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?

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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 1 month ago

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