Making Capital Investment Decisions - Chapter 10

Relevant Cash Flows and the Stand-Alone Principle

  • A relevant cash flow for a project is defined as a change in the firm’s overall future cash flow that arises as a direct consequence of the decision to undertake that specific project.

  • Incremental cash flows represent the difference between a firm’s future cash flows with a project and those same cash flows without the project.

  • Any cash flow that exists regardless of whether or not a project is undertaken is considered irrelevant and should be excluded from analysis.

  • The stand-alone principle is the assumption that the evaluation of a project may be based solely on the project’s incremental cash flows.

  • Once incremental cash flows are determined, the project is viewed as a "minifirm" with its own specific future revenues, costs, assets, and cash flows.

  • Evaluation primarily involves comparing the cash flows generated by this minifirm to the actual cost of acquiring it.

Identifying Incremental Cash Flows

  • A sunk cost is a cost that has already been incurred and cannot be removed or recovered. Because it remains regardless of the investment decision, it should not be considered in the decision-making process.

  • Opportunity cost is the most valuable alternative that must be given up if a particular investment is undertaken. This represents a relevant cash flow.

  • Side effects, or spillover effects, can be both positive and negative for the firm.

  • Erosion occurs when the cash flows of a new project come at the direct expense of a firm’s existing projects or product lines.

  • Net Working Capital (NWC) investments are typically required for projects in addition to long-term asset investments.

    • Projects generally require cash on hand for immediate expenses.

    • Initial investments in inventories and accounts receivable are usually necessary.

    • Investment in project NWC resembles a loan; it is an outflow at the start and is generally recovered at the end of the project life.

  • Financing Costs:

    • Interest paid, dividends, or principle repaid are not included in the analysis of a proposed investment.

    • The focus is strictly on the cash flow generated by the assets of the project.

    • The goal is to compare project cash flow to acquisition cost to estimate the Net Present Value (NPV).

  • Cash Flow Timing and Taxes:

    • Cash flow must be measured at the time it actually occurs, not when it accrues according to accounting standards.

    • Only aftertax cash flows are relevant because taxes represent a literal cash outflow.

Pro Forma Financial Statements and Project Cash Flow Calculations

  • Pro forma financial statements are used to project future years of operation.

  • Example: Shark Attractant Project

    • Sales projection: 50,00050,000 cans per year.

    • Price per unit: $4.00\$4.00.

    • Variable cost per unit: $2.50\$2.50.

    • Project life: 33 years.

    • Required return: 20%20\%.

    • Fixed costs: $17,430\$17,430 per year.

    • Manufacturing equipment cost: $90,000\$90,000 (to be 100%100\% depreciated over three years).

    • Equipment salvage: Market value is roughly equal to removal costs, making it effectively worthless ($0\$0) at the end of three years.

    • Initial NWC investment: $20,000\$20,000.

    • Tax rate: 21%21\%.

  • Projected Income Statement Components:

    • Sales (50,000×$450,000 \times \$4): $200,000\$200,000

    • Variable Costs (50,000×$2.5050,000 \times \$2.50): $125,000\$125,000

    • Fixed Costs: $17,430\$17,430

    • Depreciation ($90,0003\frac{\$90,000}{3}): $30,000\$30,000

    • EBIT (Earnings Before Interest and Taxes): $27,570\$27,570

    • Taxes (21%×$27,57021\% \times \$27,570): $5,790\$5,790

    • Net Income: $21,780\$21,780

  • Determining Operating Cash Flow (OCF):

    • OCF=EBIT+Depreciation−TaxesOCF = EBIT + Depreciation - Taxes

    • OCF=$27,570+30,000−5,790=$51,780OCF = \$27,570 + 30,000 - 5,790 = \$51,780

  • Project Total Cash Flows:

    • ProjectCashFlow=OCF−Change in NWC−Capital SpendingProject Cash Flow = OCF - \text{Change in NWC} - \text{Capital Spending}

    • Year 0: $0−(20,000)−(90,000)=−$110,000\$0 - (20,000) - (90,000) = -\$110,000

    • Year 1: $51,780−0−0=$51,780\$51,780 - 0 - 0 = \$51,780

    • Year 2: $51,780−0−0=$51,780\$51,780 - 0 - 0 = \$51,780

    • Year 3: $51,780−(−20,000)−0=$71,780\$51,780 - (-20,000) - 0 = \$71,780

Project Value and Evaluation Metrics

  • Net Present Value (NPV) Equation for the Shark Attractant Project:

    • NPV=−$110,000+$51,7801.2+$51,7801.22+$$71,7801.23=$10,648NPV = -\$110,000 + \frac{\$51,780}{1.2} + \frac{\$51,780}{1.2^2} + \frac{\$\$71,780}{1.2^3} = \$10,648

    • Since NPV is positive (>\$0), the project creates value and is acceptable.

