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 $25,234.00 per year for 8 years and costs $104,851.00. The UGA-3000 produces incremental cash flows of $27,583.00 per year for 9 years and cost $125,853.00. The firm’s WACC is 9.27%. What is the equivalent annual annuity of the GSU-3300? Assume that there are no taxes.

Answer format: Currency: Round to: 2 decimal places.

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 $25,989.00 per year for 8 years and costs $99,366.00. The UGA-3000 produces incremental cash flows of $29,404.00 per year for 9 years and cost $125,776.00. The firm’s WACC is 8.41%. What is the equivalent annual annuity of the UGA-3000? Assume that there are no taxes.

Answer format: Currency: Round to: 2 decimal places.

Could really use the help!! Please show all steps (not excel) for better understanding :D Thank You.

Answer 1

(1)-The Equivalent Annual Annuity (EAA) of the GSU-3300

Year	Annual Cash Inflow ($)	Present Value factor at 9.27%	Present Value of Annual Cash Inflow ($)
1	25,234	0.915164	23,093.26
2	25,234	0.837526	21,134.12
3	25,234	0.766474	19,341.19
4	25,234	0.701449	17,700.37
5	25,234	0.641941	16,198.75
6	25,234	0.587482	14,824.51
7	25,234	0.537642	13,566.86
8	25,234	0.492031	12,415.91
TOTAL		5.479709	1,38,274.97

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

= $138,274.97 - $104,851

= $33,423.97

Therefore, the Equivalent Annual Annuity (EAA) of the GSU-3300 = Net Present Value / [PVIFA 9.27%, 8 Years]

= $33,423.97 / 5.479709

= $6,099.59

(2)-The Equivalent Annual Annuity (EAA) of the UGA-3000

Year	Annual Cash Inflow ($)	Present Value factor at 8.41%	Present Value of Annual Cash Inflow ($)
1	29,404	0.922424	27,122.96
2	29,404	0.850866	25,018.87
3	29,404	0.784860	23,078.01
4	29,404	0.723973	21,287.71
5	29,404	0.667811	19,636.30
6	29,404	0.616005	18,113.00
7	29,404	0.568217	16,707.87
8	29,404	0.524138	15,411.74
9	29,404	0.483477	14,216.16
TOTAL		6.141771	1,80,592.62

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

= $180,592.62 - $125,776

= $54,816.62

Therefore, the Equivalent Annual Annuity (EAA) of the UGA-3000 = Net Present Value / [PVIFA 8.41%, 9 Years]

= $54,816.62 / 4.141771

= $8,925.22

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.