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Jacoby, Stangeland and Wajeeh, 20001 Capital Budgeting & NPV uRecall: Value of an Asset = PV(Future CFs) Note: CF g accounting income (earnings) Examples: u Value of a Project = PV(future CFs generated by project) Value of Firms Equity = PV(dividends) g PV(earnings) Capital Investment g Depreciation Chapter 7

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2 uFor the NPV of a project - use only Incremental CF uIs a CF incremental? u YES - if occurs as a result of accepting the project u No - if occurs independent of the decision uExample: Determine which is an incremental CF: u a marketing survey done 2 years ago u R&D expenses spent last year Sunk Costs are NOT Incremental CF u apparently, the machine required for the new project is found in the companys warehouse u the company already owns the office building for the new project Opportunity Costs ARE Incremental CF u buyers of the GMCs new truck, are potential buyers of GMCs SUV u advertising of the new product will increase the sales of an older product u wage increase resulting from a labour shortage due to accepting the project Side Effects ARE Incremental CF

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3 The Appropriate Discount Rate uThe Fisher Relation: Nominal Rate (r n ) Vs. Real Rate (r r ): (1+ r n ) = (1+ r r )(1+ ) where is the inflation rate uWhat rate should we use? u Nominal CFs should be discounted with r n u Real CFs should be discounted with r r uRisk and discount rates: higher risk CFs require a higher return

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4 Inflation uYour time-0 endowment is: $2,000,000 uYou can invest at a nominal rate of r n =5% p.a. uAt time-0, the cheapest house in Beverly-Hills costs $2,000,000 Real-estate prices are expected to grow at =10% p.a. uCan you afford buying a house in Beverly-Hills next year? uAt time-1 u your money grows to: $2,000,000 (1.05) = $2,100,000 u The cheapest house in B.H. will cost: $2,000,000 (1.10) = $2,200,000 uConclusion: the real value of your money has depreciated

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5 Inflation The Fisher Relation: (1+ r n ) = (1+ r r )(1+ ) Your real rate is: r r = [(1+ r n )/(1+ )] - 1 = [(1.05)/(1.10)] - 1 = - 4.55% uReal CF (C t,r ) vs. Nominal CF (C t,n ): C t,n = C t,r (1+ ) t In our example: t=1, =0.10, C 1,n = $2,200,000 (actual cost), and C t,r = C t,n /(1+ ) t = [$2,200,000 / 1.10 1 ] = $2,000,000 (time-0 value) uWhat rate should we use? u C t,n should be discounted with r n : PV = [$2,200,000 / (1+0.05) 1 ] = $2,095,238.10 u C t,r should be discounted with r r : PV = [$2,000,000 / (1 - 0.0455) 1 ] = $2,095,238.10

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6 Calculating the Net Operating Cash Flow (NOCF) Recall: CF g accounting income u We are interested in the PV of Net (after-tax) Operating CF (NOCF): NOCF = R - E - Taxes(1) where, Taxes= [R - E - D]T c (2) uPlug (2) into (1): NOCF = R - E - T c [R - E - D] = (R - E)(1- T c ) + T c D RevenuesOperating Costs EBDT(1- T c ) Tax Shield of D

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Jacoby, Stangeland and Wajeeh, 20007 Calculating NOCF - An Example Income Without CF-based Statement Depreciation (D) (with D) Revenues 100 100 100 Expenses 70 70 70 EBDT 30 30 30 Depreciation (D) 10 0 0 EBT 20 30 30 Taxes (@40%) 8 12 8 NI 12 18 22 Tax-Shield of CCA: T c % D = = $4 NOCF=(R - E)(1- T c )+T c D=EBDT(1- T c )+T c D=30(1- 0.4)+0.4 % 10= $22 l Conclusion: CCA Tax-Shield is equivalent to cash inflow Pay less taxes ($4)

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Jacoby, Stangeland and Wajeeh, 20008 Capital Cost Allowance (CCA) uRevenue Canadas rules of depreciating assets for tax purposes uAssign every asset to its asset class (pool) uFind its maximum CCA rate e.g.Brick buildings (acquired after 1987): d = 4% Electrical equipment & aircraft: d = 25% uRevenue Canadas 50% rule: CCA for the first year = d [installed cost / 2]

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9 CCA - The U-Air Case Initial Facts: uU-Air is considering the addition of 4 new planes to its fleet, at a cost of $10 M each. (ready to fly), for a new line to the Bahamas uExpected life of an airplane is 30 years uU-Air is expected to sell the airplanes for $3,691,406.25 each in 4 years uCalculate the expected CCA schedule for this purchase for the next 4 years BeginningEnding CCA Tax Shield YearUCCCCAUCC( T c CCA) 1 2 3 4....

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10 Investing in Net Working Capital (NWC) An investment in NWC, represents an increase in the NWC allocated to the project: u purchasing of raw materials and inventory u keeping cash reserves for unexpected expenses u an increase in accounts receivable u a decrease in accounts payable and taxes payable NWC - The U-Air Case: U-Air managers predict the following requirement for NWC generated by the Bahamas project: Year NWC Changes in NWC Cash Flow from NWC 01,600 K +1,600 K - 1,600 K 12,400 + 800 - 800 23,000 + 600 - 600 32,200 - 800 + 800 4 0 - 2,200 +2,200

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Jacoby, Stangeland and Wajeeh, 200011 Calculating Net Working Capital (NWC)

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Jacoby, Stangeland and Wajeeh, 200012 Capital Budgeting: The U-Air Case Facts uCosts of test marketing (already spent) $2,000 K uCurrent (time-0) market value of 4 airplanes$40,000 K uNumber of round-trip tickets per year during 4-year life of the project: (16,000, 24,000, 30,000, 22,000) uTicket price $2 K uOperating costs per ticket $1 K u Number of round-trip tickets per year (during next 4 years) lost in sales of U-Airs other Caribbean lines: (100, 200, 400, 300) with the same ticket price and variable cost uCash flows from investment in NWC: (-$1,600 K, -800, -600, +800, +2,200) uU-Air already owns a terminal which can be used for the Bahamas project. Renting a similar terminal would cost U-Air $10,000 K per year uU-Air will sell the airplanes after 4 years for $3,691.40625 K each ur =10%, and T c = 40%.

