2. Present Value with Periodic Rates . Let’s follow up with Sam Hinds, the denti

Question

2. Present Value with Periodic Rates. Let’s follow up with Sam Hinds, the dentist from Chapter 4, and his remodeling project (Problem 12). The cost of the equipment for the project is $18,000, and the purchase will be financed with a 7.5% loan over six years. Originally, the loan called for annual payments. Redo the payments based on quarterly payments (four per year) and monthly payments (twelve per year). Compare the annual cash outflow of the two payments. Why does the monthly payment plan have less total cash outflow each year?

Explanation / Answer

Quarterly rate = 7.5%/4 = 1.875%

N = 6*4 = 24

PV = -18,000

FV = 0

Payments = 924.94

Annual Payment = 938.26*4 = 3753.04

For monthly cash flows:

N = 6*12 = 72

Monthly rate = 7.5%/12 = 0.625%

PV = -18000

FV = 0

Payments = 311.22

Annual payment = 311.22 * 12 =3734.64

Monthly payments on an annual basis are less since these payents are received earlier which is associated with some time value

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