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**Using Discounted Cash Flow Analysis to Make Investment Decisions**

Chapter 8 Using Discounted Cash Flow Analysis to Make Investment Decisions

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**Topics Covered Discounted Cash Flows, Not Profits**

Incremental Cash Flows (Ping King Example) Treatment of Inflation Separate Investment & Financing Decisions Calculating Cash Flows Wednesday Example: TBA 2

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Learning Objectives Identify the cash flows attributable to a proposed new project. Calculate the cash flows of a project from standard financial statements. Understand how the company’s tax bill is affected by depreciation and how this affects project value. Understand how changes in working capital affect project cash flows.

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**Capital Budgeting Steps**

For a potential project: Forecast the project cash flows. Estimate the opportunity cost of capital Discount the future cash flows at the opportunity cost of capital. Find NPV of project = PV of future cash flows – required investment, and accept if NPV > 0.

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**Incremental Cash Flows**

Discount incremental cash flows Include All Indirect Effects Forget Sunk Costs Include Opportunity Costs Recognize the Investment in Working Capital Beware of Allocated Overhead Costs Incremental Cash Flow cash flow with project cash flow without project = - 9

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**Incremental Cash Flows**

IMPORTANT Ask yourself this question Would the cash flow still exist if the project does not exist? If yes, do not include it in your analysis. If no, include it. 11

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**Calculating Cash Flow Total Cash Flow =**

Cash Flow from Investment in Plant & Equipment + Cash Flow from Investments in Working Capital + Cash Flow from Operations

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**Cash Flow from Investment in Plant & Equipment Calculations for Ping Kings**

In general, initial cost at beginning of project and possible inflow from after-tax salvage (selling) value at end of project. Ping will need to buy and install new manufacturing equipment costing $4,500,000, which would be depreciated to zero over 5 years using straight-line depreciation. At the end of the project’s 3-year life, Ping estimates they can sell this equipment for $800,000. (tax rate = 40%)

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**Cash Flow from Investment Calculations for Ping Kings**

Initial investment in equipment today (t = 0) = -$4,500,000 For operating cash flow calculation, annual depreciation = $4,500,000/5 = $900,000 Book Value of Equipment = Original Cost – Total Depreciation Book Value at end of year 3 (BV) = $4,500,000 – 3($900,000) = $1,800,000 Year 3 Salvage Value (SV) = $800,000 Tax on SV = Tax Rate x (SV – BV) = 0.4($800,000 - $1,800,000) = $400,000 tax savings Year 3 after-tax salvage value = $800,000+$400,000 = $1,200,000: year 3 cash flow from investments

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Sunk Costs These are costs that cannot be recovered if a project is rejected. Examples: Completed Marketing & Feasibility Studies, Previous new product development and testing For the Ping Kings Project, Ping has already spent $500,000 to research and design the Ping Kings. This cost is to be ignored because it is a sunk cost.

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**Investment in Working Capital**

(Net) Working Capital = Current Assets – Current Liabilities Most new projects require additional short-term (current) assets and often additional current liabilities, such as Additional receivables from increased credit sales. Additional inventory (raw materials) necessary to produce additional new products. Additional trade credit (accounts payables) and taxes and wages payable. Any needed increase in (net) working capital is an outflow of cash, but these outflows are recovered at the end of the project.

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**Calculation of Cash Flow from Investments in Working Capital for Ping Kings Project ($000s)**

Ping estimates they will need working capital equal to 10% of sales revenue for the following year. Ping estimates they can sell 10,000 sets of Ping Kings in year 1, 15,000 sets in year 2, and 9,000 in year 3. They also estimate they can sell the Ping Kings for $640 a set in years 1 & 2, but they will only be able to sell them for $540 a set in year 3. Year Sales WC need WC Chg (474) (486) Increase in WC is an outflow, decrease in WC is an inflow

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**Methods of Calculating CF from Operations (Oper. CF)**

Method 1: Oper. CF = revenues – cash expenses – taxes Method 2: Oper. CF = net accounting profit + depreciation Method 3: (revenues – cash expenses) x (1 – tax rate) + depreciation x tax rate All these methods give the same result!

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**Ping King CF for Operations Info.**

Ping estimates they can sell 10,000 sets of Ping Kings in year 1, 15,000 sets in year 2, and 9,000 in year 3. They also estimate they can sell the Ping Kings for $640 a set in years 1 & 2, but they will only be able to sell them for $540 a set in year 3. Variable costs will be $350 a set for all three years and Ping also expects to have $300,000 in fixed manufacturing costs annually for this project. Ping’s marginal tax rate is 40%.

