中级财务会计Topic 5 Time value of money and voluation
财务会计中的货币时间价值
财务会计中的货币时间价值财务会计中的货币时间价值（Time Value of Money，简称TVM）是指货币在不同时间点的价值差异。
在财务决策中，考虑到时间价值可以帮助企业进行更准确的投资、融资和资本预算决策。
本文将讨论货币时间价值的概念、计算方法以及在财务会计中的应用。
一、货币时间价值的概念货币时间价值指的是同一笔货币在不同时间点的价值并不相等。
由于货币可以通过投资获取回报，所以同样金额的货币未来的价值会比现在的价值高。
这是因为在未来的时间里，货币可以进行投资增值或者用于消费，而当前持有的货币则无法享受到这些增值收益。
二、货币时间价值的计算方法在财务会计中，常用的货币时间价值计算方法有现值、未来值和利息计算。
1. 现值计算现值是指未来一笔现金流量的折现价值。
它表示了未来现金流量在当前时间点的价值。
现值计算需要考虑折现率和未来现金流量的时间点。
常用的现值计算公式如下：PV = CF / (1 + r)^n其中，PV代表现值，CF代表未来现金流量，r代表折现率，n代表未来现金流量发生的期数。
2. 未来值计算未来值是指当前一笔现金流量在未来某个时间点的价值。
它表示了当前现金流量经过一段时间后的价值。
未来值计算需要考虑复利计算和投资期限。
常用的未来值计算公式如下：FV = PV * (1 + r)^n其中，FV代表未来值，PV代表当前现金流量，r代表复利率，n代表投资期限。
3. 利息计算利息是指在一定时间段内所获得或支付的货币增值或减值金额。
利息计算可以通过现值和未来值的差额得出。
常用的利息计算公式如下：I = FV - PV其中，I代表利息，FV代表未来值，PV代表现值。
三、货币时间价值在财务会计中的应用货币时间价值在财务会计中具有广泛的应用，其中主要包括资本预算决策、财务报表分析和债券计息等方面。
1. 资本预算决策在进行资本预算决策时，企业需要评估不同投资项目的现金流量，并且考虑到货币时间价值的影响。
CH07TimeValueofMoney(财务管理,英文版)
Copyright © 2001 by Harcourt, Inc.
All rights reserved.
7 - 26
What interest rate would cause $100 to grow to $125.97 in 3 years?
$100 (1 + i )3 = $125.97.
2
3
100
100
All rights reserved.
7 - 21
INPUTS 3 10
100 0
N I/YR PV PMT FV
OUTPUT
-248.69
Have payments but no lump sum FV, so enter 0 for future value.
Copyright © 2001 by Harcourt, Inc.
Copyright © 2001 by Harcourt, Inc.
All rights reserved.
7 - 20
What’s the PV of this ordinary annuity?
0
1
10%
100 90.91 82.64 75.13 248.68 = PV
Copyright © 2001 by Harcourt, Inc.
0
1
2
3
10%
PV = ?
100
Copyright © 2001 by Harcourt, Inc.
All rights reserved.
