大家在备考ACCA时候，经常会遇到“present value”这个考点内容，大家也无法分清什么时候查复利现值系数表，什么时候查年金现值系数表，针对大家所出现的问题，小编今天就跟各位讲解下“present value”这个知识点。

1. 期初有一笔现金流流出(期初默认T=0时刻，现金流流出一般是指investment)

2. 从第一年开始，每年都有一笔现金流流入

3. 现金流流入发生在每年的期末

1.每笔现金流通过复利现值系数分别折现=现金流*复利现值系数(r，n)

2.复利现值系数在present value table中找，r为折现率，n为对应现金流到T=0时刻的年限

3.NPV=每笔现金流的现值之和-期初投资额

1.通过年金现值系数将所有年金往前折现一年,折现后的值=每年现金流金额*年金现值系数(r，n)

2.年金现值系数在annuity table中找，r为折现率，n为年金数量，有几笔年金，n就为几

3.NPV=每年现金流金额*年金现值系数(r，n)-期初投资额

1.通过公式把永续年金全部往前折现一年，折现后的值=每年现金流金额/r

2.r是折现率

3.NPV=每年现金流金额/r-期初投资额

接下来，分别给三个题目让大家练习一下：

An investment of $20,000 is expected to yield $5,000 in the first year, $10,000 in the second year, $8,000 in the third year. Calculate the net present value of the investment opportunity if the cost of capital is 5%

NPV=5000*复利现值系数(5%，1)+10000*复利现值系数(5%，2)+8000*复利现值系数(5%，3)-20000

=5000^0.952+10000^0.907+8000^0.864-20000=$742

An investment of $50,000 is expected to yield $5,000 for ten years. Calculate the net present value of the investment opportunity if the cost of capital is 5%.NPV=50000*年金现值系数(5%，10)-50000

=5000^7.722-50000

=-$11390

An investment of $50,000 is expected to yield $5,000 per annum in perprtuity. Calculate the net present value of the investment opportunity if the cost of capital is 5%.NPV=5000/5%-50000 =$50000

以上，就是针对present value中三种常见问题的希望对大家有所帮助。