A firm needs new copy machine. You can purchase a new one for $30000, or you...

A firm needs new copy machine. You can purchase a new one for $30000, or you can lease one for three years for a monthly lease payment of $800 (paid at the end of each month). You can borrow money at 5% APR with quarterly compounding. Do you prefer to lease or buy the machine?

Expert Solution

To decide whether to purchase or lease, we need to compare the monthly lease payment with monthly loan payment for purchasing the machine;over three years. First we need to find monthly rate for borrowing.

Purchase price of machine = Loan = $30000,

Monthly lease payment = $800, , Interest rate = APR = 8% with quarterly compounding

Quarterly rate = APR / no of quarters in a year = 8%/4 = 2% per quarter

Effective annual rate = [1+quarterly rate]^{no of quarters in
a year} - 1 = [1+2%]⁴ - 1 = (1.02)⁴ - 1 = 1.08243216 - 1 = 0.08243216 = 8.243216%

Monthly rate = [1+Effective annual rate]^1/12 - 1 = [1+ 8.243216%]^1/12 - 1 = [1.08243216]^1/12 - 1 = 1.00662270 - 1 = 0.00662270 = 0.662270%

Now we can find the monthly loan payment for purchasing the machine using PMT function in excel

Formula to be used in excel: =PMT(rate,nper,-pv)

Using PMT function in excel, we get Monthly payment of loan of purchasing = 939.36

Since monthly payment of loan for purchasing is greater than monthly lease payment, hence one should lease the machine.

Answer: Lease the machine

jeff jeffy answered 8 months ago

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