Final answer:
The Espresso Roast Corporation needs to calculate the present value of the costs of two machines using an 8% discount rate. Present value calculations for both the Quick-Roast machine and the Mellow-Roast machine factor in their respective initial costs and operating costs over their expected lifetimes. These calculations will allow the Corporation to compare which machine has a lower total cost when discounted back to present value terms.
Step-by-step explanation:
Present Value Calculation for Espresso Roast Corporation
The Espresso Roast Corporation must evaluate the present value of the costs associated with two different roaster and grinder machines. To calculate the present value (PV), we need to discount future cash flows, which include both the initial cost of the machine and the operating costs over its expected life.
The Quick-Roast machine has an initial cost of $50,000 and operating costs of $7,000 per year for 4 years. The Mellow-Roast Co. Machine costs $35,000 initially and has operating costs of $2,500 per year but only lasts for 2 years. Both scenarios should be evaluated using a discount rate of 8% to find the present value of each option.
For the Quick-Roast machine:
PV = $50,000 + ($7,000 / (1+0.08) + $7,000 / (1+0.08)² + $7,000 / (1+0.08)³ + $7,000 / (1+0.08)⁴)
This needs to be computed to find the total present value.
For the Mellow-Roast machine:
PV = $35,000 + ($2,500 / (1+0.08) + $2,500 / (1+0.08)²)
Again, this calculation will provide the total present value of the costs.
Comparing the present values of both options will help Espresso Roast Corporation decide which machine to purchase based on lower total costs.