ch06 Time Value of Money 财务管理基础课件
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财务管理基础课件：The Time Value of Money
A generalized formula for Future Value:
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
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
3章 Time Value of Money 学习课件,财务管理英文版
Banks say “interest paid daily.” Same as compounded daily.
After 1 year:
FV1 = PV + INT1 = PV + PV (i) = PV(1 + i) = $100(1.10) = $110.00.
After 2 years:
FV2 PV(1 + i)2 = $100(1.10)2 = $121.00.
After 3 years: FV3 = PV(1 + i)3 = $100(1.10)3 = $133.10.
100
Switch from “End” to “Begin”. Then enter variables to find PVA3 = $273.55.
INPUTS 3 10
100 0
N I/YR PV PMT FV
OUTPUT
-273.55
Then enter PV = 0 and press FV to find FV = $364.10.
Excel Function for Annuities Due
Change the formula to: =PV(10%,3,-100,0,1)
The fourth term, 0, tells the function there are no other cash flows. The fifth term tells the function that it is an annuity due. A similar function gives the future value of an annuity due:
N I/YR PV PMT FV
After 1 year:
FV1 = PV + INT1 = PV + PV (i) = PV(1 + i) = $100(1.10) = $110.00.
After 2 years:
FV2 PV(1 + i)2 = $100(1.10)2 = $121.00.
After 3 years: FV3 = PV(1 + i)3 = $100(1.10)3 = $133.10.
100
Switch from “End” to “Begin”. Then enter variables to find PVA3 = $273.55.
INPUTS 3 10
100 0
N I/YR PV PMT FV
OUTPUT
-273.55
Then enter PV = 0 and press FV to find FV = $364.10.
Excel Function for Annuities Due
Change the formula to: =PV(10%,3,-100,0,1)
The fourth term, 0, tells the function there are no other cash flows. The fifth term tells the function that it is an annuity due. A similar function gives the future value of an annuity due:
N I/YR PV PMT FV
ch06 Time Value of Money 财务管理基础课件
INPUTS
3
10
100
0
N
I/YR PV PMT FV
OUTPUT
-248.69
6-14
Solving for FV: 3-year annuity due of $100 at 10%
Now, $100 payments occur at the beginning of each period.
PV = FVn / ( 1 + i )n PV = FV3 / ( 1 + i )3
= $100 / ( 1.10 )3 = $75.13
6-9
Solving for PV: The calculator method
Solves the general FV equation for PV. Exactly like solving for FV, except we
The PV shows the value of cash flows in terms of today’s purchasing power.
0
1
2
3
10%
PV = ?
100
6-8
Solving for PV: The arithmetic method
Solve the general FV equation for PV:
Ordinary Annuity
0
1
2
3
i%
PMT
PMT
Annuity Due
0
1
2
i%
PMT 3
PMT
PMT
PMT
6-12
Solving for FV: 3-year ordinary annuity of $100 at 10%
二-财务管理基础价值观PPT课件
×(1+i )-m
.
21
§2.1资金的时间价值
公式二
1-(1+i)-(m+n) 1-(1+i)-m
P=A i –A i
4.永续年金计算（讨论其终值特点）
现值
A P=
i
.
22
第二节、投资的风险价值
• 一、 风险及风险报酬 • 二、 投资风险的类别 • 三、 单项资产的风险和报酬
.
23
一、 风险及风险报酬
相反，却将该公司告上了法庭，为什么
呢？原来该公司奖励的100万美元，不是
即时付清，而采用分20年、每年5万美元
支付。 这两种支付方式有何不同？对获
奖者的收益有影响吗？有多大的影响？
（分期花费，买房）.
2
• 提问：今天的1元钱与明天的1元钱（从经 济价值或效用上说）哪个更值钱？ （讨论）
• 又如： 石油勘探企业已探明一有工业价值 的油田，如目前立即开发可获利100亿元， 如5年后开发，由于价格上涨，可获利160 亿元。那么企业该如何决策？
.
8
名义利率与实际利率
i = (1+r/m)m-1
i—实际利率 r—名义利率 m—每年复利次数
§2.1资金的时间价值
.
