Question

A company is considering a project that will reduce annual operating expenses by $200,000, before income taxes each year for the next five years. The project requires an investment in equipment that costs $1,000,000 and will be depreciated using straight line depreciation over its 5-year life. At the end of the project life, the equipment is expected to be sold for $500,000. The equipment uses a different material and inventory will initially rise by $100,000 and the inventory can be sold at the end of the project for the same amount it costs. The company’s marginal tax rate applicable to this project is 40%. The company’s required return on the project is 10%.

a. What is the initial investment required by the project?

b. What is the annual OCF from the project?

c. What is the net after tax salvage value of the machine in the last year?

d. What is the NPV of the project?

e. At what discount rate would the company accept the project?

Answer 1

Part 1)

The initial investment required by the project is calculated as below:

Initial Investment = Purchase Cost of Equipment + Increase in Working Capital

Here, Purchase Cost of Equipment = $1,000,000 and Increase in Working Capital = $100,000

Initial Investment = 1,000,000 + 100,000 = $1,100,000 or -$1,100,000 (as it indicates cost)

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Part 2)

The value of annual operating cash flow from the project is arrived as below:

Annual Operating Cash Flow = (Reduction in Annual Operating Expense - Annual Depreciation)*(1-Tax Rate) + Annual Depreciation

Here, Reduction in Annual Operating Expense = $200,000, Annual Depreciation = Cost/Useful Life = 1,000,000/5 = $200,000

and Tax Rate = 40%

Using these values in the above formula, we get,

Annual Operating Cash Flow = (200,000 - 200,000)*(1-40%) + 200,000 = $200,000

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Part 3)

The net after tax salvage value of the machine in the last year is determined as below:

Gain on Sale of Equipment = Sales Value - Book Value at the End of Year 5 = 500,000 - 0 = $500,000

Tax on Gain = Gain on Sale of Equipment*Tax Rate = 500,000*40% = $200,000

Net After Tax Salvage Value = Gain on Sale of Equipment - Tax on Gain = 500,000 - 200,000 = $300,000

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Part 4)

The NPV of the project is calculated as below:

NPV = Cash Flow Year 0 + Cash Flow Year 1/(1+Required Rate of Return)^1 + Cash Flow Year 2/(1+Required Rate of Return)^2 + Cash Flow Year 3/(1+Required Rate of Return)^3 + Cash Flow Year 4/(1+Required Rate of Return)^4 + Cash Flow Year 5/(1+Required Rate of Return)^5

Substituting values in the above formula, we get,

NPV = -1,100,000 + 200,000/(1+10%)^1 + 200,000/(1+10%)^2 + 200,000/(1+10%)^3 + 200,000/(1+10%)^4 + (200,000+300,000+100,000)/(1+10%)^5 = -$93,474.12

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Part 5)

The company should accept the project which is less than the IRR as it would result in a positive NPV. IRR is the minimum rate of return acceptable from a project. At IRR, NPV is 0. IRR can be calculated with the us of IRR function/formula of EXCEL/Financial Calculator. The basic function/formula for IRR is given as below:

NPV = 0 = Cash Flow Year 0 + Cash Flow Year 1/(1+IRR)^1 + Cash Flow Year 2/(1+IRR)^2 + Cash Flow Year 3/(1+IRR)^3 + Cash Flow Year 4/(1+IRR)^4 + Cash Flow Year 5/(1+IRR)^5

IRR is calculated with the use of EXCEL as below:

where

IRR = IRR(B2:B7) = 7.15%

Based on the above calculations, it can be concluded that the company accept the project at a discount rate of less than 7.15%.