净现值为正怎么求内部收益率（每日文章六十八）

Daily article 68: Net present value and Internal rate of return，我来为大家科普一下关于净现值为正怎么求内部收益率?下面希望有你要的答案，我们一起来看看吧!

净现值为正怎么求内部收益率

Daily article 68: Net present value and Internal rate of return

Net present value ( NPV ) is the most important value when we evaluate a project or financial product in CFA exam. Just imagine that you are going to start a project or make an investment. Usually, you make an initial payment which is a cash outflow happens on day 1 and wait for the returns, which are cash inflows on different times in the future. The model is pretty simple but the key is to find whether the project is worth doing. Intuitively, you want to compare the cash inflows with the initial outflow to find the net value. Thanks to our former knowledge about the time value of money, we realize that we can’t just sum the number on different years up. Rather, we first convert the cash flows happen on different times to be on the same day, and then add them up. To make it easier to understand and calculate, we just find the present value of different cash flows and add them up to find the net present value.

We use the required rate of return of the project or interest rate of the financial product to represent the time value when calculating the present value of different cash flows. If the NPV is positive, it means the cash inflows have greater present value than cash outflows while the required rate of return is met, the project or financial product is therefore worth taking. The model can be more complicated in the real life because there are more different pattens of cash outflows and inflows. But the logic is the same: convert all cash flows to be on the same day, then sum them up.

We can also look at such questions on other perspectives. Internal rate of return (IRR) is the rate which makes the NPV to equal to 0. This time we don’t have a known rate to calculate the unknown NPV, instead we have a known NPV to calculate the unknown rate. IRR is the time value that makes the project have cash outflows equal to cash inflows in terms of present value. In models where cash outflows happen earlier than cash inflows, the required rate of return which is less than IRR will result in larger cash inflows in terms of present value and positive NPV. In conclusion, if IRR is bigger than the required rate of return, the NPV is positive and the project is worth doing, vice versa. Again, we will leave all the calculation to financial calculator and MS Excel.

在CFA考试中，净现值是我们评价一个项目和金融产品时最重要的一个指标。假设你现在要开始一个项目或者进行一笔投资，通常情况下，我们会在第一天投入一笔资金并等待未来的收益。这样形成的现金流模型是：第一天有一笔现金流出，以后不同时间点有多笔现金流入。我们需要判断这笔投资值不值。自然而然的，我们会想到把所有现金流出流入加在一起，看看是正是负。但回顾一下之前关于时间价值的学习，发生在不同时间点的现金流是不能直接相加的。我们应该先把所有的现金流转化为同一天发生，再把这些价值相加。为了理解和计算方便，我们计算每一笔现金流的现值然后相加，得出净现值。

在计算不同现金流的现值的时候，我们用项目的必要收益率或者金融产品的利率来代入公式作为时间价值计算。如果得出的净现值为正，就表示在必要收益率满足的情况下，现金流入比现金流出的现值更大（说白了就是流入的钱更多），这个项目可以做。在实际生活中，这个模型会更加复杂，现金流出和流入的模式也会更多，但背后的计算逻辑是一样的：把现金流转化到同一天，然后加总计算。