Question 9 You own a manufacturing business and are thinking

Question 9 You own a manufacturing business and are thinking about purchasing a labor-saving device at a cost of $225,000.00. The device will last 20 years and save the company $1,800.00 per month in labor costs. You need to earn 9% compounded monthly on your money, what is the present value of the savings the device will deliver?

Solution

Monthly Cost Saving = $1,800
Annual Interest Rate = 9%
Monthly Interest Rate = 9%/12 = 0.75%
Life of device = 20 years or 240 months

Present Value of Cost Saving = $1,800/1.0075 + $1,800/1.0075^2 + $1,800/1.0075^3 + $1,800/1.0075^4 + .... + $1,800/1.0075^240
Present Value of Cost Saving = $1,800 * (1 - (1/1.0075)^240) / 0.0075
Present Value of Cost Saving = $1,800 * 111.145
Present Value of Cost Saving = $200,061

So, present value of the savings the device will deliver is $200,061