  • Internal Rate of Return (IRR):

    • Calculated via trial and error to be approximately 25.8%25.8\%.

  • Payback Period:

    • Approximately 2.12.1 years.

  • Average Accounting Return (AAR):

    • AAR=Average Net IncomeAverage Book ValueAAR = \frac{\text{Average Net Income}}{\text{Average Book Value}}

    • Average Net Income = $21,780\$21,780

    • Average Book Value = $110,000+80,000+50,000+20,0004=$65,000\frac{\$110,000 + 80,000 + 50,000 + 20,000}{4} = \$65,000

    • AAR=$21,780$65,000=0.3351AAR = \frac{\$21,780}{\$65,000} = 0.3351 or 33.51%33.51\%

Detailed Dynamics of Net Working Capital

  • Net working capital changes affect cash flow by reflecting the difference between accounting accruals and actual cash movement.

  • Example Case:

    • Sales = $500\$500, Costs = $310\$310, EBIT = $190\$190.

    • Depreciation and Taxes = 00.

    • Accounts Receivable (A/R): Beginning = $120\$120, Ending = $150\$150. (ΔA/R=+$30\Delta A/R = +\$30).

    • Accounts Payable (A/P): Beginning = $105\$105, Ending = $160\$160. (ΔA/P=+$55\Delta A/P = +\$55).

  • NWC Analysis:

    • Beginning NWC = $120−105=$15\$120 - 105 = \$15

    • Ending NWC = $150−160=−$10\$150 - 160 = -\$10

    • Change in NWC = $(−10)−15=−$25\$(-10) - 15 = -\$25

    • A decline in NWC of $25\$25 means cash was freed up.

  • Total Cash Flow Calculation:

    • TotalCF=OCF−ΔNWC−Capital SpendingTotal CF = OCF - \Delta NWC - \text{Capital Spending}

    • TotalCF=$190−(−$25)−0=$215Total CF = \$190 - (-\$25) - 0 = \$215

  • Verification via Cash Inflows and Outflows:

    • Cash Inflow = Sales−ΔA/R=$500−30=$470\text{Sales} - \Delta A/R = \$500 - 30 = \$470

    • Cash Outflow = Costs−ΔA/P=$310−55=$255\text{Costs} - \Delta A/P = \$310 - 55 = \$255

    • Net Cash Flow = $470−255=$215\$470 - 255 = \$215

Depreciation and Tax Laws

  • Depreciation itself is a noncash deduction; its only cash flow consequence is its impact on the tax bill (the tax shield).

  • Modified Accelerated Cost Recovery System (MACRS):

    • Every asset is assigned to a specific class determining its tax life.

    • Depreciation is calculated by multiplying the original cost by a fixed percentage corresponding to the year and class.

    • Salvage value and economic life are not used in calculating annual MACRS depreciation.

  • Common MACRS Classes:

    • 3-year: Equipment used in research.

    • 5-year: Autos, computers.

    • 7-year: Most industrial equipment.

  • Example of MACRS Calculation (5-year Property):

    • Asset cost: $12,000\$12,000.

    • Year 1 (20%20\%): $12,000×0.20=$2,400\$12,000 \times 0.20 = \$2,400

    • Year 2 (32%32\%): $12,000×0.32=$3,840\$12,000 \times 0.32 = \$3,840

  • Bonus Depreciation:

    • PATH Act of 2015: Permitted 50%50\% bonus depreciation in 2017.

    • Tax Cuts and Jobs Act of 2017: Increased bonus depreciation to 100%100\% for 2018 through 2022.

    • Phasedown: Drops by 20%20\% per year after 2022 until reaching zero after 2026.

  • Book Value vs. Market Value:

    • Book value = Cost−Accumulated Depreciation\text{Cost} - \text{Accumulated Depreciation}.