Solve FVn = PV(1 + i )n for PV:
PV
=
FVn
1+ in
财务管理基础课件：The Time Value of Money
Where FV = Future value PV = Present value i = Interest rate n = Number of periods;
In the previous case, PV = $1,000, i = 10%, n = 4, hence;
1st year……$1,000 X 1.10 = $1,100 2nd year…...$1,100 X 1.10 = $1,210 3rd year……$1,210 X 1.10 = $1,331 4th year……$1,331 X 1.10 = $1,464
9-4
Future Value – Single Amount (Cont’d)
• The time value of money is used to determine whether future benefits are sufficiently large to justify current outlays
• Mathematical tools of the time value of money are used in making capital allocation decisions
annuity
9-25
Yield – Present Value of a Single Amount
• To calculate the yield on an investment producing $1,464 after 4 years having a present value of $1,000:
Table 9–5
《Unit5TheValueofMoneyReadingandThinking》教案（附导学案）1
Unit5The Value of MoneyReading and Thinking【教学目标】1.Know the writer Mark Twain and his representative works.2.Learn the main idea of the play and understand the implied meaning.3.Critically think Ts money everything^.【教学重难点】1.Learn the main idea of the play and understand the implied meaning.2.Critically thiiik"Money is everything”.【教学过程】Step1Lead in一Small talkWe know money is very important.We can use money to do a lot of things.So what would you do if you had a million-pound bank note?Get the sb.to discuss the question and share their opinions.Step2Before reading—About Mark TivalnThe Mill i on Pound Bank Note is partly selected from the works by American writer Mark Twain.Now let's know more about the greatest writer in the19,h century.His main novels:Tlie Adventures of Tom Sawyer（《汤姆索亚历险记》）The Prince and the Pauper（《皇子与贫儿》）The Adventures of H ucklebeny Finn（《哈克贝利费恩历险记》）Step3While reading一Task1Read the text and answer the following questions.Then have the Ss share their answers.QI:What bet did Roderick and Oliver make?Q2:How did Henry come to Britain?Q3:How does Henry want the brothers to help him?Q4:Why do you think Hemy does not want the brothers'charity?Q5:Why do you think the brothers chose Henry for their bet?Step4While reading—Task2According to the text,think about what kind of person Henry was and give the reasons.1.He was honest.Evidence:1)Well,I can't say that I have any plans.Well,to be honest,I have none.2)I don't want your charity.I just want a job that earns an honest income.3)He promised not to open the envelope until2o'clock.2.He was hard-working.Evidence:Could you offer me work here?I just want a job that earns an honest income.Step5Post reading一Study the languageUnderstand implied meaningSome sentences have an implied meaning which is not clearly stated.This implied meaning often indicates people's feelings,attitudes,or motives.You can find this implied meaning by looking at the context.You have to read between the lines because the real messages are often hidden beneath the literal meaning.1.Read these sentences and describe Henry's feelings using suitable adjectives.1)Who?Me,sir?(surprised)2)Well, I can t say that I have any plans.As a matter of fact,I landed in Britain by accident,(honest)3)I'm afraid I don't quite follow you,sir.(puzzled)4)Well, it may seem lucky to you but not to me!If this is your idea of some kindof j oke,I don't tliiiik it's very hinny,(angiy)5) Well,why don't you explain what this is all about?