今日分享
临渊羡鱼，不如退而结网。Don't dream it, be it.
现值与终值
现值（Present value PV）与终值（Future Value FV）是一组对应的概念。各类金融资产会给投资者在未来不同时间点带来现金流（既可以是现金流入，也可以是现金流出）。现值PV是指将金融资产各个阶段的现金流按复利形式折算到投资期初的价值之和。终值FV：是指将金融资产各阶段的现金流按照复利形式折算到投资期末的价值之和。不难看出，现值和终值实际上是同一组现金流在不同时间点的价值，两者之间的相互转换公式如下：
Present value and final value are a set of corresponding concepts. Various types of financial assets will bring cash flow to investors at different time points in the future (either cash inflows or cash outflows). The present value PV refers to the sum of the value of the cash flow of each stage of financial assets converted to the beginning of the investment period in the form of compound interest. Final value FV: refers to the sum of the value of the cash flow of each stage of financial assets converted to the end of the investment period in the form of compound interest. It is not difficult to see that the present value and the final value are actually the values of the same group of cash flows at different time points. The conversion formulas between the two are as follows:
其中，n表示投资期，r表示计息期利率。Among them, n denotes the investment period and R denotes the interest rate of the interest period.
从上面的两个公式可以看出现值、终值与利率水平之间的关系：（1）给定利率水平r，FV随着计息周期数n上升而上升（2）给定计息周期数n，FV随着利率水平r上升而上升（3）在给定时间段内，利率水平r越大，现值PV越小。
From the above two formulas, we can see the relationship between present value, final value and interest rate level.(1) Given the interest rate level r, FV rises with the increase of the number of interest-bearing cycles n.(2) Given the number of interest-bearing cycles n, FV rises with the increase of interest rate level R.(3) In a given period of time, the higher the interest rate level r, the smaller the present value PV.
例题1假定利率是10%，每年计息一次，初期投资2000元，求两年后的终值。解析从现在开始必须养成画现金流图的习惯，对后续理解复杂的估值与定价模型有很大的帮助Example1Assuming that the interest rate is 10%, the interest rate is calculated once a year, and the initial investment is 2,000yuan, the final value after two years is calculated.analysisFrom now on, we must develop the habit of drawing cash flow graphs, which is very helpful to understand complicated valuation and pricing models in the future.
现金流图中，横轴标识时间轴，数字代表各时期序列号。例如，数字0表示第0期，即投资期初：数字1所在位置表示第一期末或第二期初。直接利用FV=PV×(1 r)n公式可计算两年后终值FV=2000×(1 10%)2=2000×1.21=2420 In the cash flow chart, the horizontal axis identifies the time axis and the number represents the serial number of eachperiod. For example, the number 0 denotes the beginning of the investmentperiod: the location of the number 1 denotes the end of the first period or thebeginning of the second period.The final value after two years can becalculated directly by FV=PV×(1 r)nformula.FV = 2000×(1 10%) 2 = 2000×1.21 = 2420
例题2:假定利率是10%，每年计息一次，若两年后要收回2000元，现在应该投资多少元解析:先画现金流图Example 2Assuming that the interest rate is 10%, theinterest rate is charged once a year. If 2,000 yuan is to be recovered aftertwo years, how much should we invest now?analysisDraw a cash flow chart first
解析：同样将现金流示意图画出，利用公式PV=可以求出Analysis:Similarly, the cash flow sketch is drawn, andthe formula PV=FV/(1 r)n can be used to calculate it.PV=2000÷(1 10%)2=1652.9
内容来源于网络公开信息。
风险提示：本文仅作为知识分享，不构成任何投资建议，对内容的准确与完整不做承诺与保障。过往表现不代表未来业绩，投资可能带来本金损失；任何人据此做出投资决策，风险自担。如有侵权请联系我们,我们将及时处理。
The content comes from publicly available information on the Internet.Risk tip: this article is only for knowledge sharing, does not constitute any investment advice, and does not promise and guarantee the accuracy and integrity of the content.Past performance is not indicative of future performance and investment may result in principal loss;Anyone makes an investment decision based on this, at their own risk.If there is any infringement, please contact us and we will deal with it in time.
