Mathematics of Money

Your company wants to get a loan to finance the purchase of earth-moving equipment. You have provided by your bank with a loan plan and you consider purchasing Machine A or Machine B. Consider the following to answer this problem:

• Machine A costs $525,000 to buy and can produce 25 yd3 per hour.
• Machine B costs $625,000 to buy and can produce 35 yd3 per hour.

Assume equal operating and maintenance costs and that the salvage value of both machines (A & B) is zero at the end of their use (15 years).

• The machine will be operated for 2,000 hours per year and the company has contracts for the next 15 years to move earth for $1 per yd3.

Which investment alternative (Machine A or Machine B) should be selected assuming 5% interest rate?

Problem

DATA

The data shows the costs and production of both machines A and B. The analysis is directed on calculating suitable machines for the company. Machine A costs 525,000 while it produces 25 yd³per hour. On the other hand, Machine B costs more at $625,000 while its produce is at 35 yd³per hour.

The other data is shown in the table below regarding the life of machines, interest rate, machine hours, labor costs, labor hours, salvage value and maintenance costs.

Machine A:

The equation that would be used for calculation of the investment value is;
Investment=Initial Cost+Interest Amount+Maintenance Cost
But first we need to calculate the interest amount.
Interest on Initial Cost=Prt
Interest on Initial cost=525,000x 5%x15
Interest on Initial Cost=393750

Now the investment is calculated as.
Let Maintenance cost = X
Using the above equation.
Investment = 525000 + 393750 + X
Investment = 918750 + x
Production Calculation:
Production: 15 x 2000 x 25 x 1
Production = 750000
Loss = 918750-750000+x
Loss: 168750+ x

For the Machine B:

The equation that would be used for calculation of the investment value is;
Investment=Initial Cost+Interest Amount+Maintenance Cost
But first we need to calculate the interest amount.
Interest on Initial Cost=Prt
Interest on Initial cost=625,000x 5%x15
Interest on Initial Cost=468750

Now the investment is calculated as.
Let Maintenance cost = X
Using the above equation.
Investment = 625000 + 468750 + X
Investment = 1093750 + x
Production Calculation:
Production: 15 x 2000 x 35 x 1
Production = 1050000
Loss = 1093750-1050000+x
Loss: 43750+ x
The loss on Machine B is lower, which makes it a better investment.