(confused)2.Explain what the speakers mean by saying these sentences.1)I went to the American consulate to seek help,but...Anyway, I didn't daie to try again.The American consulate didn't give him any help and might insult him.which made him gave up asking for help form American consulate forever.2)Ybu mustn't wony about that.It's an advantage.We would help you.We want to find a person like you who can't also seek any help.3) What luck!Brother,what luck!Roderick is very excited about finding such a right person.4)Oh,this is silly.Now that you give it to me,I can open it.It's silly of you to ask me to open until 2o'clock.Step6Post reading—RetellComplete the passage according to the text in Activity5.Then check the correct answers with the class.Step7Critical thinkingSome people think money is very important.Please write an essay with the topic "Is money important?"and present your o\vn idea.Step8HomeworkRetell the story after class.Unit5The Value of MonevReading and Thinking导学案【学习目标】1.Know the writer Mark Twain and his representative works.2.Learn the main idea of the play and understand the implied meaning.3.Critically think"Is money everything”.【学习重难点】1.Learn the main idea of the play and understand the implied meaning.2.Critically think “Money is everything".【学习过程】Step1Lead in一Small talkWe know money is very important.We can use money to do a lot of things.So what would you do if you had a million-pound bank note?Step2Before reading一About Mark TivainThe Million Pound Bank Note is partly selected from the works by the American writer Mark Twain.Now let's know more about the greatest writer in the19th century.Mark Twain（1835-1910）,once said,"To believe yourself to be brave is to be brave;it is the only essential thing?"His main novels:Tlie Adventures of Toni Sawyer（《汤姆索亚历险记》）The Prince and the Pauper（《皇子与贫儿》）The Adventures of H uckleberiy Finn（《哈克贝利费恩历险记》）Step3While reading一Task1Read the text and answer the following questions.QI:What bet did Roderick and Oliver make?Q2:How did Henry come to Britain?Q3:How does Henry want the brothers to help him?Q4:Why do you think Henry does not want the brothers'charity?Q5:Why do you think the brothers chose Henry for their bet?Step4While reading—Task2According to the text,think about what kind of person Henry was and give reasons.1.He was.Evidence:2.He was____________Evidence:Step5Post reading—Studv the languageUnderstand implied meaning or feelingSome sentences have an implied meaning which is not clearly stated.Thisimplied meaning often indicates people's feelings,attitudes,or motives.You can find this implied meaning by looking at the context.You have toread between the lines because the real messages are often hidden beneathth e literal meaning.,1.Read these sentences and describe Henry's feelings using suitable adjectives.1)Who?Me,sir?()2)Well, I can't say that I have any plans.As a matter of fact,I landed in Britain by accident.()3)I'm afraid I don't quite follow you,sir.()4)Well, it may seem lucky to you but not to me!If this is your idea of some kind of j oke,I don't tliink it's very Hinny.()5) Well,why don't you explain what tills is all about?()2.Explain what the speakers mean by saying these sentences.1)I went to the American consulate to seek help,but...Anyway;I didn't dare to try again.2)Ybu mustn't wony about that.It's an advantage.3)What luck!Brother,what luck!4)Oh,this is silly.Step6Post reading一RetellComplete the passage according to the text.Henry,a San Francisco businessman,found himself(1)(carry)out to sea by a strong wind.When he was just about to give himself up.he(2)(spot) by a ship,so he landed in London(3)accident.Hungry and alone,he walked on the streets of the city when he was(4)(expect)called into a house,(5) two rich brothers,Oliver and Roderick,gave him a letter and told him not to open it till two o'clock of the day.Not(6)(know)it was a million-pound bank note,Henry left the house and went into a cheap restaurant to stuff his stomach. Everybody was rude to him(7)he looked poor.Then. Io his surprise,he handed the owner a million-pound bank note to pay(8)the meal.Seeing the note, all the people in the restaurant became polite and tried their best (9)(please)Henry.Don't you think it's(10)most incredible tale in the world? Step7Critical thinkingSome people think money is very important.Please write an essay with the topic "Is money is important?” and present your own idea.。
