Estimating NPV: Special Applications InflationUnequal Lives Calculating Bid Prices

Nominal vs. Real Cash Flows 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 Real CF r are measured in terms of prices, P 0 prevailing at some reference date, 0. If h is the annual inflation rate: P n = P 0 (1 + h) n CF r = CF n /(1 + h) n

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

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)

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 A5 Yrs Machine B 3 Yrs

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

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

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