Your firm has to replace one of its fender-bender machine. One of your financial

Question

Your firm has to replace one of its fender-bender machine. One of your financial wizards has determined that the appropriate discount rate for the machine cash flows is 10%. your firm has two alternatives:

A: Fender-bender machine A costs $400,000 and produces annual net cash flows of $200,000 at the end of each year of its six years of life.

B: Fender-bender machine B costs $200,000 but has only a two-year life. However, it produces a $300,000 annual cash flow at the end of each of these two years.

Calculate the equivalent Annual Annuity (also, known as "the Equivalent Annual Annuity Cash Flow"; EAA) (Hint: You have to calcualte NPV first. Please refer to the lecture notes)

Please show all formulas.

Year Machine A Machine B 0 -400 -200 1 200 300 2 200 300 3 200 4 200 5 200 6 200

Explanation / Answer

A NPV

A EAA:

B NPV:

B:EAA

Discount rate =   10.000% Year 0 1 2 3 4 5 6 Cash flow stream -400 200 200 200 200 200 200 Discounting factor 1 1.1 1.21 1.331 1.4641 1.61051 1.771561 Discounted cash flows project -400 181.8182 165.2893 150.263 136.6027 124.1843 112.8948 Sum of discounted future cashflows = 471.0521 =NPV Discounting factor = (1 + Required rate)^(CORRESPONDING PERIOD IN YEARS) Discounted Cashflow= Cash flow stream/discounting factor

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