A township wants to buy a new piece of equipment that will reduce costs by...

 What Are We Solving For?

We are calculating thepresent value (PV)of $20,550 to be received at theend of year 2using a discount rate of10%.

The formula for present value is: PV=FV(1+r)nPV = \frac{FV}{(1 + r)^n}PV=(1+r)nFV​ Where:

FVFVFV = Future Value = $20,550

rrr = Discount Rate = 10% or 0.10

nnn = Time Period = 2 years

 Calculation:

PV=20,550(1+0.10)2PV = \frac{20,550}{(1 + 0.10)^2}PV=(1+0.10)220,550​ PV=20,550(1.10)2PV = \frac{20,550}{(1.10)^2}PV=(1.10)220,550​ PV=20,5501.21PV = \frac{20,550}{1.21}PV=1.2120,550​ PV≈16,983PV ≈ 16,983PV≈16,983

 Why Other Options Are Incorrect:

A. $16,440:Results from incorrect discounting for one year instead of two.

C. $18,495:Results from applying a lower discount rate or an incorrect formula.

D. $20,550:This is the future value, not the present value.

 References and Documents:

GAO Financial Analysis Guide:Explains present value calculations for investment decision-making.

AICPA Present Value Guidelines:Provides step-by-step guidance on time value of money calculations.