An industrial firm needs a 40000 piece of machinery that has

An industrial firm needs a $40,000 piece of machinery that has a useful life of 5 years. Knowing that the machine will have to be replaced every 5 years, the firm has the option of leasing a machine for $10,000 per year, or borrowing $40,000 to buy the machine. The 1st National Bank can provide a $40,000 loan at 7.8% compounded annually over 5 years. Over the 5-year life of the machine: is it cheaper to lease, or to borrow the money and buy the machine? Show all work to support your choice: a simple “one or the other” answer, even if it’s correct, will result in zero credit!

Solution

To compare the two options, first we would find the amount accumlated on loan with interest on $40,000 after

5 years.

Amount = Principal( 1 +rate/100)^n

7.8% compounded annually over 5 years

rate = 0.078 ; n = 5

So,Amount = 40,000( 1 +0.078 )^5 = $ 58230.94

So, this the amount he would pay to the bank

If he leases the macine for 5yrs , he would pay $10,000 x 5 = $ 50,000

Its better to lease the equipment than to purchase it on loan