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Estimating NPV: Special Applications

Estimating NPV: Special Applications. Inflation. Unequal Lives. Calculating Bid Prices. Nominal If a CF is received in year n, nominal CF n is measured in terms of year n prices, P n (i.e., we record the number of $ actually received at that time. Real

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Estimating NPV: Special Applications

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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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