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第一节 货币时间价值
本节讨论的主要问题是货币时间价值的本质与现金流量的计量及等值运算方法。同样金额的现金流量在不同时点价值不同的原因就是货币时间价值的存在,对现金流量进行计量的方式主要有现值、终值及年金等形式,计算现金流量在不同时点价值的方法是等值运算,即运用现值和终值公式计算现金流量在其收付时点与任何另一时点之间的等值价值转换。
一、货币时间价值的含义
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0033_0025.jpg?sign=1739527931-0mscCWvCDuH1jpoN8LuhJJcndUN52IJR-0-bec6806d8ce159960b666509550cab58)
二、终值与现值
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0034_0026.jpg?sign=1739527931-zDPOcmGCqcEfW25Oco2de1oOgicIaWKT-0-126b30b72b4b659795a742f294d30bcb)
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0035_0027.jpg?sign=1739527931-FBL8Bu03ij4UAawopH41qapgFMOrGMiG-0-6a7f1d8b2a7c72c47d3df06734e5aacd)
三、年金
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0036_0028.jpg?sign=1739527931-mNyjPQPv08GsRSPu0L9eijrYvs82SoUu-0-eba94b64d166e9cbb1020526d4b59bb5)
(一)普通年金
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0036_0029.jpg?sign=1739527931-lPrAjtKAAqq17j74lj2W5kc8d8g18nBV-0-19c5000e8745b923f6fcc2144463e7b6)
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0037_0030.jpg?sign=1739527931-3HuNa7dZ4JCWHGACU8A5poAciS6krDTP-0-985888db80de30cd5fc6bef890f9d29d)
图2-1 普通年金示意图
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0037_0031.jpg?sign=1739527931-4IbNCNbjh0b872FfbyPgbGJyefU35c2Z-0-803ac25843dce326ecf95a5bae2fe2ae)
图2-2 普通年全终值示意图
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0037_0032.jpg?sign=1739527931-vPTu0k6mxRRy67Qh8ZjXtG6LeGb4wtlB-0-c8b7b973f9c6ee1b691ff2aaaa68098f)
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0038_0033.jpg?sign=1739527931-LrqR1EtdFfkOyEZTv36RqbRU6fxwUt4o-0-d19ad72886f2689c0f55a0a175216018)
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0038_0034.jpg?sign=1739527931-BdXU4drlqyRUwpZhB1UxGFQxVKE0vFvQ-0-13bcfabde102afa4d517b6e4dbce6e25)
图2-3 普通年金现值示意图
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0039_0035.jpg?sign=1739527931-YE5fh03Hhd0Raics0LucpWxtsbmULHQH-0-c1a115a3ecc1a85594c1dcd939f9d781)
(二)先付年金
先付年金是指在每期期初发生的等额现金流量,又称预付年金或即付年金,如图2-4所示。
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0039_0036.jpg?sign=1739527931-RInWlAzqwpJKbniOWTEnmyqlxsNgE2Rf-0-e945a3646719e36ca32daa0ba741b4c0)
图2-4 先付年金示意图
由于先付年金现金流量在期初发生,实际上只是比普通年金提前了一期,因此计算其终值和现值较为简单。
1.先付年金终值的计算
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0040_0037.jpg?sign=1739527931-MUV4HGBo9LXEpcHlJRkolNVWDj5XIFuw-0-257440bc5629a7c4643ae324faa7a8bb)
2.先付年金现值计算
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0041_0038.jpg?sign=1739527931-fXIVn8OW5p7O4xhWyLtUByZfu1qTfA9V-0-77b9cbc91cf0db92b1d03388abed3b90)
3.递延年金
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0042_0039.jpg?sign=1739527931-HcjhHM010BlCRPorgPniK6gYgfTTfoNu-0-7e08ca98f1c06cd168430bf14e067d10)
图2-5 递延年金示意图(一)
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0043_0040.jpg?sign=1739527931-AZB0QdbMq6CmR6uL89ZHySGBgqXLDKnN-0-1aef0c150fe7314a72cf259fa23cf3b6)
图2-6 递延年金现值示意图(二)
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0043_0041.jpg?sign=1739527931-s94a1ARyzrk9znZdYCin0x9wbQQv3inb-0-0a1ba4e9a780c95c82b5bc117a457ade)
图2-7 递延年金现值示意图(三)
4.永续年金
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0043_0042.jpg?sign=1739527931-hIny4wRNExU14Mtwzj3hZ5B5S5GI4Bnl-0-078d1b6855abe65a197b10fcc8502ccd)
四、复合现金流量的等值运算
现实生活中,有时现金流量的分布形式是复合形式的,并不呈现严格的规律性,对这类复合现金流量,可以视为由几部分现金流量叠加而成。
下面通过一个例子来介绍这种混合现金流量问题的解题方法。
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0044_0043.jpg?sign=1739527931-dBqZwJ8cIiK4NxH9vOypNmkD6399uN3x-0-180ae12773fc24ab1421328d39cf2d7e)
图2-8 现金流示意图
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0044_0044.jpg?sign=1739527931-ccorRd3ptop2YauVL1hZeAdhjeh3M5wl-0-18ef05cec2de3275c212969050f7e23c)
图2-9 现金流计算方法示意图(一)
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0045_0045.jpg?sign=1739527931-yuViiOO56A2KWOXe10X1O6j8BAfKijEC-0-5d01141c9ecddf0defd88d78f3f337dc)
图2-10 现金流计算方法示意图(二)
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0045_0046.jpg?sign=1739527931-qxob1GM0ndlnannKOKGejF28G1qopRAD-0-9233e3af22dc9e58e6f809fe571bc902)
图2-11 现金流计算方法示意图(三)
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0045_0047.jpg?sign=1739527931-19z0YHVHHM1DaloN5eSsEZ4wJHfIblk3-0-72af614762a0848389efd6e2f6a2dea4)
图2-12 现金流计算方法示意图(四)
五、复利期间与实际利率
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0046_0048.jpg?sign=1739527931-I7xXUftC3hjAvisY0M6Tr6zeILkeXwwd-0-04983ae671647e97eb57adc2b47f8b87)
表2-1 1年内多次复利1元复利终值计算表
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0047_0049.jpg?sign=1739527931-UYxwXNoq9khs8wN0dcnj7Z2WwjFWwOPU-0-89b1ecf46cba39f760a56a001f15a72a)
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0047_0050.jpg?sign=1739527931-6n3WMiFLNXwU4XI25SKJ1AADjDfT9XqW-0-a34c227fe6991f923032a70931513991)
六、贷款的分期偿还
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0048_0051.jpg?sign=1739527931-95C7UQHfEpYWj4SRg1kjUNp6ODZY3xrC-0-e44b81898fc80b19885e461466405a58)
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0049_0052.jpg?sign=1739527931-YpOaeFrxZJEfZRj44uyBZXAP0IUKRX9D-0-7edf0bdc5c5fa35373f717e1b2ec1448)
表2-2 贷款分摊
单位:元
![](https://epubservercos.yuewen.com/0D4A2C/21701636101472106/epubprivate/OEBPS/Images/figure_0049_0053.jpg?sign=1739527931-RhnTWCAB3WKZJeXaRm1vewqnZ70RgC7Q-0-bd851c17fb4565d025501fee6a5380a8)
实务中常用的另一种还款方式是等额本金还款法,即每个还款期内等额偿还贷款本金,利息则按照实际占用的本金额和计息期利率来计算。这种方法无须对本金和利息进行分摊,但是前期的还款额较大。