Chapter 10 Lecture Notes
Making Capital Investment Decisions

  1. Cash Flow Estimation
    1. This is a very difficult step in the process.
    2. We want to consider only relevant cash flows.
    3. Cash Flow Differs from Accounting Profit (Net Income) for a number of reasons:
      1. Sales may be on a credit not a cash basis
      2. There may be accruals such as taxes and wages which do not constitute cash flows from the firm during the period in question
      3. Depreciation reduces income for tax purposes but does not represent an actual cash flow from the firm

    4. Cash flow calculation
      1. Operating cash flow
        1. A project's net income after taxes plus depreciation
        2. OCFt = (Rt - OCt)(1 - T) + TDt
        3. where: R = project revenues
                   OC = operating costs
                      T = Marginal tax rate
                      D = Depreciation
                       t = a particular time period.

          Note: This is what your textbook calls "The Tax Shield Approach." See page 314.

          Let TDt = (1 - T)Dt + Dt

          Rewrite:

          OCFt = (Rt - OCt - Dt)(1 -T) + Dt

          Depreciation Goes to War

          IRS Publication 946: How to Depreciate Property

      2. Consider only incremental cash flows or those cash flows which result directly from the project.
        1. Special problems in determining incremental cash flows
          1. Sunk Costs
            • An outlay that has already occurred or committed
            • Not relevant in decision making
            • Example: $5,000 option to purchase land for $100,000. If another site is available for $98,000 you wouldn't consider the $5,000 sunk cost in your decision

          2. Opportunity Cost
            • The value of a good or service in its next best use
            • Example: Floor of a factory could be used to produce a new product or be rented out for $1,200 a month
            • All relevant opportunity costs must be included in the analysis

          3. Effects on other parts of the firm
            • Existing products: If a new product reduces sales of a current product line, must include in the analysis.
            • Example: A firm which manufactures VCRs might decide to make a video machine which uses DVD

    5. Changes in net working capital
      1. NWC = Current Assets - Current Liabilities
      2. With a new product
        1. May need more inventories and increase accounts receivables. These may need financing
        2. Financing needs will be reduced through increases in Accounts Payable and Accruals on the current liabilities side
        3. If Increase in Current Assets > Increase in Current Liabilities, financing will be needed above and beyond that required for fixed assets
        4. ⇒ An increase (↑) in NWC is a cash outflow (↓)

          ⇒ A decrease in (↓) NWC is a cash inflow (↑)

        5. An increase or decrease in net working capital is not taxable since it is only a buildup or reduction in current accounts

  2. Cash Flow estimation for expansion projects
    1. Step One: Consider the cash flow at the time the investment is made (t0)
      1. Purchase Price including transportation, installation, and modification costs. This is also known as the depreciable base.
      2. Any changes in NWC
      3. The net of these items equals the project's net investment outlay.

    2. Step Two: Consider the operating cash flows
    3. OCFt = (Rt - OCt - Dt)(1 - T) + Dt

      1. Simplified Straight-Line Depreciation
        1. Where: Depreciable Base = Cost of Asset plus installation, transportation, modification costs;
          N = the life of the project. If a tax life is given, use the tax life as N instead of the project life.

        2. Note that under simplified straight-line the salvage value is not subtracted from the cost of the asset
        3. Example: 7. Calculating Salvage Value [LO1] Consider an asset that costs $548,000 and is depreciated straight-line to zero over its eight-year tax life. The asset is to be used in a five-year project; at the end of the project, the asset can be sold for $105,000.

          The depreciation allowance for each year under simplified straight-line is $548,000 ÷ 8 = $68,500

      2. MACRS Depreciation
        1. With MACRS use Table 10.7 on page 309 of the text along with the depreciable base to determine the depreciation allowance for each year.
        2. Table 10.7

          MACRS Depreciation Allowances
          Property Class
          Year 3-Year 5-Year 7-Year 10-Year 15-Year 20-Year
          1 % % % % % %
          2                        
          3                        
          4                        
          5                    
          6                    
          7                
          8                
          9            
          10            
          11            
          12        
          13        
          14        
          15        
          16        
          17    
          18    
          19    
          20    
          21    

        3. Example: An asset used in a four-year project falls in the five-year MACRS class for tax purposes. The asset has an acquisition cost of $7,900,000 and will be sold for $1,400,000 at the end of the project. Find the depreciation allowances for the first three years of the project.

          Depreciation Allowance for Year 1 = $7,900,000 × 0.20 = $1,580,000
          Depreciation Allowance for Year 2 = $7,900,000 × 0.32 = $2,528,000
          Depreciation Allowance for Year 3 = $7,900,000 × 0.1920 = $1,516,800

    4. Step Three: Cash flows at the end of the project's life (Terminal Cash Flow)
      1. Salvage Value
        1. If the assets are sold for more than book value, taxes must be paid on the difference between the sale price and the book value.
        2. Tax on Sale of Equipment = (Book Value - Sale Price)×(Tax Rate)

          After-tax cash flow from sale of equipment = Sale Price + (Book Value - Sale Price) × (Tax Rate)

        3. If the assets are sold for less than book, there is a tax savings on the difference between the sale price and book value.
        4. Click here to access an interactive web page that can help you learn to calculate book value using MACRS Depreciation.
        5. Click here to access an interactive web page that can help you learn to calculate book value using simplified straight-line depreciation.

