In: Finance
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 $24,581.00 per year for 8 years and costs $104,374.00. The UGA-3000 produces incremental cash flows of $28,483.00 per year for 9 years and cost $126,299.00. The firm’s WACC is 7.73%. What is the equivalent annual annuity of the UGA-3000?
Equivalent Annual Annuity (EAA) of the UGA-3000
Year |
Annual Cash Inflow ($) |
Present Value factor at 7.73% |
Present Value of Annual Cash Inflow ($) |
1 |
28,483 |
0.928247 |
26,439.25 |
2 |
28,483 |
0.861642 |
24,542.14 |
3 |
28,483 |
0.799816 |
22,781.16 |
4 |
28,483 |
0.742426 |
21,146.53 |
5 |
28,483 |
0.689155 |
19,629.19 |
6 |
28,483 |
0.639705 |
18,220.73 |
7 |
28,483 |
0.593804 |
16,913.33 |
8 |
28,483 |
0.551197 |
15,699.74 |
9 |
28,483 |
0.511647 |
14,573.23 |
TOTAL |
6.317638 |
1,79,945.29 |
|
Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment
= $1,79,945.29 - $126,299
= $53,646.29
Equivalent Annual Annuity (EAA) = Net Present Value / [PVIFA 7.73%, 9 Years]
= $53,646.29 / 6.317638
= $8,491.51 per year
“Hence, the Equivalent Annual Annuity (EAA) of the UGA-3000 would be $8,491.51 per year”
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.