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Takoda is the financial advisor for his company and is considering the purchase of excavation equipment which will cost $66,000.The purchase of this equipment is expected to save his company $6,828 at the end of every year for 12 years.At the end of the 12 years, he expects the excavation equipment to have a residual (inflow) value of $15,800. The company requires a 5.8% rate of return.Round PV to the nearest cent. Round NPV to the nearest whole number. 1) What is the Net Present Value (NPV) of this equipment investment?

Question

Takoda is the financial advisor for his company and is considering the purchase of excavation equipment which will cost 66,000.Thepurchaseofthisequipmentisexpectedtosavehiscompany66,000.The purchase of this equipment is expected to save his company 6,828 at the end of every year for 12 years.At the end of the 12 years, he expects the excavation equipment to have a residual (inflow) value of $15,800. The company requires a 5.8% rate of return.Round PV to the nearest cent. Round NPV to the nearest whole number. 1) What is the Net Present Value (NPV) of this equipment investment?

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Solution

To calculate the Net Present Value (NPV), we need to calculate the present value (PV) of the cash inflows and outflows.

Step 1: Calculate the present value of the annual savings.

The formula for the present value of an annuity is:

PV = Pmt * [(1 - (1 + r)^-n) / r]

where: Pmt = payment per period (annual savings) = $6,828 r = interest rate per period (rate of return) = 5.8% = 0.058 n = number of periods (years) = 12

PV = 6,828[(1(1+0.058)12)/0.058]PV=6,828 * [(1 - (1 + 0.058)^-12) / 0.058] PV = 6,828 * 8.472 PV = $57,819.22

Step 2: Calculate the present value of the residual value.

The formula for the present value of a single sum is:

PV = FV / (1 + r)^n

where: FV = future value (residual value) = $15,800

PV = 15,800/(1+0.058)12PV=15,800 / (1 + 0.058)^12 PV = 15,800 / 1.898 PV = $8,327.19

Step 3: Calculate the net present value.

The formula for the net present value is:

NPV = PV inflows - PV outflows

where: PV inflows = PV of annual savings + PV of residual value = 57,819.22+57,819.22 + 8,327.19 = 66,146.41PVoutflows=costofequipment=66,146.41 PV outflows = cost of equipment = 66,000

NPV = 66,146.4166,146.41 - 66,000 NPV = $146.41

So, the Net Present Value (NPV) of this equipment investment is approximately $146.

This problem has been solved

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