Question

A firm is must choose to buy the GSU-3300 or the UGA-3000. Both machines make the firm’s production process more efficient which in turn increases incremental cash flows. The GSU-3300 produces incremental cash flows of $25,703.00 per year for 8 years and costs $103,084.00. The UGA-3000 produces incremental cash flows of $28,092.00 per year for 9 years and cost $124,042.00. The firm’s WACC is 7.28%. What is the equivalent annual annuity of the UGA-3000? Assume that there are no taxes.

Answer 1

Equivalent Annual Annuity (EAA) of UGA-3000

Net Present Value (NPV)

Year	Annual cash flows ($)	Present Value Factor (PVF) at 7.28%	Present Value of annual cash flows ($) [Annual cash flow x PVF]
1	28,092	0.932140	26,185.68
2	28,092	0.868885	24,408.73
3	28,092	0.809923	22,752.36
4	28,092	0.754962	21,208.39
5	28,092	0.703730	19,769.19
6	28,092	0.655975	18,427.65
7	28,092	0.611461	17,177.16
8	28,092	0.569967	16,011.52
9	28,092	0.531289	14,924.98
TOTAL		6.438333	180,865.65

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $180,865.65 - $124,042

= $56,823.65

Equivalent Annual Annuity (EAA) of UGA-3000

Equivalent Annual Annuity (EAA) of UGA-3000 = Net Present Value / [PVIFA 7.28%, 9 Years]

= $56,823.65 / 6.438333

= $8,825.83

“Therefore, the Equivalent Annual Annuity (EAA) of UGA-3000 will be $8,825.83”

NOTE    

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.