9
• 例：
1.将10万元用于投资报酬率为15%的项目， 计算20年后（1）以单利计算的本利和（2） 以复利计算的本利和
2.某人拟在5年后获得本利和100000元， 假设投资报酬率（存款利率）为10%，他 现在应投入多少元？
第二章、财务管理的基础价 值观 ——资金 的时间价值、
投资的风险价值
第一节、 资金的时间价值@ 第二节、投资的风险价值@
《财务管理基础》PPT课件_OK
• V≤B, S=0,
非财务2人02员1/的8/财30务管理 Page 31
债权人索偿权≤ B
公司价值 （V）
31
3. 股东伤害债权人利益的具体表现
☆ 股东不经债权人同意，可能要求经营者改变借入资金的原定用 途，将其投资于风险更高的项目。
☆ 股东可能未征得债权人同意，而要求经营者发行新债券或举借 新债，致使债权人旧债价值降低。
非财务2人02员1/的8/财30务管理 Page 34
34
百年粘合剂老店富勒公司（H. B. Fuller): 客户第一，员工第二，股东第三，社区第四。这是我们的信条。
联想集团：
为客户：联想将提供信息技术、工具和服务，使人们的生活和工 作更加简便、高效、丰富多彩
为股东：回报股东长远利益 为员工：创造发展空间，提升员工价值，提高生活质量 为社会：服务社会文明进步
根据对待顾客（2）、雇员和社会责任三项
标准的分析显示：在这三方面得分最高的公 非财务2人02员1/的8/财30务管理 Page 23
23
财务管理的目标： 综合平衡各方面利益，实现真实价值增长。
非财务2人02员1/的8/财30务管理 Page 24
24
二、目标实施与代理问题
契约模型
股东
管理者
职工 社区
8. 如果能够出现一套全球统一的会计准则和财务报告标准，将大大简化企业的披 露成本。
CFO将成为企业战略的领导人与执行者
非财务2人02员1/的8/财30务管理 Page 9
9
学习与职业
角色：CFO、投资银行、投资公司、咨询 顾问
趋势：资本化（证券化）过程需要大量的 新一代财务精英
准备：CPA作、业C（F选A做）：职业生涯规划
财务管理基础观念1课件
财务管理基础观念(1)
*
普通年金
普通年金又称后付年金，是指发生在每期期末的等额收付款项，其计算包括终值和现值计算。
财务管理基础观念(1)
*
普通年金终值公式 :
F = A
i
i
n
1
)
1
(
-
+
称为普通年金终值系数或1元 年金终值，它反映的是1元年金在利率为i时，经过n期的复利终值，用符号（F/A，i，n）表示，可查“年金终值系数表”得知其数值。
财务管理基础观念(1)
*
某项目投资预计5年后可获利1000万元，假定投资报酬率为12%，现在应投入多少元？ P=1000 ×（P/F，12%，5) =1000 ×0.567=567（万元）
p =1000 × （1+12%）-5
财务管理基础观念(1)
*
年金
年金是指一定时期内等额、定期的系列收付款项。租金、利息、养老金、分期付款赊购、分期偿还贷款等通常都采取年金的形式。 年金按发生的时点不同，可分为普通年金、预付年金、递延年金和永续年金。
*
3．递延年金
递延年金是等额系列收付款项发生在第一期以后的年金，即最初若干期没有收付款项。没有收付款项的若干期称为递延期。
……
A
A
1
2
m
m+1
……
m+n
A
A
递延年金示意图
财务管理基础观念(1)
*
递延年金终值
递延年金终值的计算与递延期无关，故递延（p/A，i，n） × （p/F，i，m） 公式二： p=A[（p/A，i，m+n）-（p/A，i，m）]
i
i
n
)
*
普通年金
普通年金又称后付年金，是指发生在每期期末的等额收付款项，其计算包括终值和现值计算。
财务管理基础观念(1)
*
普通年金终值公式 :
F = A
i
i
n
1
)
1
(
-
+
称为普通年金终值系数或1元 年金终值，它反映的是1元年金在利率为i时，经过n期的复利终值，用符号（F/A，i，n）表示，可查“年金终值系数表”得知其数值。
财务管理基础观念(1)
*
某项目投资预计5年后可获利1000万元，假定投资报酬率为12%，现在应投入多少元？ P=1000 ×（P/F，12%，5) =1000 ×0.567=567（万元）
p =1000 × （1+12%）-5
财务管理基础观念(1)
*
年金
年金是指一定时期内等额、定期的系列收付款项。租金、利息、养老金、分期付款赊购、分期偿还贷款等通常都采取年金的形式。 年金按发生的时点不同，可分为普通年金、预付年金、递延年金和永续年金。
*
3．递延年金
递延年金是等额系列收付款项发生在第一期以后的年金，即最初若干期没有收付款项。没有收付款项的若干期称为递延期。
……
A
A
1
2
m
m+1
……
m+n
A
A
递延年金示意图
财务管理基础观念(1)
*
递延年金终值
递延年金终值的计算与递延期无关，故递延（p/A，i，n） × （p/F，i，m） 公式二： p=A[（p/A，i，m+n）-（p/A，i，m）]
i
i
n
)
财务管理价值基础课件(PPT 46页)
预付年金终值 ：
预付年金终值是指每期期初等额收付款项的复利终 值之和。
A
1
A
2
A…………A
A n-1
n
计
A·(1+i)1
算
示
A·(1+i)2
意
A·(1+i)n-2
图
A·(1+i)n-1
A·(1+i)n
预付年金终值公式推导过程：
FV先=A(1+i)1+A(1+…i)2…+ +A(…1+…i…)n
①
示 意
A·(1+i)-2
图
A·(1+i)-(n-2)
A
A
A…………A
A
1
2
n-1 n
A·(1+i)-(n-1)
