Book Value at the end of Year 5 = Initial Depreciable Cost - Accumulated Depreciation Book Value = $312,000 - $294,076.80 = $17,923.20

Since the sale price ($25,000) is greater than the book value ($17,923.20), there is a taxable gain:

Gain on Sale = $25,000 - $17,923.20 = $7,076.80 Taxes on Gain = $7,076.80 * 0.35 = $2,476.88

The terminal cash flow also includes the return of the initial investment in net working capital (inventory).

Terminal Cash Flow = Sale Price - Taxes on Gain + Return of Net Working Capital Terminal Cash Flow = $25,000 - $2,476.88 + $11,000 Terminal Cash Flow = $33,523.12

Therefore, the net cash flow in Year 5 will be the operating cash flow plus the terminal cash flow:

Net Cash Flow (Year 5, including terminal value) = $117,129.64 + $33,523.12 = $150,652.76

Summary of Net Cash Flows:

T = 0: -$323,000
Year 1: $152,815
Year 2: $203,359
Year 3: $149,445.40
Year 4: $117,129.64
Year 5: $150,652.76

4. What is the NPV of the investment?

To calculate the Net Present Value (NPV), we will discount each year's net cash flow back to the present using the required rate of return of 11.99%.

$NP V = \sum_{t = 0 n} ( 1 + r ) ^{t} C F ^{t}$

Where: $C F_{t}$ = Net cash flow in year t $r$ = Required rate of return (0.1199) $n$ = Number of years (5)

$NP V = ( 1 + 0.1199 ) ^{0} -$323 , 000 + ( 1 + 0.1199 ) ^{1} $152 , 815 + ( 1 + 0.1199 ) ^{2} $203 , 359 + ( 1 + 0.1199 ) ^{3} $149 , 445.40 + ( 1 + 0.1199 ) ^{4} $117 , 129.64 + ( 1 + 0.1199 ) ^{5} $150 , 652.76$

$NP V = - $323, 000 + 1.1199 $152 , 815 + 1.25417601 $203 , 359 + 1.40453509 $149 , 445.40 + 1.57284059 $117 , 129.64 + 1.76145838 $150 , 652.76$

$NP V = - $323, 000 + $136, 459.59 + $162, 148.78 + $106, 401.38 + $74, 479.48 + $85, 526.69$

$NP V = $242, 015.92$

5. What is the IRR of the investment?

The Internal Rate of Return (IRR) is the discount rate at which the NPV of the project equals zero. We would need to solve for 'r' in the following equation:

$0 = ( 1 + I RR ) ^{0} -$323 , 000 + ( 1 + I RR ) ^{1} $152 , 815 + ( 1 + I RR ) ^{2} $203 , 359 + ( 1 + I RR ) ^{3} $149 , 445.40 + ( 1 + I RR ) ^{4} $117 , 129.64 + ( 1 + I RR ) ^{5} $150 , 652.76$

This equation typically requires a financial calculator or spreadsheet software to solve directly. Using such tools, the IRR is approximately 31.05%.

6. What is the payback period for the investment?

The payback period is the time it takes for the cumulative net cash inflows to equal the initial investment.

Year 0: -$323,000
Year 1: -$323,000 + $152,815 = -$170,185
Year 2: -$170,185 + $203,359 = $33,174

The payback occurs sometime in Year 2. To find the exact point:

Payback Period = Number of full years until positive cumulative cash flow + (Remaining investment at the start of the payback year / Cash flow during the payback year) Payback Period = 1 + ($170,185 / $203,359) Payback Period = 1 + 0.8368 years Payback Period ≈ 1.84 years

7. What is the profitability index for the investment?

The profitability index (PI) is the ratio of the present value of future cash flows to the initial investment.

$P I = Initial Investment P V of Future Cash Flows$

$P V of Future Cash Flows = 1.1199 $152 , 815 + 1.25417601 $203 , 359 + 1.40453509 $149 , 445.40 + 1.57284059 $117 , 129.64 + 1.76145838 $150 , 652.76$ $P V of Future Cash Flows = $136, 459.59 + $162, 148.78 + $106, 401.38 + $74, 479.48 + $85, 526.69 = $565, 015.92$

$P I = $323 , 000 $565 , 015.92$ $P I \approx 1.75$

8. According to the decision rules for the NPV and those for the IRR, is the project acceptable?

NPV Decision Rule: If the NPV is greater than zero, the project is acceptable. In this case, the NPV is $242,015.92, which is greater than zero. Therefore, the project is acceptable based on the NPV rule.

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