• Net Present Value (NPV)
  The net present value (NPV) of a purchase The present value of all future cash flows produced by an purchase Less the initial cost of the purchase:
  Xt= The savings each period n> = the number of time periods or life of the product rp= the required return on the purchase purchase.
  The NPV Decision rule
  In determining whether to accept or reject a particular purchaseed, the NPV decision rule is	NPV > 0 Accept purchase NPV < 0 Reject purchase NPV = 0 Indifferent

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• NPV Computations

  Purchase purchase Year 0 1 2 ... 25 Cash Flow -100 11 11 11 11

  Your product costs $100 to buy Annual savings are $11 per year The buyer wants a rate of return for this purchase rp =10% Should the buyer purchase? Applying the NPV rule here requires the calculation of the present value of the future cash flows followed by a comparison with the purchase cost of $100 million.

  Since NPV < 0 the buyer will this purchase.

  Your product costs 62,000 to buy Annual savings are 39,020 Buyer wants a 10% rate of return

  Year 0 1 2 3 4 5 6 7 Cash Flow -62,000 39,020 39,020 39,020 39,020 39,020 39,020 45,020

  Since NPV < 0 the buyer will this purchase.

  Four basic rules for calculating net cash flows:

  Use inflows and outflows of cash when they occur Use after-tax net cash flows Discount after-tax cash flows at the after-tax interest rate. Identify all real options and include in purchase evaluation

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• Comparing Two Purchases

  Your Product Competitor Inital Costs 3000 2000 Annual Savings 1000 700 Desired Rate 10% 10%

  Year 0 1 2 3 4 5 Your Product Cash Flow -3,000 1,000 1,000 1,000 1,000 1,000 Competitor Product Cash Flow -2,000 700 700 700 700 700

  Your product has the greater NVP

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  Alternative Calculations

  Internal Rate of Return (IRR)

  Payback Period

  Profitability Index

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  Internal Rate of Return (IRR)

  The rate of return which makes the present value of the purchase's cash flows to zero or the rate of return which makes the present value of inflows equal to present value of outflows. The internal rate of return (IRR) solves the following equation:

  IRR > rp Accept purchase IRR< rp Reject purchase IRR = rp Indifferent

  Buyer should make the purchase with highest IRR

  Example 1

  Your product costs $1000 Your product saves (or earns) the buyer $400 per year.

  Year 0 1 2 3 4 Cash Flow -1,000 400 400 400 400

  Is this a worthwhile purchase?

  We have to interpolate or use an iterative technique such as Excel's Solver to find the IRR The internal rate of return of this purchase turns out to be 21.86%.

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• Comparing purchases with Different Lives

  Machine NPV Machine Life A 2000 3 Years B 3000 5 Years

  Assume that Machine A will be replaced at the end of year 3 Thus its NPV is understated. Machines of type A are replaced on a 3-year cycle Machines of type B will be replaced on a 5-year cycle. Compare the annual equivalent cash flows of the two alternative purchases. Machine A has a NPV of $2,000, and the annual equivalent (AE) of:

  at the end of each of the 3 years.

  AE Annual Equivalent R Annual Equavelent i rate An Net Present Value of

  Assume machine is going to be used indefinitely Buyer will receive the annual equivalent cash flow of $804.25 indefinitely.

  In general, the annual equivalent cash flow is given by:

  The annual equivalent cash flow of machine B is thus given by:

  Machine NPV Machine Life annual equivalent cash flow A 2000 3 Years 804.27 B 3000 5 Years 791.40

  Buyer should accept purchase A.

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• Comparing Two Purchases With Different Lives

  Do not compare the NPVs directly. Convert these NPVs to annual equivalent cash flows (AE) where:

  Buyer should take the purchase with the highest AE. This applies to cases Considering one type of machine which is to be replaced indefinitely Alternative type of machine that is to be replaced indefinitely.

  Example: Replacing an existing machine with a new machine.

  New Machine Price $60,000 Installation Cost $2,000 Revenues generated $155,000 Annual expenses $100,000 Machine Life 7 Years Salvage Value $6000 Old Machine Book Value $40000 Remaining Life 5 years Immediate Resale Price 15000 Revenues Generated $150,000 Annual expenses $110000 Other Factors Finance Costs 12% Tax Bracket 34%

  Step 1 - Determine the Cash Flows

  Old Machine -- First compute the tax expense.

  Year   Revenues   Expenses   Depreciation   Taxable Income   Tax Paid   0                       1   150,000   -110,000   8,000   32,000   -10,880   2   150,000   -110,000   8,000   32,000   -10,880   3   150,000   -110,000   8,000   32,000   -10,880   4   150,000   -110,000   8,000   32,000   -10,880   5   150,000   -110,000   8,000   32,000   -10,880

  Now, compute net cash flow:

  Year Revenues Expenses Tax Paid Net Cash Flow 0 1 150,000 -110,000 10,880 29,120 2 150,000 -110,000 10,880 29,120 3 150,000 -110,000 10,880 29,120 4 150,000 -110,000 10,880 29,120 5 150,000 -110,000 10,880 29,120

  New Machine -- First, compute the tax expense

  Year Revenues Expenses Depreciation Taxable Income Tax Paid 0 -25,000b 8,500 1 155,000 -100,000 -8,000a 47,000 -15,980 2 155,000 -100,000 -8,000 47,000 -15,980 3 155,000 -100,000 -8,000 47,000 -15,980 4 155,000 -100,000 -8,000 47,000 -15,980 5 155,000 -100,000 -8,000 47,000 -15,980 6 155,000 -100,000 -8,000 47,000 -15,980 7 155,000 -100,000 -8,000 47,000 -15,980

  Notes:

  a. (60,000+2,000-6,000)/7 b. Book loss on sale of old machine (40,000-15,000) generates a tax credit of $8,500

  Now, compute the net cash flows:

  Year Revenues Expenses Salvage Cost Tax Paid Net Flows 0 15,000a -62,000 8,500 -38,500 1 155,000 -100,000 -15,980 39,020 2 155,000 -100,000 -15,980 39,020 3 155,000 -100,000 -15,980 39,020 4 155,000 -100,000 -15,980 39,020 5 155,000 -100,000 -15,980 39,020 6 155,000 -100,000 -15,980 39,020 7 155,000 -100,000 6,000b -15,980 45,020

  Notes:

  a. Old Machine b. New Machine

  Step 2 - Determine Net Present Value

  Old Machine

  New Machine

  Step 3 - Make the decision

  NPV new machine > NPVold machine Buyer should replace the machine