财务管理专业英语-The Time Value of Money
5 years: PV = 500 / (1.1)5 = 310.46 10 years: PV = 500 / (1.1)10 = 192.77
4
Effects of Compounding
Simple interest Compound interest Consider the previous example
FV with simple interest = 1000 + 50 + 50 = 1100 FV with compound interest = 1102.50 The extra 2.50 comes from the interest of .05(50)
12
PV – One Period Example
Suppose you need $10,000 in one year for the down payment on a new car. If you can earn 7% annually, how much do you need to invest today?
8
Future Values – Example 3
Suppose you had a relative deposit $10 at 5.5% interest 200 years ago. How much would the investment be worth today?
FV = 10(1.055)200 = 447,189.84
16
财务管理 公司理财基本理论(资金时间价值)
利用查表方式： （F/P，i, n） F=10000×（1+6%）2
=10000 ×(F/P, 6%, 2) =10000 ×1.1236 =11236
1）复利现值的计算：
复利现值是复利终值的对称概念,指未来一 定时间的特定资金按复利计算的现在价值,或者 说是为取得将来一定本利和现在所需要的本金。
时间（期数）：n
二、一次性收付款项的时间价值
1、单利
1）单利终值的计算
终值：一定量的资金在未来某一时点上的本利和。
F=P+I
•
= P + P×i×n
•
= P（1+i×n)
2）单利现值的计算 现值：若干年后收入或支出一笔资本的现在价 值。（Present Value) P = F/（1+i×n）
（ 单利终值的计算和单利现值的计算互为逆运算）
4、实务中一般不单独反映。
例：已探明一个有工业价值的矿产资源，目前立 即开发可获利100亿元，若5年后开发，由于价 格上涨可获利160亿元。
不考虑资金的时间价值：5年后投资；
若考虑资金的时间价值： 若现在获利100亿元，则即有另一项投资机会，
平均每年获利15%，则5年后将有资金：100× （1+15%）5=200
• 例：某公司决定连续5年于每年年初存入100 万元作为住房基金，银行存款利率为10%。 则该公司在第5年末能一次取出本利和为多 少？
（2）即付年金现值
相当第0年价值
0 1 2 3 ……n-2 n-1 n A A A A …… A A
A A(1+i)-1 A(1+i)-2 A(1+i)-3 ……. A(1+i)-(n-2) A(1+i)-(n-1)
Chapter 05- The Time Value Of Money 现代财务管理英文版课件
FVIFAi, n =
(1 + i)n – 1 i
Formula for IF
FVANn = PMT(FVIFAi, n)
Table If an Ordinary Annuity
1–
1
PVIFAi, n = (1 + i)n
i
Formula
PVAN0 = PMT( PVIFAi, n) Table IV
12
Example Using Table II
PV0 = FVn(PVIFi, n) = $100(.887) = $ 88.70
From Table II
13
14
Annuity
A series of equal dollar CFs for a specified number of periods
PVPER0 = PMT/i
26
Interest Compounded More Frequently Than Once Per Year
m = # of times interest is compounded n = # of years
Future Value
( ) FVn = PV0
1 + inom m
22
23
24
25
Other Important Formulas
Sinking Fund
PMT = FVANn/(FVIFAi, n) Table III
Payments on a Loan
PMT = PVAN0/(PVIFAi, n) Table IV
Present Value of a Perpetuity
3
Future Value of a Cash Flow
中级财务管理第二章第一节知识点
中级财务管理第二章财务管理基础第一节货币时间价值知识点中级财务管理第二章财务管理基础中，第一节货币时间价值的知识点主要涉及以下几个方面：一、货币时间价值的定义货币时间价值（Time Value of Money, TVM）是指在没有风险和没有通货膨胀的情况下，货币经历一定时间的投资和再投资所增加的价值，也称为资金的时间价值。
这种增加的价值是由于货币的时间延续而带来的额外收益。
二、货币时间价值的表现形式货币时间价值通常通过终值和现值来表现：1. 终值（Future Value, FV）：指当前的一定量资金在若干期后所具有的价值。
通常用于计算未来某一时点的资金总额，包括本金和利息的总和。
2. 现值（Present Value, PV）：指未来某一时点一定量的资金折算到当前（基准时点）所具有的价值。
现值计算用于评估未来收益在当前的价值，以便进行投资决策。
三、利息的计算方式计算利息的两种方式包括单利和复利：1. 单利（Simple Interest）：指按照固定的本金计算利息的一种计息方式，所生利息均不加入本金重复计算利息。
其计算公式为：利息= 本金× 利率× 时间。
2. 复利（Compound Interest）：指不仅对本金计算利息，还将各期的利息加入本金再去计算下期利息的一种逐期滚动计算方式。
复利使得资金的增长速度更快，因为利息也在产生利息。
其计算公式为：终值= 本金× (1 + 利率)^时间。
四、年金的计算年金是指间隔期相等的系列等额收付款项，包括普通年金、预付年金、递延年金和永续年金等类型：1. 普通年金（Ordinary Annuity）：从第一期起，在一定时期内每期期末等额收付的系列款项。
其终值和现值的计算考虑了每期期末的等额收付。
2. 预付年金（Prepaid Annuity或Annuity Due）：从第一期起，在一定时期内每期期初等额收付的系列款项。
由于收付发生在期初，因此其终值和现值的计算需要考虑提前收付的影响。
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Example 4
You want to get a mortgage, but can only afford to pay $1,000 per month. How much can you borrow, if the interest rate is 5% annually for a 30 year mortgage?