预付年金现值公式推导过程： p=A+A(1+i)-1+A(1+i)-2+……+A(1+i)-(n-1) ………④ 根据等比数列求和公式可得下式：
p=A·11--
(1 (1
i)-n i) -1
P 10000 P A,10%,3
100002.4869 24,869
• (4)年资本回收额的计算（已知年金现值P，求年金 A）
• 例6 ：某公司以10%的利率借款20，000元，投资 于某个寿命为10年的项目，每年要至少收回多少 投资才是有利的？
A20000AP,10%,10200006.11446
第二章 财务管理价值基础
第一节 资金时间价值
二、资金时间价值的计算
（三）复利终值和现值 • 例：某项投资4年后可得收益40 000元。按年利率6%计
ch06 Time Value of Money 财务管理基础课件
PV = FVn / ( 1 + i )n PV = FV3 / ( 1 + i )3
= $100 / ( 1.10 )3 = $75.13
6-9
Solving for PV: The calculator method
Solves the general FV equation for PV. Exactly like solving for FV, except we
6-6
Solving for FV: The calculator method
Solves the general FV equation. Requires 4 inputs into calculator, and will
solve for the fifth. (Set to P/YR = 1 and END mode.)
The PV shows the value of cash flows in terms of today’s purchasing power.
0
1
2
3
10%
PV = ?
100
6-8
Solving for PV: The arithmetic method
Solve the general FV equation for PV:
INPUTS
3
10 -100
0
N
I/YR PV PMT FV
OUTPUT
133.10
6-7
What is the present value (PV) of $100 due in 3 years, if I/YR = 10%?
Finding the PV of a cash flow or series of cash flows when compound interest is applied is called discounting (the reverse of compounding).
= $100 / ( 1.10 )3 = $75.13
6-9
Solving for PV: The calculator method
Solves the general FV equation for PV. Exactly like solving for FV, except we
6-6
Solving for FV: The calculator method
Solves the general FV equation. Requires 4 inputs into calculator, and will
solve for the fifth. (Set to P/YR = 1 and END mode.)
The PV shows the value of cash flows in terms of today’s purchasing power.
0
1
2
3
10%
PV = ?
100
6-8
Solving for PV: The arithmetic method
Solve the general FV equation for PV:
INPUTS
3
10 -100
0
N
I/YR PV PMT FV
OUTPUT
133.10
6-7
What is the present value (PV) of $100 due in 3 years, if I/YR = 10%?
Finding the PV of a cash flow or series of cash flows when compound interest is applied is called discounting (the reverse of compounding).
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have different input information and are solving for a different variable.
INPUTS
3
10
0
100
N
I/YR PV PMT FV
OUTPUT
-75.13
6-10
Solving for N: If sales grow at 20% per year, how long before sales double?
Set calculator to “BEGIN” mode.
INPUTS
3
10
0
-100
N
I/YR PV PMT FV
OUTPUT
364.10
6-15
Solving for PV: 3 year annuity due of $100 at 10%
Again, $100 payments occur at the beginning of each period.
