# NPV Definition

Hey guys, Please can you help me understand NPV, its strange because the other day i understood it but seem to have lost the thought process. For example A company is considering the purchase of a copier that costs \$5,000. Assume a cost of capital of 10 percent and the following cash flow schedule: Year 1: \$3,000 Year 2: \$2,000 Year 3: \$2,000 Right the NPV is \$883 which is the present value of the cash flows…correct? but what does it actually mean? that the investment is worth \$5,883 ? and how would you work out what the FV of the \$5,000 would be in 3 years time, what would pmt be? Thanks again.

To answer your question, you have to pay for the photocopier now, not in 3 years time. This would leave the the NPV equation as follows: NPV=PV(cash inflows)-PV(cash ouflows) PV(Cash inflows) = to the PV of the annual payments, which is \$5883 PV(Cash outflows) = to the PV of the photocopier, since you are paying for it straight away it is \$5000 therefore NPV = \$5883 - \$5000 = \$883 If you had bought the photocopier and did not have to pay for three years the PV of the photocopier would be (5000)/(1.1^3) =\$3756.57 This would make the investment that much more appealing

NPV measures how much wealth an investment adds. So investing \$5000 today nets a wealth increase of \$883 (the discounted value of future net cashflows).

Thanks Jaco, One last issue… : ( Determining the weighted cost of cap A firm is considering a \$200,000 project that will last 3 years and has the following financial data: Annual after-tax cash flows are expected to be \$90,000. Target debt/equity ratio is 0.4. Cost of equity is 14%. Cost of debt is 7%. Tax rate is 34%. The debt to equity is .40, so i’m i right in saying that its 2/3 = 2/5(7)(.66)+3/5(14) 1.85+8.40 = 10.25% wacc SChweser used the following: First, calculate the weights for debt and equity wd + we = 1 we = 1 − wd wd / we = 0.40 wd = 0.40 × (1 − wd) wd = 0.40 − 0.40wd 1.40wd = 0.40 wd = 0.286, we = 0.714 So is my way incorrect?

For this one you have to start out by calculating the WACC WACC = (Equity/Value)xRe + (Debt/Value)xRdx(1-tax rate) =(2.5/3.5)x0.14+(1/3.5)x0.07x(1-0.34) =0.10+0.0132 =0.1132 Now that you have the WACC you can find the PV of a 3yr annuity of \$90,000 PV = \$218716.02 therefore NPV = \$18716.02 therefore the investment should be considered if it meets strategic objectives and there is no other mutually exclusive projects with a higher NPV

Cheers Mate