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Question

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Cochrane, Inc., is considering a new three-year expansion project that requires an initial fixed asset life. The project is estimated to generate $2,240,000 in annual sales, with costs of $1,230,000. The project requires an initial investment in net working capital of $159,000, and the fixed asset will have a market value of $184,000 at the end of the project. Assume that the tax rate is 35 percent and the required return on the project is 9 percent. Requirement 1: What are the net cash flows of the project for the following years? (Do not round intermediate calculations. A negative amount should be indicated by a minus sign. Enter your answers in dollars, not millions of dollars (e.g., 1,234,567).) Year Cash Flow $2529000 933000 933000 Requirement 2: What is the NPV of the project? (Do not round intermediate calculations. Enter your answer in dollars, not millions of dollars (e.g., 1,234,567). Round your answer to 2 decimal places (e.g., 32.16).) NPV

Explanation / Answer

Part A)

Requirement 1 - Year 3 Cash Flow

Since, the annual cash flow from Year 0 to Year 2 have been correctly calculated, we need to calculate the cash flow for Year 3. The formula for calculating cash flow for Year 3 can be dervied as follows:

Cash Flow Year 3 = Annual Cash Inflow + Market Value*(1-Tax Rate) + Recovery of Working Capital

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Using the values calculated and provided in the question, we get,

Cash Flow Year 3 = 933,000 + 184,000*(1-35%) + 159,000 = $1,211,600

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Requirement 2 - NPV

NPV is the difference between the present value of cash inflows and cash outflows. The formula for calculating NPV is:

NPV = Cash Flow Year 0 + Cash Flow Year 1/(1+Discount Rate)^1 + Cash Flow Year 2/(1+Discount Rate)^2 + Cash Flow Year 3/(1+Discount Rate)^3

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Using the values cash flow values calculated and other details provided in the question, we get,

NPV = - 2529000 + 933000/(1+9%)^1 + 933000/(1+9%)^2 + 1211600/(1+9%)^3 = $47,828.24

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Part 2)

We will have to calculate the value of annual cash flows in order to arrive at the NPV. The relevant formulas are:

Cash Flow Year 0 = -Initial Investment - Investment in Working Capital

Annual Cash Inflow (Year 1 and Year 5) = (Savings in Pre-Tax Cost - Depreciation)*(1-Tax Rate) + Depreciation

Cash Inflow = Annual Cash Inflow + Salvage Value*(1-Tax Rate) + Recovery of Working Capital

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NPV = NPV = Cash Flow Year 0 + Cash Flow Year 1/(1+Discount Rate)^1 + Cash Flow Year 2/(1+Discount Rate)^2 + Cash Flow Year 3/(1+Discount Rate)^3 + Cash Flow Year 4/(1+Discount Rate)^4 + Cash Flow Year 5/(1+Discount Rate)^5 + Cash Flow Year 6/(1+Discount Rate)^6

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Cash Flow Year 0 = -789,000 - 54,000 = -843,000

Cash Inflow (Year 1 to Year 5) = (196,000 - 789,000/6)*(1-35%) + 789,000/6 = 173,425

Cash Inflow (Year 6) = 173,425 + 108,000*(1-35%) + 54,000 = 297,625

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NPV = -843,000 + 173,425/(1+7%)^1 + 173,425/(1+7%)^2 + 173,425/(1+7%)^3 + 173,425/(1+7%)^4 + 173,425/(1+7%)^5 + 297,625/(1+7%)^6 = $66,396.84

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