Question

Raindrip Corp. can purchase a new machine for​ $1,875,000 that will provide an annual net cash flow of​ $650,000 per year for five years. The machine will be sold for​ $120,000 after taxes at the end of year five. What is the net present value of the machine if the required rate of return is​ 13.5%.

Answer 1

The net present value of the machine is $468,719.

Step-by-step explanation:

To calculate the net present value (NPV) of the machine, we need to find the present value of the cash flows it will generate. The cash flows include the annual net cash flow of $650,000 for five years and the sale price of $120,000 after taxes at the end of year five. First, we calculate the present value of the annual cash flow using the formula: PV = CF / (1 + r)^n, where CF is the cash flow, r is the required rate of return, and n is the number of years. So, the present value of the annual cash flow is $650,000 / (1 + 0.135)^1 + $650,000 / (1 + 0.135)^2 + $650,000 / (1 + 0.135)^3 + $650,000 / (1 + 0.135)^4 + $650,000 / (1 + 0.135)^5 = $2,281,339.

Next, we calculate the present value of the sale price of the machine at the end of year five using the same formula: PV = Sale Price / (1 + r)^n. So, the present value of the sale price is $120,000 / (1 + 0.135)^5 = $62,380.

Finally, we calculate the net present value by subtracting the initial cost of the machine from the sum of the present values: NPV = Sum of Present Values - Initial Cost. So, the net present value is $2,281,339 + $62,380 - $1,875,000 = $468,719. Therefore, the net present value of the machine is $468,719.

Answer 2

The net present value of the machine if the required rate of return is​ 13.5% is $447,292

Step-by-step explanation:

Year Cash Flows PV Factor at 13.5% Net Present Value

0 ($1,875,000) 1 ($1,875,000)

1 $650,000 0.881057269 $572,687.22

2 $650,000 0.776261911 $504,570.24

3 $650,000 0.683931199 $444,555.28

4 $650,000 0.602582554 $391,678.66

5 $650,000 0.530909739 $345,091.33

5 $120,000 0.530909739 $63,709.17

Net Present Value $447,292

therefore, The net present value of the machine if the required rate of return is​ 13.5% is $447,292