net present value
concept
Net present value (NPV): It means that Y yuan in a certain year in the future is equivalent to X yuan in this year.
Two concepts need to be paid attention to:
Interest rate: The interest rate is the ratio of the amount of interest due each period to the face value of the amount borrowed, deposited or borrowed (called the principal amount).
Discount rate refers to the interest rate used to change the future payment into the present value, or refers to the interest rate used by the bank to deduct the interest in advance when the bearer requests the bank to cash in the undue bill.
Calculation formula
P=F/（1+i）n
F: Net cash flow in year n
P: Net cash flow for this year
i: interest or discount rate
n: refers to the nth year
example
The annual profit of a certain project from the year of commissioning is shown in the table below, and the investment discount rate is 10%, then the total net present value of the project’s profit at the end of 2015 is () yuan.
profit distribution |
year 2013 |
Year 2014 |
2015 |
2016 |
profit value |
—— |
10000 |
11000 |
12100 |
Analysis: According to the net present value formula P=F/(1+i)n, we can know:
P=10000/(1+10%)+11000/(1+10%) (1+10%)=18181 yuan
payback period
concept
The payback period is also known as the "investment payback period". The time (years) required for the total income obtained after the investment project is put into production to reach the total investment invested in the investment project is the reciprocal of the investment return rate.
Calculation formula
Static payback period = (the number of years in which the accumulated net cash flow begins to show a positive value - 1) + (the absolute value of the accumulated net cash flow in the previous year / the net cash flow in the year in which the positive value appears)
Dynamic investment payback period = ( the number of years in which the present value of the accumulated net cash flow has a positive value - 1) + the absolute value of the present value of the accumulated net cash flow in the previous year / the present value of the net cash flow in the year in which the positive value appears
Note: The difference between static and dynamic is that one is net cash flow and the other is the present value of net cash flow;
example
The project manager has formulated the project balance sheet (unit: yuan), as shown in the table below. The static investment payback period of the project is ( ) years, and the dynamic investment payback period is ( ) years (one decimal place is reserved).
Analysis: Seeing such problems, you can first calculate several key indicators in the figure below, and then apply the formula
Static payback period: 3-1+(35000+1000+1500-20000-10000)/(12000-2000)=2+7500/10000=2.7
动态回收期：3-1+（35000+（1000-20000）*0.91+（1500-10000）*0.83+（12000-2000）*0.75）/(15000-1000)*0.68=3.331
示例：E公司长期投资项目累计的净现金流量资料如下表所示:
要求:E公司目前的资本结构（负债/权益）为1/1，税前债务成本为8%，β权益为2，当前市场的无风险报酬率为4%，权益市场的平均风险溢价为5%。E公司适用的企业所得税税率为25%。
1.计算该项目各年的净现金流量；
2.计算该项目的静态回收期；
3.计算E公司当前的加权平均资本成本。
4.计算该项目的动态回收期。
5.计算净现值。
分析与提示:
1.净现金流量
3.股权资本成本＝4%＋2×5%＝14%2.静态回收期＝3+=3.14（年）
加权资本成本＝14%×50%＋8%×（1－25%）×50%＝10%
4.动态回收期
5.NPV＝－1 000－200×（P/F，10%，1）＋500×（P/F，10%，2）＋600×（P/F，10%，3）＋700×（P/F，10%，4）＋800×（P/F，10%，5）＋1 000×（P/F，10%，6）＝1 221.48（万元）动态回收期＝3＋＝3.66（年）
示例：一项投资可以在未来8年内带来每年790美元的现金流入。如果初始投资为3200美元，那么该项目的投资回收期应为多少？当初始投资为4800美元时呢？为7300美元时呢？
题目关键词：投资回收期
考点定位：投资回收期——投资评价方法
总结：遇到计算回收期
1）先画时间轴、
2）现金流相加找到第一次现金流的和大于初始投资额的年份n、
3）带入回收期的计算公式：
Ps：当现金流入是年金的形式（每期现金流流入一致），公式可以简化为
计算增长年金终值的简便方法
【案例】：某软件企业2006年初计划投资2000万人民币开发某产品，预计从2007年开始盈利，各年产品销售额如下表所示。根据表中的数据，该产品的静态投资回收期是 （1） 年，动态回收期是 （2） 年。（提示：设贴现率为0.1）
（1）A. 1.8 B. 1.9 C. 2 D. 2.2
（2）A. 2 B. 2.1 C. 2.4 D. 3
【解析】：这里题目要求的是回收期，就是总投资与收益相等的时间点，即NPV = 0。
（1）静态回收期不考虑贴现，根据表内的投资收益额，可知2008年底NPV = 990 + 1210 - 2000=200>0，可知投资回收期在1~2年之间，即为 1+ （1- 200/1210）≈ 1.8，四舍五入后选 (A) （2）动态回收期考虑贴现，现根据贴现率求得每年的现值如下：
由上图可知第3年可收回成本，900 + 1000 + 900 - 2000 = 800 > 0；可知回收期在2~3年之间，即为 2 + （1-800/900）≈ 2.1 , 选 （B）。