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Understanding NPV and Special Applications in Finance

Learn to estimate NPV effectively in light of inflation, unequal lives, and bid prices. Understand the difference between nominal and real cash flows and explore equipment options with unequal lives in finance.

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Understanding NPV and Special Applications in Finance

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  1. Estimating NPV: Special Applications Inflation Unequal Lives Calculating Bid Prices

  2. Nominal If a CF is received in year n, nominal CFn is measured in terms of year n prices, Pn (i.e., we record the number of $ actually received at that time Real Real CFr are measured in terms of prices, P0 prevailing at some reference date, 0. If h is the annual inflation rate: Pn = P0(1 + h)n CFr = CFn /(1 + h)n Nominal vs. Real Cash Flows

  3. The Fisher Effect (see p. 155, Eq. 5.2) • R is the nominal interest rate • r is the real interest rate • Investors care about real rates, so they demand that nominal rates compensate them for anticipated inflation

  4. NPV in the face of Inflation Discount real cash flows using a real discount rate or, equivalently, discount nominal cash flows at a nominal rate (but don’t mix)

  5. Equipment Options with Unequal Lives • Consider 2 machines that do the same work • If both have the same useful life we can compare the present values of the associated costs • If the lives are unequal, this won’t work, because the cost and benefit streams aren’t comparable Machine A 5 Yrs Machine B 3 Yrs

  6. Equivalent Annual Cost (EAC) • When equipment lives are unequal, we need to consider the chain of future replacements • EAC technique • First calculate PV of all associated “costs” (anything besides the benefit of the equipment’s work) • Then, find the payment on an annuity, having the same life as the equipment in question, and also the same PV • Comparing EAC for two machines is like considering a continuous stream of replacements

  7. EAC as a Rental Rate • If you bought a machine, had to incur associated costs and depreciation tax shields, but rented it out to someone, you would be willing to accept the EAC as the annual rental payment • This would allow you to just earn the cost of capital on your investment, so it is a competitive rental rate

  8. Happy Thanksgiving

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