今日分享
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如果你總和別人比，你會過得很苦。如果你不斷和現在的自己比，那你會變得更好!
If you continuously compete with others, you become bitter.
If you continuously compete with yourself,you become better.淨現值
Net present Value
在許多分析現金流的場合下，淨現值NPV與內部回報率IRR是兩個反覆被使用的概念，其中，最常見的運用就是資本運算（Capital Budgeting）.資本預算是指公司在長期項目與投資之間進行資金分配，這涉及比較不同項目或投資的未來現金流。比較不同項目現金流有兩種基本方法，即淨現值與內部回報率法。
In many cases of cash flow analysis, NPV and IRR are two frequently used concepts, among which capital operation is the most common one. Capital budgeting refers to the allocation of funds between long-term projects and investments, which involves comparing future cash flows of different projects or investments. There are two basic methods to compare cash flows of different projects, namely, net present value and internal rate of return.
淨現值NPV是指未來現金流入現值與流出現值之間的差額。利用NPV法則判斷是否應該投資一個項目包括以下五個步驟：
（1）確定項目未來所有的現金流（同時包括現金流流出與流入）
（2）確定項目現金流的折現率或機會成本R
（3）利用折現率，計算出所有現金流的現值（現金流流入用正好表示，提升NPV值；反之流出用負號表示，降低NPV值）。
（4）將所有現金流現值加總，即可得NPV值
（5）利用NPV法則進行判斷：若該項目NPV值為正數，則該項目可以投資；反之，若NPV為負數，則該項目不能投資，如果投資者只能在兩個備選項目中投資一個（Mutually exclusive project ）,投資者應當選擇NPV 較大的項目
NPV refers to the difference between the present value of future cash inflows and the present value of outflows. Using NPV rule to determine whether a project should be invested includes the following five steps:
(1)Determine all future cash flows of the project (including both outflows and inflows)
(2)Determining the discount rate or opportunity cost R of project cash flow
(3) Using the discount rate, the present value of all cash flows is calculated (cash inflows are represented by positive signs to increase NPV value, where as outflows are represented by negative signs to reduce NPV value).
(4) NPV can be obtained by summing up all cash flow present values.
(5) Use NPV rule to judge: if the NPV value of the project is positive, then the project can be invested; otherwise, if the NPV is negative, then the project can not be invested. If the investor can only invest in one of the two alternative projects, the investor should choose the project with larger NPV.
NPV公式（formula）
tips: ∑公式計算：表示起和止的數。比如說下面t=0,N=3，表示從0起到3止的和。
Formula calculation: Number indicating beginning and ending. For example, let's say t = 0, N = 3, which means the sum from 0 to 3.
其中CFt 表示第T期的現金流，N表示項目持續時間、r表示資金的折現率或機會成本。
資金的機會成本r指如果資金沒有投資該項目，而是進行其他投資可以獲得的收益率。
換言之，r表示了投資該項目，投資者期望的最低收益率。因此，如果按此貼現率計算出的NPV為正，表明該項目增加了股東財富；反之則減少了股東財富。
Among them, CFt represents the cash flow of the T period, N represents the duration of the project, R represents the discount rate or opportunity cost of the fund.
Opportunity cost r of funds refers to the rate of return that can be obtained if the funds do not invest in the project but make other investments.
In other words, R represents the lowest rate of return expected by investors when investing in the project. Therefore, if the NPV calculated at this discount rate is positive, it shows that the project increases share holder wealth; on the contrary, it decreases shareholder wealth.
例題
某項目需要在期初投入研發成本200萬元，項目持續3年，預計分別能在第一年、第二年與第三年末收到50萬元、75萬元、與135萬元。如果折現率為10%，該項目是否值得投資？
Example
A project needs to invest 2 million yuan in research and development cost at the beginning of the period and lasts for three years. It is expected to receive 500,000 yuan, 750,000 yuan and 1.35 million yuan in the first year, the second year and the end of the third year, respectively. If the discount rate is 10%,is the project worth investing?
解析
直接帶入NPV 公式計算即可。
淨現值=未來現金流入現值與流出現值之間的差額
NPV=-200（流出現值）+50/（1+10%）+75/（1+10%）2+135/（1+10%）3=8.7
NPV大於零，因此該項目值得投資
analysis
The NPV formula can be calculated directly.
Net present value = the difference between the present value of future cash inflows and the present value of cash outflows
NPV=-200（outflow present value）+50/（1+10%）+75/（1+10%）2+135/（1+10%）3=8.7
NPV is greater than zero, so the project is worth investing.
