Question

5. A $10,000 investment can be made today that will produce savings of $2,000 annually for the next 7 years. There is no salvage value involved. Calculate the present worth of the investment at MARR = 10%. Show that the same PW results when the constant-dollar savings inflate at 8% annually. Apply the combined interest-inflation rate to discount the actual-dollar cash flow

Answer 1

Note - MARR means minimum acceptable rate of returns.

Present worth of the investment = Annuity * Present value annuity factor ( MARR, number of years )

                                              = 2,000 * PVAF ( 10%, 7 )

                                              = 2,000 * [ 1/1.10 + 1/1.10² + ..... + 1/1.10⁷ ]

                                              = 2,000 * 4.8684

                                              = $ 9,736.84 Answer

With inflation

Sum of Geometric progression -

where a = first term

         r = common ratio

Present worth of the investment = [ { 2,000 * ( 1.08 / 1.18 ) } + { 2,000 * ( 1.08 / 1.18 )² + ..... + { 2,000 * ( 1.08 / 1.18 )⁷ } ]

                                              = { 2,000 * ( 1.08 / 1.18 ) } [ { 1 - ( 1.08 / 1.18 )⁷ } / { 1 - ( 1.08 / 1.18 ) } ]

                                              = 9979.17 Answer