6-17
Solving for PV: Uneven cash flow stream
Input cash flows in the calculator’s “CFLO” register:
CF0 = 0 CF1 = 100 CF2 = 300 CF3 = 300 CF4 = -50
CHAPTER 6 Time Value of Money
Future value Present value Annuities Rates of return Amortization
6-1
Time lines
0
1
2
3
i%
CF0
CF1
CF2
CF3
Show the timing of cash flows.
INPUTS
3
10
0
-100
N
I/YR PV PMT FV
OUTPUT
331
6-13
Solving for PV: 3-year ordinary annuity of $100 at 10%
$100 payments still occur at the end of each period, but now there is no FV.
PV = FVn / ( 1 + i )n PV = FV3 / ( 1 + i )3
= $100 / ( 1.10 )3 = $75.13
6-9
Solving for PV: The calculator method
Solves the general FV equation for PV. Exactly like solving for FV, except we
Solves the general FV equation for I.
INPUTS
3
-100
0
125.97
N
I/YR PV PMT FV
OUTPUT
8
6-19
The Power of Compound Interest
A 20-year-old student wants to start saving for retirement. She plans to save $3 a day. Every day, she puts $3 in her drawer. At the end of the year, she invests the accumulated savings ($1,095) in an online stock account. The stock account has an expected annual return of 12%.
Tick marks occur at the end of periods, so Time 0 is today; Time 1 is the end of the first period (year, month, etc.) or the beginning of the second period.
To find the required annual contribution, enter the number of years until retirement and the final goal of $1,487,261.89, and solve for PMT.
INPUTS
25
12
Ordinary Annuity
0
1
2
3
i%
PMT
PMT
Annuity Due
0
1
2
i%
PMT 3
PMT
PMT
PMT
6-12
Solving for FV: 3-year ordinary annuity of $100 at 10%
$100 payments occur at the end of each period, but there is no PV.
Lesson: It pays to start saving early.
INPUTS
25
12
0 -1095
N
I/YR PV PMT FV
OUTPUT
146,001
6-22
Solving for PMT: How much must the 40-year old deposit annually to catch the 20-year old?
0
1,487,262
N
I/YR PV PMT FV
OUTPUT
-11,154.42
6-23
Will the FV of a lump sum be larger or smaller if compounded more often, holding the stated I% constant?
INPUTS
3
10
100
0
N
I/YR PV PMT FV
OUTPUT
-248.69
6-14
Solving for FV: 3-year annuity due of $100 at 10%
Now, $100 payments occur at the beginning of each period.
The PV shows the value of cash flows in terms of today’s purchasing power.
0
1
2
3
10%
PV = ?
100
6-8
Solving for PV: The arithmetic method
Solve the general FV equation for PV:
100
100
3
100
6-3
6-4
6-5
Solving for FV:
The arithmetic method
After 1 year: FV1 = PV ( 1 + i ) = $100 (1.10) = $110.00
After 2 years: FV2 = PV ( 1 + i )2 = $100 (1.10)2 =$121.00
How much money will she have when she is 65 years old?
6-20
Solving for FV: Savings problem
If she begins saving today, and sticks to her plan, she will have $1,487,261.89 when she is 65.
LARGER, as the more frequently compounding
occurs, interest is earned on interest more often.
0
1
2
3
10%
100 Annually: FV3 = $100(1.10)3 = $133.10
0
0
1
5%
1
2
3
2
4
5
133.10
3 6
100 Semiannually: FV6 = $100(1.05)6 = $134.01 134.01
6-24
Classifications of interest rates
Nominal rate (iNOM) – also called the quoted or state rate. An annual rate that ignores compounding effects.
Solves the general FV equation. Requires 4 inputs into calculator, and will
solve for the fifth. (Set to P/YR = 1 and END mode.)
INPUTS
3
10 -100
0
N
I/YR PV PMT FV
INPUTS
45
12
0 -1095
N
I/YR PV PMT FV
OUTPUT
1,487,262
6-21
Solving for FV: Savings problem, if you wait until you are 40 years old to start
If a 40-year-old investor begins saving today, and sticks to the plan, he or she will have $146,000.59 at age 65. This is $1.3 million less than if starting at age 20.
INPUTS
3
10
0
100
N
I/YR PV PMT FV
OUTPUT
-75.13
6-10
Solving for N: If sales grow at 20% per year, how long before sales double?
Set calculator to “BEGIN” mode.