    • If an asset is sold, taxes must be paid at the ordinary income tax rate on the difference between the sale price (market value) and the book value.

Alternative Definitions of Operating Cash Flow (OCF)

  • Baseline Assumptions:

    • Sales = $1,500\$1,500, Costs = $700\$700, Depreciation = $600\$600.

    • EBIT = $1,500−700−600=$200\$1,500 - 700 - 600 = \$200.

    • Tax Rate (TCT_C) = 21%21\%.

    • Taxes = $200×0.21=$42\$200 \times 0.21 = \$42.

    • Standard OCF = $200+600−42=$758\$200 + 600 - 42 = \$758.

  • The Bottom-Up Approach:

    • Starts with Net Income and adds back noncash deductions.

    • ProjectNetIncome=EBIT−Taxes=$200−42=$158Project Net Income = EBIT - Taxes = \$200 - 42 = \$158

    • OCF=Net Income+Depreciation=$158+600=$758OCF = \text{Net Income} + \text{Depreciation} = \$158 + 600 = \$758

    • This is only valid if no interest expense was subtracted from Net Income.

  • The Top-Down Approach:

    • Starts with Sales and subtracts cash costs and taxes.

    • Noncash items like depreciation are ignored.

    • OCF=Sales−Costs−TaxesOCF = \text{Sales} - \text{Costs} - \text{Taxes}

    • OCF=$1,500−700−42=$758OCF = \$1,500 - 700 - 42 = \$758

  • The Tax Shield Approach:

    • Divides OCF into two components: the project's after-tax cash flow without depreciation and the tax savings from depreciation.

    • OCF=(Sales−Costs)×(1−TC)+Depreciation×TCOCF = (\text{Sales} - \text{Costs}) \times (1 - T_C) + \text{Depreciation} \times T_C

    • OCF=($1,500−700)×0.79+$600×0.21OCF = (\$1,500 - 700) \times 0.79 + \$600 \times 0.21

    • OCF=$632+126=$758OCF = \$632 + 126 = \$758

    • The term Depreciation×TC\text{Depreciation} \times T_C is known as the depreciation tax shield.

Special Case: Evaluating Cost-Cutting Proposals

  • Example: Automation Investment

    • Equipment cost: $80,000\$80,000.

    • Annual savings (pretax): $22,000\$22,000.

    • Life: 55 years.

    • Depreciation: Straight-line to zero ($16,000\$16,000 per year).

    • Salvage Value: $20,000\$20,000 in five years.

    • Tax Rate: 21%21\%

    • Discount Rate: 10%10\%

  • Incremental Cash Flows:

    • Aftertax salvage: $20,000×(1−0.21)=$15,800\$20,000 \times (1 - 0.21) = \$15,800

    • Increased EBIT: $22,000−16,000=$6,000\$22,000 - 16,000 = \$6,000

    • Increased Taxes: $6,000×0.21=$1,260\$6,000 \times 0.21 = \$1,260

    • OCF=EBIT+Depreciation−Taxes=$6,000+16,000−1,260=$20,740OCF = EBIT + Depreciation - Taxes = \$6,000 + 16,000 - 1,260 = \$20,740

  • Evaluation:

    • Year 0: $(−80,000)\$(-80,000)

    • Years 1-4: $20,740\$20,740

    • Year 5: $20,740+15,800=$36,540\$20,740 + 15,800 = \$36,540

    • NPVNPV at 10%10\% is $8,431\$8,431, so the proposal should be accepted.

Special Case: Setting a Bid Price

  • Competitive bidding requires submitting the lowest price while still meeting the required return.

  • Example: Truck Modification Project

    • Quantity: 55 trucks per year for 44 years (Total = 2020).

    • Required Return: 20%20\%

    • Costs per year: Lease = $24,000\$24,000; Platform = $10,000\$10,000; labor/material per truck = $4,000\$4,000.

    • Total Costs per year: $24,000+5×($10,000+$4,000)=$94,000\$24,000 + 5 \times (\$10,000 + \$4,000) = \$94,000.

    • Investment: Equipment = $60,000\$60,000 (straight-line to zero over 44 years, salvage = $5,000\$5,000); NWC = $40,000\$40,000.

