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 $24,841.00 per year for 8 years and costs $101,854.00. The UGA-3000 produces incremental cash flows of $28,223.00 per year for 9 years and cost $123,371.00. The firm's WACC is 9.15%. What is the equivalent annual annuity of the GSU-3300? unanswered not submitted Submit Answer format: Currency: Round to: 2 decimal places.

Answer 1

Given Details in the above question -

1. GSU-3300 machine - Incremental cash flow per year of $24841.00 for 8 yrs, cost of investment $101854.00.

2. UGA-3000 machine - Incremental cash flow per year of $28223.00 for 9 yrs, cost of investment $123371.00.

3. WACC @9.15%.

Firstly we will have to calculate NPV ( Net Present Value) the future cash flows for each machine by discounting the same @ 9.15% (WACC).

So, NPV for GSU-3300 will be calculated as per the formula -

GSU-3300 NPV = (Cash flow)/(1+ r)n, where cash flow is $24841.00 per year for 8 yrs, r is the discount rate @9.15% and cash flow for the period 8 yrs.

ie. NPV = 24841/(1+.0915)^1+24841/(1+.0915)^2+24841/(1+.0915)^3+24841/(1+.0915)^4+24841/(1+.0915)^5+24841/(1+.0915)^6+24841/(1+.0915)^7+24841/(1+.0915)^8.

so, NPV = $136727.00. Out flow of the machine is $101854.00 (A)

So, NPV for UGA-3000 will be calculated as per the formula -

UGA-3000 NPV = (Cash flow)/(1+ r)n, where cash flow is $28223.00 per year for 9 yrs, r is the discount rate @9.15% and cash flow for the period 9 yrs.

ie. NPV = 28223/(1+.0915)^1+28223/(1+.0915)^2+28223/(1+.0915)^3+28223/(1+.0915)^4+28223/(1+.0915)^5+28223/(1+.0915)^6+28223/(1+.0915)^7+28223/(1+.0915)^8+28223/(1+.0915)^9

so, NPV = $168177.00. Out flow of the machine is $123371.00 (B)

Now, we can calculate the Equivalent Annual Annuity (EAA) for both the machine.  

EAA for GSU-3300 = (r * NPV)/ (1- (1+r)-n)

EAA for GSU-3300 = (0.0915 * 136727)/(1-(1+0.0915)-8)

= 12510.52/(1-0.496)

= $24822.00

EAA for UGA-3000 = (r * NPV)/ (1- (1+r)-n)

EAA for UGA-3000 = (0.0915 * 168177)/(1-(1+0.0915)-9)

= 15388.20/(1-0.455)

= $28235.00

For More and better understanding we have calculated the EAA for both the machines.