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**Chapter 7: Capital Budgeting Cash Flows**

In this chapter, we forecast the annual cash flows for a project. After all the cash flows are forecasted, then we can calculate the NPV or IRR (as covered in Chapter 6) and recommend that the project be either accepted or rejected. As in Chapter 6, the relevant cash flows that we consider are always after-tax cash flows. Note the similarity between project after-tax cash flows and the Free Cash Flow model that is covered in Chapter 5.

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**Issues associated with capital budgeting cash flows**

The key to analyzing a new project is to always think incrementally. We calculate the incremental cash flows that are associated with the project, i.e., how will the corporation’s total after-tax cash flows change if this project is accepted. Don’t forget about future inflation when estimating future cash flows! Include all side effects within the corporation: the project may either cannibalize or enhance existing operations. Do not include sunk costs: any money spent in the past is irrelevant. The only cash flows that matter are those that occur now and in the future. Include any opportunity costs. Any asset used for a project might have a higher value in some alternative use.

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**The two types of investment in business assets**

Business investment requires investment in two types of assets: long-term and short-term assets. The long-term assets are the plant, property, and equipment, i.e., assets that will be depreciated over the coming years. The short-term assets include the increased cash, accounts receivable, or inventory that are necessary to support a project. Any increase in short-term assets that is funded or financed with investor’s (debt or equity) capital is called Net Working Capital and must be included in the calculation of a project’s NPV.

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**An Example: Analysis of a proposed five-year project**

If accepted today (t=0), the project is expected to generate positive net cash flows for each of the following five years (t=1 through t=5). A new machine will be put into operation. The new machine costs $1,000,000. Shipping and installation will cost an additional $500,000. Thus the Installed Cost is $1,500,000. This new machine will be sold five years from today when this project is completed. We believe that it can be sold for an estimated $100,000 salvage value in five years (t=5). The project will increase annual revenues and operating expenses (before depreciation) by $800,000 and $300,000 in each year, for years 1 through 5. Continued on next slide.

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**Analysis of a proposed five-year project, continued**

More information: A $50,000 initial increase in Net Working Capital (NWC) is required today and this amount will be recovered in 5 years when the project is terminated. No other changes in NWC will be required during the project’s life. If project is accepted, then an old, fully depreciated machine must be removed and sold. It can be sold today for $50,000. This project’s Installed Cost will be depreciated using an IRS 5-year MACRS schedule: year 1, 20%; year 2, 32%; year 3, 19.2%; year 4, 11.52%; year 5, 11.52%; and year 6, 5.76%. Note that this schedule actually covers a sixth year. The project’s cost of capita is r=11%. The corporate tax rate is 40%.

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**Project’s annual depreciation expense Remaining acct. book value**

Calculating the annual depreciation of the project’s Installed Cost of $1,500,000 This project’s Installed Cost must be depreciated using a 5-year MACRS schedule (schedule actually covers 6 years). Below are the annual depreciation amounts. The year 6 depreciation amount of $86,400 will never be realized, since the project will terminate with year 5. Project Year IRS MACRS % Project’s annual depreciation expense Remaining acct. book value 1 20% $300,000 $1,200,000 2 32% $480,000 $720,000 3 19.2% $288,000 $432,000 4 11.52% $172,800 $259,200 5 $86,400 6 5.76%

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**Issues related to the project’s depreciation and project’s liquidation**

The project has a five year life. However, the IRS MACRS depreciation schedule spills over into a sixth year. When the project is liquidated at year 5, the remaining accounting book value of the machine will be $86,400, the amount that would have been expensed in year 6. Today, we believe the asset can be sold for an estimated $100,000 salvage value in five years. The estimated tax on the sale of the asset at t=5 years is estimated as follows: TAX = [tax rate][sale price – remaining book value] = [0.40][100,000 – 86,400] = $5400, paid at year t=5.

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**Issues related to the t=0 disposal of the old, fully depreciated machine**

If project is accepted today, then an existing, fully depreciated machine must immediately be removed and sold. This existing machine can be sold today for $50,000. The estimated tax on the sale of the (fully depreciated) asset today is estimated as follows: TAX = [tax rate][sale price – remaining book value] = [0.40][50,000 – 0] = $20,000, paid at today at t=0.

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**Estimating the project’s Initial Investment or Capital Expenditure**

We estimate of the new project’s initial cost. There are two asset costs: Installed Cost and Net Working Capital. Purchase of Machine 1,000,000 + Installation and Shipping 500,000 Installed Cost 1,500,000 + Initial increase in Net Working Capital (NWC) 50,000 - Proceeds from existing asset sales Net investment before taxes + tax on sale of existing assets 20,000 Total Initial Net Investment (an outflow of cash) $1,520,000

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**Estimating the project’s annual incremental operating Cash Flows for years 1 through 5**

These are essentially incremental Free Cash Flows (FCF). Free Cash Flow estimation was covered earlier in Chapter 5 (in Addendum 2). The project Net Cash Flows must always ignore the interest costs associated with any debt financing. Thus these Free Cash Flows appear as if the project were all equity financed. The actual interest cost of any debt financing is actually reflected in the cost of capital r that is used to calculate the NPV. The project cost of capital r=11% represents a weighted average of the equity and debt costs of financing this project.