  • Step 1: Cash flow targets for NPV=0NPV = 0

    • Initial Outlay: $60,000+40,000=$100,000\$60,000 + 40,000 = \$100,000

    • Terminal Non-operating Cash Flow: Salvage after-tax ($5,000×0.79=$3,950\$5,000 \times 0.79 = \$3,950) + NWC recovery ($40,000\$40,000) = $43,950\$43,950

    • PV of Terminal CF: $43,9501.204=$21,195\frac{\$43,950}{1.20^4} = \$21,195

    • PV required from OCF: $100,000−21,195=$78,805\$100,000 - 21,195 = \$78,805

  • Step 2: Solve for OCF

    • 78,805=OCF×Annuity Factor(4 years,20%=2.58873)78,805 = OCF \times \text{Annuity Factor}(4\text{ years}, 20\% = 2.58873)

    • OCF=$30,442OCF = \$30,442

  • Step 3: Solve for Sales Price

    • OCF=Net Income+DepreciationOCF = \text{Net Income} + \text{Depreciation}

    • 30,442=Net Income+$60,000430,442 = \text{Net Income} + \frac{\$60,000}{4}

    • Net Income=$15,442\text{Net Income} = \$15,442

    • Net Income=(Sales−Costs−Depreciation)×(1−TC)\text{Net Income} = (\text{Sales} - \text{Costs} - \text{Depreciation}) \times (1 - T_C)

    • $15,442=(Sales−$94,000−$15,000)×0.79\$15,442 = (\text{Sales} - \$94,000 - \$15,000) \times 0.79

    • Sales = $128,546\$128,546

    • Bid Price per truck = $128,5465=$25,709\frac{\$128,546}{5} = \$25,709

Special Case: Equipment Options with Different Lives

  • Applicable when evaluating mutually exclusive assets with different economic lives that must be replaced indefinitely.

  • Example: Machine A vs. Machine B (10%10\% discount rate)

    • Machine A: Cost = $100\$100, Operating cost = $10\$10/year, Life = 22 years.

    • Machine B: Cost = $140\$140, Operating cost = $8\$8/year, Life = 33 years.

  • PV of Costs Analysis:

    • PVA=−$100−$101.1−$101.12=−$117.36PV_A = -\$100 - \frac{\$10}{1.1} - \frac{\$10}{1.1^2} = -\$117.36

    • PVB=−$140−$81.1−$81.12−$81.13=−$159.89PV_B = -\$140 - \frac{\$8}{1.1} - \frac{\$8}{1.1^2} - \frac{\$8}{1.1^3} = -\$159.89

  • Equivalent Annual Cost (EAC):

    • The PV of project costs calculated on an annual basis.

    • EACA=−$117.361.7355=−$67.62EAC_A = \frac{-\$117.36}{1.7355} = -\$67.62

    • EACB=−$159.892.4869=−$64.30EAC_B = \frac{-\$159.89}{2.4869} = -\$64.30

    • Machine B is chosen because it has the lower equivalent annual cost.

Questions & Discussion

  • What are the relevant incremental cash flows for project evaluation?     Relevant incremental cash flows are those future cash flows that change as a direct result of accepting the project, specifically looking at the "with vs. without" difference.

  • Explain what erosion is and why it is relevant.     Erosion is the loss of sales or cash flow from existing products due to the introduction of a new project. It is relevant because it represents a negative incremental cash flow for the firm as a whole.

  • What is the definition of project operating cash flow? How does this differ from net income?     OCF is EBIT+Depreciation−Taxes\text{EBIT} + \text{Depreciation} - \text{Taxes}. It differs from net income because it adds back noncash charges (depreciation) and ignores financing costs (interest).

  • Why is it important to consider changes in net working capital in developing cash flows? What is the effect of doing so?     NWC accounts for the timing differences between accounting recognition and actual cash flow. It usually creates an initial cash outflow and a terminal cash inflow.

  • What are the top-down and bottom-up definitions of operating cash flow?     Bottom-up: Net Income+Depreciation\text{Net Income} + \text{Depreciation}. Top-down: Sales−Cash Costs−Taxes\text{Sales} - \text{Cash Costs} - \text{Taxes}.

  • In setting a bid price, we used a zero NPV as our benchmark. Explain why this is appropriate.     A zero NPV at the required return represents the minimum price at which the firm can undertake the project while still meeting its financial objectives and compensating its investors properly.