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**Cash Flow from Operations for Ping Kings (using Method 2)**

Year Unit Sales 10, ,000 9,000 $/Unit $640 $640 $540 VC/Unit $350 $350 $350 Sales($000) 6,400 9,600 4,860 -Variable Costs 3,500 5,250 3,150 -Fixed Costs -Depreciation Pre-tax Profit 1,700 3, -Tax(40%) , Net Profit 1,020 1, +Depreciation Operating Cash Flow 1,920 2,790 1,206

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**Year 1 Ping King CF from Operations using Methods 1 & 3**

Method 1: Oper. CF = revenues – cash expenses – taxes = 6400 – = 1920 Method 3: (revenues – cash expenses) x (1 – tax rate) + depreciation x tax rate = (6400 – 3800)(1 – 0.4) + 900(0.4) = 1920

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**Total Incremental Cash Flows & Decision for Ping Kings ($000s)**

Year Cap Inv (4500) WC Inv (640) (320) Oper CF Total CF (5140) CF0 C01 C02 C03 NPV at 18% = or $320,247 IRR = 21.5%

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Indirect CF Effects Include impact that a new project would have on existing company sales and expenses. Example: Callaway Golf considers making a new line of irons. They must consider lost sales on existing product line of irons.

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What about this? Ping’s current line of irons is the Ping i3, which have an estimated product life of 1 year remaining. Should Ping go ahead with the Ping Kings project if they thought next year’s Ping i3 sales and variable costs would decrease by $1,000,000 and $500,000 respectively on a BEFORE-TAX basis.

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**This would affect the year 1 CF from Operations: Indirect Effect**

Year Orig 1 Change New 1 Revenue($000) 6,400 (1,000) 5,400 -Variable Costs 3,500 (500) 3,000 -Fixed Costs -Depreciation Pre-tax Profit 1,700 (500) 1,200 Tax(40%) (200) Net Profit 1,020 (300) +Depreciation Oper Cash Flow 1,920 (300) 1,620 New year 1 total cash flow = 1620 – 320 = 1300, NEW NPV at 18% = or $66,009 New IRR = 18.7%

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**Inflation and Projected Cash Flows**

INFLATION RULE Be consistent in how you handle inflation!! Use nominal interest rates to discount nominal cash flows. Use real interest rates to discount real cash flows. You will get the same results, whether you use nominal or real figures 12

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**Separation of Investment & Financing Decisions**

When valuing a project, ignore how the project is financed (exclude interest expense from cash flow forecast). Following the logic from incremental analysis ask yourself the following question: Is the project existence dependent on the financing? If no, you must separate financing and investment decisions. 17

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**MACRS Depreciation vs. Straight-Line for Ping Kings**

Fastest depreciation method that corporations are allowed to use for tax purposes. Assume our Ping Kings equipment (cost = $4,500,000) falls into the 5-year MACRS class. (recall tax rate of 40%, r = 18%). Should MACRS be used? Depreciation Tax Shield (Savings) = Deprec. X tax rate Dep Diff in PV of Year Dep% M Dep S-L Dep Diff TaxShd TaxShd , , ,440, , , , ,128 , ,000 (36,000) (14,400) (8,764) , , ,364 , ,000 ,200 MACRS Year 3 Book Value = 1,296,000 Straight-Line Year 3 Book Value = 1,800,000 *Difference in After-tax Salvage Value = .4(1,296,000 – 1,800,000) = -201,600 PV of After-Tax Salvage Value Difference = -201,600/(1.18)3 = -122,700 Change in NPV = 146,364 – 122,700 = 23,664

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**MACRS Cash Flows for Ping Kings (using Method 2)**

Year Unit Sales 10, ,000 9,000 $/Unit $640 $640 $540 VC/Unit $350 $350 $350 Sales($000) 6,400 9,600 4,860 -Variable Costs 3,500 5,250 3,150 -Fixed Costs -Depreciation , Pre-tax Profit 1,700 2, -Tax(40%) , Net Profit 1,020 1, +Depreciation , Operating Cash Flow 1,920 3,006 1,192 WC Cash Flow (320) After-Tax SV Total Cash Flow 1,600 3,480 2,676 Initial CF (T=0) = 5140 NPV at 18% = $343,910 vs. $320,247 under straight-line depreciation

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**Comprehensive Example (Last half of Wednesday’s Lecture)**

Will post example on website Monday, that we will work through in Wednesday’s lecture.

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