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**Estimating the project’s annual incremental operating Cash Flows for years 1 through 5**

For each operating year of this project (years 1 through 5), the annual net after-tax incremental cash flows ΔCF1 through ΔCF5 must be estimated. The general formula follows: ΔCFi = ΔNOPAT + Δdepreciation – ΔNWC +/– Salvage or Terminal cash flows, otherwise expressed as shown below ΔCFi = [Δrevenue – Δcosts – Δdepreciation][1 – tax rate] + Δdepreciation – ΔNWC(a) +/– Salvage or Terminal cash flows(b) (a) ΔNWC represents changes in Net Working Capital. ΔNWC is positive when additional investment in NWC is needed. (b) The Salvage or Terminal cash flows include such items as: sale of assets and taxes on the sale of those assets, and costs associated with the disposal of a project, e.g., environmental cleanup costs.

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**Estimating the project’s annual incremental operating Cash Flows for years 1 through 5**

ΔCFi = [Δrevenue – Δcosts – Δdepreciation][1 – tax rate] + Δdepreciation – ΔNWC +/– Salvage or Terminal cash flows ΔCF1 = [800,000 – 300,000 – 300,000][1 – 0.4] + 300,000 – 0 = $420,000 ΔCF2 = [800,000 – 300,000 – 480,000][1 – 0.4] + 480,000 – 0 = $492,000 ΔCF3 = [800,000 – 300,000 – 288,000][1 – 0.4] + 288,000 – 0 = $415,200 ΔCF4 = [800,000 – 300,000 – 172,800][1 – 0.4] + 172,800 – 0 = $369,120

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**Estimating the project’s annual incremental operating Cash Flows for years 1 through 5**

Note that CF5 must include the recovery of the original $50,000 of NWC, final sale of machine for $100,000, and tax payment of $5440 on the sale of the machine. ΔCF5 = [Δrevenue – Δcosts – Δdepreciation][1 – tax rate] + Δdepreciation – ΔNWC +/– Salvage or Terminal cash flows ΔCF5 = [800,000 – 300,000 – 172,800][1 – 0.4] + 172,800 – (–50,000) + 100,000 – [0.40][100,000 – 86,400] = $513,680

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**Final NPV and IRR analysis of the five-year project**

This five-year project has the following estimated after-tax cash flows.The project also has a cost of capital r=11%. Now this example becomes a Chapter 6 NPV/IRR analysis. Year Incremental Cash Flow -1,520,000 1 420,000 2 492,000 3 415,200 4 369,120 5 513,680

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**Final NPV and IRR analysis of the five-year project**

Using a financial calculator, at a cost of capital of r=11%, the NPV is $109,282. The IRR is 13.8%, which is greater than r=11%. If this is an independent project, then it should be accepted.

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**A further look at the five-year project’s Net Working Capital**

$50,000 is initially spent on NWC if the project is accepted. This $50,000 is considered to be recovered at t=5 years, when the project is liquidated or terminated. For five years, this $50,000 is tied up for the project and cannot be used elsewhere in the firm, and thus represents an opportunity cost. This $50,000 had to be borrowed at r=11% for five years. Most firms take strong action to minimize investment in inventory and other short-term assets, as these items represent a use of investor’s capital.

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**Other issues associated with the capital budgeting process**

The analysis of the five-year project obviously provides a budget for the project, consisting of forecasts of future revenue and costs. Over the life of the project, actual performance will be evaluated and then compared to the original capital budgeting forecast. Be very aware of the games that may be played within firms with the capital budgeting process.

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**Investments of unequal lives; an example**

We evaluate a machine, having a four year economic life (t=0 to t=4 years). The machine costs $12,000 today to purchase. The machine costs $3000 per year to maintain. The machine can be sold for $2000 salvage value at the end of year 4 (t=4). The machine can be replaced with an identical machine, having the same annual costs, at t=4 years. The real cost of capital is r=6% per year. We will use the Equal Annual Cost Method (EAC).

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**Investments of unequal lives; an example, continued**

The timeline of costs for the 4-year machine is shown below. In order to estimate the Equivalent Annual Cost or EAC, a two step procedure is required. Step 1: Calculate the PV0 of all the (net annual) costs. Step 2: Express the PV0 from Step 1 as the cash flow of an n=4 year annuity and calculate the annual cash flow of this annuity. t=0 t=1 t=2 t=3 t=4 -12,000 -3000 -3000 -3000 - 3000 + 2000 = -1000

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**Investments of unequal lives; an example, continued**

Below are Steps 1 and 2, as described in the previous slide. Step 1 calculate the PV0 of the annual net costs, while Step 2 converts the PV0 into the cash flows of a 4-year annuity.

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**Investments of unequal lives; an example, continued**

This 4-year machine thus has an Equivalent Annual Cost or EAC=$ per year. What if the firm had to decide between two consecutive 4-year machines versus an 8-year machine that has an EAC=$6500 per year. In such a case, choose the machine with the lower EAC, in this case the 4-year machine has the lower EAC.

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**The decision to replace an existing asset**

An existing machine has the annual maintenance and salvage costs shown below. This machine performs the same function as the 4-year machine with an EAC=$ When should the existing machine be replaced with the new 4-year machine? Year Maintenance Costs Salvage Value 0 (now) 8000 1 4000 6000 2 4500 3 5000 2000 4 5500 1000 5

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**The decision to replace an existing asset, continued**

What is the PV0 of keeping the existing machine in operation for one more year? PV0 = /(1+0.06) – 6000/(1+0.06) = $ This $ figure still cannot be compared to the new 4-year machine’s EAC=$ , as the new machine’s EAC falls from t=1 to t=4 on the timeline. The PV0 of the old machine must be multiplied by 1+r to bring it up to t=1 years. FV1 = ( )(1+0.06) = $6480 The $ EAC of the new machine is less than the FV1=$6480 of allowing the old machine to remain for the next year. Replace the existing machine today at t=1.

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Risk, Return, and the Time Value of Money

Risk, Return, and the Time Value of Money

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