Trustee Collateral Bond rating
Bond valuation formual
Bond prices and return current yield yield to maturity
Common stock valuation
Solution 1
A= $100 i = 6% per year compounded monthly, which = .5% interest per month = .005 n = the number of compounding time periods = 120 in 10 years. Substituting these values into the equation for the future value of an ordinary annuity: 100 * ((1+.005)120 -1)/.005 = $36,387.93
我国正在完善的城镇职工养老保险体系，是由 基本养老保险、企业年金和个人储蓄性养老保 险等三个部分组成。因此，企业年金被称为城 镇职工养老保险体系的“三个支柱”的重要组成 部分之一。 在实行现代社会保险制度的国家中，企业年金 已经成为一种较为普遍实行的企业补充养老金 计划，又称为“企业退休金计划”或“职业养老金 计划”，并且成为所在国养老保险制度的重要 组成部分。
年金的分类
年金按其每次收付款项发生的时点不同，可以 分为 普通年金（后付年金）、 即付年金（先付年金，预付年金）、 递延年金(延期年金)、 永续年金等类型。
企业年金的定义
企业年金是指在政府强制实施的公共养老金或 国家养老金之外，企业在国家政策的指导下， 根据自身经济实力和经济状况建立的，为本企 业职工提供一定程度退休收入保障的补充性养 老金制度。企业年金基金是指根据企业年金计 划筹集的资金及其投资运营收益形成的企业补 充养老保险基金。
1、普通年金 普通年金是指从第一期起，在一定时期内每期 期末等额收付的系列款项，又称为后付年金。 2、即付年金 即付年金是指从第一期起，在一定时期内每期 期初等额收付的系列款项，又称先付年金。即 付年金与普通年金的区别仅在于付款时间的不 同。
3、递延年金 递延年金是指第一次收付款发生时间与第一期 无关，而是隔若干期（m）后才开始发生的系 列等额收付款项。它是普通年金的特殊形式。 4、永续年金 永续年金是指无限期等额收付的特种年金。它 是普通年金的特殊形式，即期限趋于无穷的普 通年金。
Part 3 Annuity
4 types of annuity ordinary annuity; annuity due; deferred annuity; perpetuity
Annuity
annuity，年金，是定期或不定期的时间内一 系列的现金流入或流出。 参与年金计划是一种很好的投资安排，而提供 年金合同的金融机构一般为保险公司和国库券 等 比如你购买养老保险，其实就是参与年金合同。 年金终值包括各年存入的本金相加以及各年存 入的本金所产生的利息，但是，由于这些本金 存入的时间不同，所以所产生的利息也不相同。
Example 3
You win a $1,000,000 lottery, which is paid in annual installments of $50,000 over 20 years. How much did you really win, assuming that you could earn 5% interest, compounded annually?
DCF valuation
Three elements Three steps
Bond valuation
How many types of contractual provisions of a typical bond? What does par value mean? Coupon & coupon value Maturity
Valuation fundamental
Going-concern value Liquidation value Book value Market value Intrinsic value
Valuation approach
Questions , 1. How many valuation approaches in this paragraph? 2. What’s make a difference between DCF and market price? 3. How many relative valuations are referred?
Example 5 You want to borrow $200,000 to buy a house. What are the monthly mortgage payments if the interest rate is 6% for 30 years?
Solution 5
The interest rate for each month = .06/12 =.005 The number of months in 30 years = 12 x 30 = 360.
Example 2
A 20 year old wants to retire as a millionaire by the time she turns 70. (With life spans increasing, and the social security fund being depleted by baby boomers, the retirement age will have invariably risen by the time she reaches 65 years of age, probably to something even higher than 70, actually.) How much will she have to save at the end of each month if she can earn 5% compounded annually, tax-free, to have $1,000,000 by the time she is 70?
Solution 2
Since i = 5% = .05, and n = 50, the interest factor (1 + i)n - 1)/i = (1.0550 - 1)/.05 = 209.35, rounded to 2 decimal places. To find A, we divide both sides of the equation for the future value of an annuity by this interest factor, which yields 1,000,000/209.35 = $4,776.69. So she would have to save $4,776.69 dollars per year, or $398.06 per month, to have $1,000,000 in 50 years—assuming, of course, that she could save it tax-free!
Ordinary annuity& Annuity due
Ordinary annuity cash flows occur at the end of each time period. Annuity due cash flows occur at the beginning of each time period. Ordinary annuity compounding interest rate at the end that you can multiply all the "N". Annuity due compounding interest rate at the beginning and you have to multiply total "N1".
Solution 4
Solution: The monthly payments constitute an annuity, whose present value is the amount of the loan. Loan Amount = 1,000 * (1 - (1 + .004166667)-360)/.004166667 = $186,281.62 i = the monthly interest rate = .05/12 = .004166667. n = the number of months in 30 years = 12 x 30 = 360.
Bond valuation
Who can get benefit from following policy? Call provisions Sinking fund provisions Conversion rights Put provisions Indenture
பைடு நூலகம்
Bond valuation
Part 1 Central Concepts in Financial Management
How many central concepts in financial management? What’s central concepts in financial management?