      2. Any change in NWC at time 0 (or any other time during the project’s life) will now be offset

    5. Step Four: Find NPV or IRR of Cash Flows
    6. Step Five: Make an accept or reject decision on project
    7. Cash Flow Estimation Example: and spreadsheet.

      Example: (Expansion Project) GODEF Recording Studios Inc. has the opportunity to invest in some new recording equipment. The equipment will enable them to reduce recording times and produce their final product more quickly. The equipment costs $, has an expected useful life of years, will be depreciated using the -Year MACRS schedule, and has an expected sale value of $ at the end of year . It is expected that net working capital will amount to percent of revenues in the following year. Additional operating revenues of $ will be generated in the first year of operation, but cash operating expenses will increase by $ per year. Revenues should grow at percent per year while operating expenses are expected to grow at percent per year. GODEF's cost of capital is % and its effective tax rate is %. Should the new equipment be purchased?

    -Year MACR Allowances   % % % % % % % % % %
                           
    Year 0 1 2 3 4 5 6 7 8 9 10
    Revenues   $ $ $ $ $ $ $ $ $ $
    Operating Costs  
    Depreciation  
    Earnings Before Taxes  
    Less Taxes  
    Earnings After Taxes  
    Add Back Depreciation  
    Operating Cash Flows  
    Initial Outlay -$                    
    Net Working Capital $ $ $ $ $ $ $ $ $ $  
    Δ in NWC  
    Sale of Equipment                     $
    Tax on Sale of Equipment                    
    Recover NWC                     $
    Net Cash Flows
                           
    Book Value  
    Net Present Value:                    
    Internal Rate of Return: 21.05%                    

    Here's this spreadsheet for this example.

  3. Replacement Decisions
    1. Net Initial Outlay at t = 0
      1. Payment for new equipment is a cash outflow
      2. Old equipment sales is an inflow (tax considerations)

    2. Operating Cash Flows
      1. New Inflows are based on old inflows
      2. (Δ Rt - Δ OCt)(1 - T) + TΔ Dt
      3. Where: Δ Rt = (Revenue New)t - (Revenue Old)t
                    Δ OCt = (Costs New)t - (Costs Old)t
                    Δ Dt = (Depreciation New)t - (Depreciation Old)t

      4. Salvage value of old machine
        1. The salvage value is a cash outflow at the end of the old project's life
        2. If you accept the project you will forgo the old machine's salvage value (opportunity cost)
    3. Example: The Lamp Post Company purchased a machine 2 years ago at a cost of $100,000. It had an expected life of 6 years at the time of purchase and an expected salvage value of $10,000 at the end of 6 years. It has a 5-Year Class Life, and is being depreciated using the straight line method.
    4. A new machine can be purchased for $150,000, including installation costs. Over the next four years, it will reduce cash operating expenses by $50,000 per year. Sales are not expected to change in years 1-4. Revenues for the new machine in years 5 and 6 will be $140,000 while operating costs will be $90.000. At the end of its useful life, the machine is estimated to be worthless. The new machine falls into the 5-year class, and will be depreciated using the straight line method.

      The old machine can be sold today for $65,000. The firm's tax rate is 30%. The appropriate discount rate is 15%. Should the machine be replaced?

      Net Initial Outlay:
      Price of New Machine ($150,000)  
      S.V. on old machine 65,000  
      Tax on old machine         1,500 = 0.30 × [65,000 - (100,000 -10,000-20,000)] = 0.30 × (-5,000)
      Initial Cash Flow ($83,500)  

      Operating Cash Flows:

      YEAR Deprec. Allowance
      (NEW)
      Deprec. Allowance
      (OLD)
      CHANGE
      Δ(D)

      TΔD

      1
      2
      3
      4
      5
      6
      15,000
      30,000
      30,000
      30,000
      30,000
      15,000
      20,000
      20,000
      20,000
      10,000
      -   
      -   
      -5,000
      10,000
      10,000
      20,000
      30,000
      15,000
      -1,500
      3,000
      3,000
      6,000
      9.000
      4,500

      Depreciable base (New) = $150,000

      Cash Flows:

        Years 1-4: (ΔR -Δ OC) = 50,000; (ΔR - ΔOC)(1 - T) = 35,000

        Years 5&6: (R-OC) = 140,000 - 90,000 = 50,000; 50,000(1-.3)=35,000

        YEAR 1 2 3 4 5 6
        Δ(R-OC)(1-T)
        + TΔD
        35,000
        -1,500
        35,000
        3,000
        35,000
        3,000
        35,000
        6,000
        35,000
        9,000
        35,000
        4,500
        Operating
        CFs
        33,500 38,000 38,000 41,000 44,000 39,500
        Nonoperating CFs     SV Old
        Tax
        -10,000
        3,000
           
        Net CFs 33,500 38,000 38,000 34,000 44,000 39,500

        NPV @ 15% = $57,741.84; Accept

        IRR = 37.43%; Accept

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