Vandalay Industries is considering the purchase of a new machine for the production of latex. Machine A costs $2,190,000 and will last for 7 years. Variable costs are 38 percent of sales, and fixed costs are $122,000 per year. Machine B costs $4,530,000 and will last for 11 years. Variable costs for this machine are 27 percent of sales and fixed costs are $73,000 per year. The sales for each machine will be $9.06 million per year. The required return is 10 percent and the tax rate is 35 percent. Both machines will be depreciated on a straight-line basis. If the company plans to replace the machine when it wears out on a perpetual basis, what is the EAC for machine A? If the company plans to replace the machine when it wears out on a perpetual basis, what is the EAC for machine B?

Question

Vandalay Industries is considering the purchase of a new machine for the production of latex. Machine A costs $2,190,000 and will last for 7 years. Variable costs are 38 percent of sales, and fixed costs are $122,000 per year. Machine B costs $4,530,000 and will last for 11 years. Variable costs for this machine are 27 percent of sales and fixed costs are $73,000 per year. The sales for each machine will be $9.06 million per year. The required return is 10 percent and the tax rate is 35 percent. Both machines will be depreciated on a straight-line basis. If the company plans to replace the machine when it wears out on a perpetual basis, what is the EAC for machine A? If the company plans to replace the machine when it wears out on a perpetual basis, what is the EAC for machine B?

Answer 1

To find the EAC (Equivalent Annual Cost) for each machine, we need to calculate the annual cash flows for each machine and then determine the present value of those cash flows. The EAC is the level annual cost that would provide the same net present value as the original investment.

To calculate the annual cash flows, we need to consider the fixed costs, variable costs, and depreciation expense. The annual cash flows can be calculated using the following formula:

Annual Cash Flow = Sales Revenue - Variable Costs - Fixed Costs - Depreciation

Let's calculate the annual cash flows for each machine:

For Machine A:
Sales Revenue = $9.06 million
Variable Costs = 38% * $9.06 million
Fixed Costs = $122,000
Depreciation = $2,190,000 / 7 years

Annual Cash Flow = $9.06 million - (38% * $9.06 million) - $122,000 - ($2,190,000 / 7 years)

For Machine B:
Sales Revenue = $9.06 million
Variable Costs = 27% * $9.06 million
Fixed Costs = $73,000
Depreciation = $4,530,000 / 11 years

Annual Cash Flow = $9.06 million - (27% * $9.06 million) - $73,000 - ($4,530,000 / 11 years)

Now that we have the annual cash flows, we need to calculate the Present Value (PV) of each machine. The formula to calculate the PV is as follows:

PV = Annual Cash Flow / (1 + r)^n

Where:
Annual Cash Flow is the annual cash flow calculated earlier
r is the required return rate (in decimal form)
n is the number of years

Let's calculate the PV for each machine assuming a required return rate of 10%:

For Machine A:
PV = Annual Cash Flow / (1 + 0.10)^7

For Machine B:
PV = Annual Cash Flow / (1 + 0.10)^11

Finally, to calculate the EAC for each machine, we can use the following formula:

EAC = PV / ((1 - (1 / (1 + r)^n)) / r)

Let's calculate the EAC for each machine:

For Machine A:
EAC = PV / ((1 - (1 / (1 + 0.10)^7)) / 0.10)

For Machine B:
EAC = PV / ((1 - (1 / (1 + 0.10)^11)) / 0.10)

By plugging in the calculated values, we can find the EAC for each machine.