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Jacoby, Stangeland and Wajeeh, 200013 The Worksheet for Cash Flows of U-Airs Bahamas Project I. Income Year 0Year 1Year 2Year 3Year 4 CF from Ticket Sales Ticket Sales Revenues32,00048,00060,00044,000 Sales - Side effects ( 200) (400) (800) (600) 31,80047,60059,20043,400 Operating costs Fixed costs (Opportunity cost) 10,00010,00010,000 10,000 Variable costs16,00024,00030,00022,000 V. costs - Side effects ( 100) (200) (400) (300) (25,900) (33,800) (39,600) (31,700) EBDT 5,900 13,800 19,600 11,700 EBDT(1- T c ) * 0 3,540 8,28011,760 7,020 * Calculated with T c = 40%. ($ thousands) (All cash flows occur at the end of the year.)

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Jacoby, Stangeland and Wajeeh, 200014 II. Investments Year 0Year 1Year 2Year 3Year 4 Airplanes(40,000) 14,765.625 Change in NWC (1,600) (800) (600) 800 2,200 Total investment cash flow (ICF)(41,600) (800) (600) 800 16,965.625 Calculating the NPV of the Project (@ r = 10%) PV of EBDT(1- T c ) 23,691.37 PV of ICF(30,634.34) PV of CCA Tax-Shield 8,027.63 NPV of the Bahamas Project 1,084.66 ($ thousands) (All cash flows occur at the end of the year.) The Worksheet for Cash Flows of U-Airs Bahamas Project (Contd) Case – Part 1 - Q1 & Q2

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Jacoby, Stangeland and Wajeeh, 200015 The PV of CCA Tax Shield uIf U-Air never sells the airplanes, then the CCA tax shield will be a growing perpetuity with a negative growth rate, and the twist of Revenue Canadas 50% rule uSince U-Air will sell the airplanes in 4 years (for $3,691,406.25 each), to calculate the PV of CCA tax shield, we use the growing perpetuity formula, adjusted for Revenue Canadas 50% rule and the sale of the airplanes. uIn this course, we deal with the simplest case where there are no capital gains and the asset pool is not terminated after the sale (The total value of U-Airs class-9 asset pool is not expected to be below a level of $350 million over the next four years.) uThe PV of CCA tax shield is given by: Where: S = Min[sale value of assets, original price of assets] = Min[$14,765,625.25, $40,000,000]= $14,765,625.25 C = the original price of the assets = $40,000K d = 25% for Electrical equipment & aircraft. n = the time when assets are sold = 4 years

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16 Year 0 Year 1 Year 2 Year 3 Year 4 EBDT(1- T c ) 0 3,540 8,280 11,760 7,020 Total investment cash flow (ICF)(41,600) (800) (600) 800 16,965.625 Total Project CF (Excluding CCA Tax-Shield) (41,600) 2,740 7,680 12,560 23,985.625 CCA Tax-Shields: Annual CCA 5,000 8,750 6,562.5 4,921.875 Annual Tax-Shield ( T c CCA) 2,000 3,500 2,625 1,968.75 Total Project Cash Flow: (41,600) 4,740 11,180 15,185 25,954.375 Calculating the NPV of the Project (@ r = 10%) NPV of the Bahamas Project: 1,084.66 ($ thousands) (All cash flows occur at the end of the year.) Total Project Cash Flow Approach

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Jacoby, Stangeland and Wajeeh, 200017 Nominal CFs Year 0Year 1Year 2Year 3Year 4 EBDT(1- T c ) 0 3,540 8,28011,760 7,020 Investment CF (ICF)(41,600) (800) (600) 800 16,965.625 We have an annual inflation rate of: = 4% We convert nominal CFs to real CFs, with: C t,r = C t,n / (1+ ) t Real CFs Year 0 Year 1 Year 2 Year 3 Year 4 EBDT(1- T c ) 0 3,403.85 7,655.33 10,454.60 6,000.73 Investment CF (ICF) (41,600.00) (769.23) (554.73) 711.20 14,502.29 ($ thousands) (All cash flows occur at the end of the year.) The Worksheet for REAL Cash Flows of U-Airs Bahamas Project Case – Part 1 – Q3

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Jacoby, Stangeland and Wajeeh, 200018 We calculate the NPV of the REAL CFs of the Project with the real rate: Fisher Relation: r r = [(1+ r n )/(1+ )] - 1= [(1.10)/(1.04)] - 1= 5.769231% The NPV of the Project: PV of EBDT(1- T c ) 23,691.37 PV of ICF(30,634.34) PV of CCA Tax-Shield * 8,027.63 NPV of the Bahamas Project 1,084.66 The Worksheet for REAL Cash Flows of U-Airs Bahamas Project (Contd) * CCA Tax-Shield is a stream of nominal CF => calculate NPV with the nominal rate Same as calculated with the nominal CF

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