INPUTS
3
10
0
-100
N
I/YR PV PMT FV
OUTPUT
364.10
6-15
Solving for PV: 3 year annuity due of $100 at 10%
Again, $100 payments occur at the beginning of each period.
6-17
Solving for PV: Uneven cash flow stream
Input cash flows in the calculator’s “CFLO” register:
CF0 = 0 CF1 = 100 CF2 = 300 CF3 = 300 CF4 = -50
CHAPTER 6 Time Value of Money
Future value Present value Annuities Rates of return Amortization
6-1
Time lines
0
1
2
3
i%
CF0
CF1
CF2
CF3
Show the timing of cash flows.
INPUTS
3
10
0
-100
N
I/YR PV PMT FV
OUTPUT
331
6-13
Solving for PV: 3-year ordinary annuity of $100 at 10%
$100 payments still occur at the end of each period, but now there is no FV.
PV = FVn / ( 1 + i )n PV = FV3 / ( 1 + i )3
= $100 / ( 1.10 )3 = $75.13
6-9
Solving for PV: The calculator method
Solves the general FV equation for PV. Exactly like solving for FV, except we
Solves the general FV equation for I.
INPUTS
3
-100
0
125.97
N
I/YR PV PMT FV
OUTPUT
8
6-19
The Power of Compound Interest
A 20-year-old student wants to start saving for retirement. She plans to save $3 a day. Every day, she puts $3 in her drawer. At the end of the year, she invests the accumulated savings ($1,095) in an online stock account. The stock account has an expected annual return of 12%.
Tick marks occur at the end of periods, so Time 0 is today; Time 1 is the end of the first period (year, month, etc.) or the beginning of the second period.
To find the required annual contribution, enter the number of years until retirement and the final goal of $1,487,261.89, and solve for PMT.
INPUTS
25
12
Ordinary Annuity
0
1
2
3
i%
PMT
PMT
Annuity Due
0
1
2
i%
PMT 3
PMT
PMT
PMT
6-12
Solving for FV: 3-year ordinary annuity of $100 at 10%
$100 payments occur at the end of each period, but there is no PV.
Lesson: It pays to start saving early.
INPUTS
25
12
0 -1095
N
I/YR PV PMT FV
OUTPUT
146,001
6-22
Solving for PMT: How much must the 40-year old deposit annually to catch the 20-year old?
0
1,487,262
N
I/YR PV PMT FV
OUTPUT
-11,154.42
6-23
Will the FV of a lump sum be larger or smaller if compounded more often, holding the stated I% constant?
INPUTS
3
10
100
0
N
I/YR PV PMT FV
OUTPUT
-248.69
6-14
Solving for FV: 3-year annuity due of $100 at 10%
Now, $100 payments occur at the beginning of each period.
The PV shows the value of cash flows in terms of today’s purchasing power.
0
1
2
3
10%
PV = ?
100
6-8
Solving for PV: The arithmetic method
Solve the general FV equation for PV:
100
100
3
100
6-3
6-4
6-5
Solving for FV:
The arithmetic method
After 1 year: FV1 = PV ( 1 + i ) = $100 (1.10) = $110.00
After 2 years: FV2 = PV ( 1 + i )2 = $100 (1.10)2 =$121.00
How much money will she have when she is 65 years old?
6-20
Solving for FV: Savings problem
If she begins saving today, and sticks to her plan, she will have $1,487,261.89 when she is 65.
LARGER, as the more frequently compounding
occurs, interest is earned on interest more often.
0
1
2
3
10%
100 Annually: FV3 = $100(1.10)3 = $133.10
0
0
1
5%
1
2
3
2
4
5
133.10
3 6
100 Semiannually: FV6 = $100(1.05)6 = $134.01 134.01
6-24
Classifications of interest rates
Nominal rate (iNOM) – also called the quoted or state rate. An annual rate that ignores compounding effects.
Solves the general FV equation. Requires 4 inputs into calculator, and will
solve for the fifth. (Set to P/YR = 1 and END mode.)
INPUTS
3
10 -100
0
N
I/YR PV PMT FV
INPUTS
45
12
0 -1095
N
I/YR PV PMT FV
OUTPUT
1,487,262
6-21
Solving for FV: Savings problem, if you wait until you are 40 years old to start
If a 40-year-old investor begins saving today, and sticks to the plan, he or she will have $146,000.59 at age 65. This is $1.3 million less than if starting at age 20.