(Break-even analysis) Acquiring more energy-efficient equipment would cost $80,000 now and yield savings of $20,000 in energy costs every year for the next 8 years, after which its salvage value will be 0. The discount rate is 8%.
(1) Based on a before-tax analysis, what is the economic break-even point for the yearly savings?
(2) You now realize that you forgot to consider something in part (1.1). If you acquire new energy-efficient equipment, you can dispose of some of your old equipment for a salvage value of $12,000. Taking this into consideration, redo part (1).
To calculate the economic break-even point for the yearly savings in a before-tax analysis, we need to find the time period at which the present value of the savings equals the initial cost of acquiring the equipment.
(1) The steps to calculate the economic break-even point are as follows:
Step 1: Calculate the present value of the annual savings for the given time period using the discount rate.
PV = A x (1 - (1 + r)^-n) / r
Where PV is the present value, A is the annual savings, r is the discount rate, and n is the number of years.
PV = $20,000 x (1 - (1 + 0.08)^-8) / 0.08
PV = $20,000 x (1 - 0.5897) / 0.08
PV = $7,614.10
Step 2: Compare the present value of the savings to the initial cost of acquiring the equipment ($80,000) to determine the break-even point.
$80,000 - $7,614.10 = $72,385.90
Therefore, the economic break-even point for the yearly savings, based on a before-tax analysis, is approximately $72,385.90.
(2) If we consider the salvage value of the old equipment ($12,000) in the analysis, the steps to calculate the economic break-even point change slightly.
Step 1: Calculate the net initial cost by subtracting the salvage value of the old equipment from the cost of acquiring the new equipment.
Net Initial Cost = Initial Cost - Salvage Value
Net Initial Cost = $80,000 - $12,000
Net Initial Cost = $68,000
Step 2: Calculate the present value of the annual savings as before.
PV = A x (1 - (1 + r)^-n) / r
PV = $20,000 x (1 - (1 + 0.08)^-8) / 0.08
PV = $20,000 x (1 - 0.5897) / 0.08
PV = $7,614.10
Step 3: Compare the present value of the savings to the net initial cost to determine the break-even point.
$68,000 - $7,614.10 = $60,385.90
Therefore, after considering the salvage value of the old equipment, the economic break-even point for the yearly savings is approximately $60,385.90.