 Net Present Value(NPV) NPV = \$ € £ ¥ CHF RUB ₩ SAR Bs Discount rate (annually): Initial invest - Year 0 : Year Cash-In Cash-Out/ Net Cash Flow Discounted Cash Flow Investment 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Total: "0" "0" "0" "0"
 References Net Present Value (NPV) What is PV (present value)? To better understand NPV (Net Present Value), let's first look at what is present value (PV). PV is the current worth of a future amount of money. "A dollar today is worth more than a dollar tomorrow", this is referred to as the time value of money. A given amount of money today has different (usually higher or equal) buying power than the same amount of money in the future. In finance and investment, PV is used to evaluate the future cash flows. PV formula PV = Ct (1 + i)ᵗ What is discount rate? Discount rate is a key factor to calculate present value of future cash flows properly. The higher the discount rate, the lower the present value of the future cash flows. Typically 7% - 10% is a good range for most projects in today’s market conditions. What is Net Present Value (NPV) and how to calculate NPV? NPV is the sum of the present value (PV) of the future individual cash flows (including in flows and out flows) minus initial investment. NPV formula: N NPV = Ʃ Ct - Co (1+i)ᵗ t=1 Let's see the example: Let’s use NPV to evaluate a 5-years project: Initial investment at year 0 is \$ 100,000; discount rate is 7% annually. Annually profit from the end of the first year to the end of the fifth year is: ·        \$20,000 ·        \$30,000 ·        \$30,000 ·        \$30,000 ·        \$25,000 At the end of third year, there is \$5,000 maintenance expense. Then the PV of each year is: ·        Year 0: -100,000 ·        Year 1: 20,000/(1+0.07) = 18,691.59 ·        Year 2: 30,000/(1+0.07)² = 26,203.16 ·        Year 3: 30,000/(1+0.07)³ – 5,000/(1+0.07)³ = 20,407.45 ·        Year 4: 30,000/(1+0.07)⁴ = 22,886.86 ·        Year 5: 25,000/(1+0.07)⁵ = 17,824.65 We get NPV by adding all PVs above from year 0 to year 5. NPV = 6,013.71 NPV tells how much value an investment or project will bring in. If NPV > 0, the investment may be accepted. If NPV < 0, the investment should be rejected. Using NPV to determine an investment is certainly not enough. IRR (Internal Rate of Return) will tell you other variable over project economics. The rate of return so should be used to compare different investments.