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? Cash InflowsCash Inflows Payments (Savings) Residual (Inflow)P/Y = C/Y = N = I/Y = % %PV = $ $PMT = $ $FV = $ $ (If the NPV is negative, enter it as a negative number. If the NPV is zero, enter 0.)NPV = $ (round to the nearest whole number)2) Should this equipment purchase be made according to the NPV criterion?YesNo
Question
Takoda is the financial advisor for his company and is considering the purchase of excavation equipment which will cost 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 (round to the nearest whole number)2) Should this equipment purchase be made according to the NPV criterion?YesNo
Solution
The Net Present Value (NPV) is a calculation that forecasts the profitability of a given investment. It does this by subtracting the initial cost of the investment from the present value of its future cash inflows, discounted at a specified rate of return.
Here's how to calculate the NPV for the excavation equipment:
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First, calculate the present value (PV) of the annual savings. The formula for PV is:
PV = PMT * [(1 - (1 + r)^-n) / r]
Where: PMT = annual savings = $6,828 r = rate of return = 5.8% = 0.058 n = number of years = 12
Plugging in these values, we get:
PV = 52,926.67 (rounded to the nearest cent)
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Next, calculate the present value of the residual inflow. This is done by discounting the residual value back to the present using the formula:
PV_residual = FV / (1 + r)^n
Where: FV = future value = $15,800
Plugging in these values, we get:
PV_residual = 7,879.68 (rounded to the nearest cent)
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Now, add the two present values together to get the total present value of the cash inflows:
PV_total = PV + PV_residual = 7,879.68 = $60,806.35
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Finally, subtract the cost of the equipment from the total present value to get the NPV:
NPV = PV_total - cost = 66,000 = -$5,193.65
Rounded to the nearest whole number, the NPV is -$5,194.
So, the NPV of the equipment investment is -$5,194.
According to the NPV criterion, an investment should be made if the NPV is positive, and not made if the NPV is negative. Since the NPV of this equipment investment is negative, the equipment purchase should not be made.
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