lecture 03 time value, interest rate and risk premia
Lecture 3 interest rates
Current nominal Interest rates for
banking in Chinese banks (/)
Term n(year)
Interest rate of saving
1/4
1/2
1
2
3
5
3.33 3.78 4.14 4.68 5.4 5.85
– imonth=0.8%; – i(4)=10.00%; – d= 9.5%
Practice
For each kind of following nominal interest rates calculate its annual effective rate: Current Interest rates for banking in Chinese
The nominal rate of interest over a given time period is usually given by a financial institution the nominal rate of interest per unit time payable pthly is p times of the effective rate of interest i for the period of length 1/p: i(p) = i×p Nominal rates or expressing rates from banks
An immediate annuity
1
t1
A(t1, t2)
t2
A(t1, t2)
1 t1
t2
Examples
Ex.1. If the nominal rate of interest convertible monthly for the first half year is 18% and that convertible quarterly for the next half year is 20% . Calculate:
Chapter 3 The Time Value of Money 货币的时间价值 财务管理(双语版) 教学课件
年金现值：PVAn（Present Value of an Ordinary Annuity）
n 1
11i n
PV nR A t 11it R i
R PVi,nI
PVIFAi,n 年金现值系数（the Present Value Interest Factor of an Annuity at i for n periods）
P0V P 0FnV 1inFnV PVi,nIF
7. PVIFi,n : （the Present Value Interest Factor at i for n
periods）
8.
复利现值系数，利率为i,期数为n
6. Annuities 年金
系列、等额的收付
Ordinary Annuity 普通年金 收付款发生于每期期末 Annuity Due 预(即)付年金 收付款发生于每期期初
Perpetuity 永续年金
无限期支付的普通年金
Ordinary Annuity(普通年金)
0
R
R
R
R
年金终值：FVAn（Future Value of an Annuity）
FV nR A t n11intR1iin1RFVi,nIFA
FVIFAi,n 年金终值系数（the Future Value Interest Factor of an Annuity at i for n periods）
1
每年计息一次时产生的利息=名义利率每年计息m次时产生的利息
FV n A R F DV i,n 1 I 1 FA
现值 （Present Value）
比普通年金少折现一期
PV n A R P D V i,nI 1 F i A
lecture 3
What is Margin?
Margin includes three components: the Margin Loan, the Margin Deposit and the Margin Requirement. The Margin Loan is the amount of money that an investor borrows from his broker to buy securities. The Margin Deposit is the amount of equity contributed by the investor toward the purchase of securities in a margin account. The Margin Requirement is the minimum amount that a customer must deposit and it is commonly expressed as a percent of the current market value. Their relation is expressed as: Margin Loan + Margin Deposit = Market Value of Security
9
B. Short Selling
In a short sale, the investor borrows a security, say a stock, from his broker, and sells it. The short seller must buy back the security (or “cover the short position”) later and return it to the broker. If the price at which the investor covers his short position is lower than the price he sold it short, then he realizes profits. Otherwise, the investor loses.
货币的时间价值chapter3-Timevalueofmoney专题培训课件
Compounding and Discounting of Single Sums
Annuities Types of Interest Rates
3-1
To find the answer, you’ll have to know
worth more than $1 in the future.
This is due to opportunity costs.
The opportunity cost of receiving
$1 in the future is the interest we
could have earned if we had
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
After n years (general case):
3-5
Time lines
0
1
2
3
i%
CF0
CF1
CF2
CF3
Show the timing of cash flows.
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.
货币时间价值 主要参数
货币时间价值主要参数货币时间价值（Money Time Value，MTV）是一个基本的财务概念，用于衡量货币在不同时间点的价值。
在金融领域，MTV是计算投资回报率、债务利息、现金流量等重要财务指标的基础。
了解和应用MTV对于个人和企业做出明智的财务决策至关重要。
主要参数是指在计算MTV时所需的重要因素和数值。
这些参数包括现值（Present Value，PV）、未来值（Future Value，FV）、利率（Interest Rate，R）和时间（Time，T）。
在计算MTV时，这些参数相互关联，通过不同的组合和计算方法可以得出MTV的数值。
现值（PV）是指在未来某个时间点的一笔或一系列现金流的现在价值。
在计算MTV时，PV是一个重要的参数，它代表了货币在未来的时间价值，即未来的一笔现金流在当前时点的价值。
PV的计算可以使用现值因子（Present Value Factor，PVF）和未来值来进行，PV = FV / (1 + R)^T，其中，FV是未来值，R是利率，T是时间。
未来值（FV）是指在当前时点的一笔或一系列现金流在未来某个时间点的价值。
FV是计算MTV时的另一个重要参数，它代表了货币在未来的时间价值，即当前时点的一笔现金流在未来时点的价值。
FV的计算可以使用未来值因子（Future Value Factor，FVF）和现值来进行，FV = PV x (1 + R)^T，其中，PV是现值，R是利率，T是时间。
利率（R）是计算MTV时的关键参数之一，它代表了货币的时间价值。
利率是指单位时间内的货币增长率，通常以百分比表示。
利率的大小直接影响到货币的时间价值，较高的利率意味着货币的时间价值更高，而较低的利率则意味着货币的时间价值较低。
利率的选择对于个人和企业的投资决策至关重要，需要考虑风险、通货膨胀和市场状况等因素。
时间（T）是计算MTV的另一个关键参数，它代表了货币的时间跨度。
时间的大小直接影响到货币的时间价值，较长的时间意味着货币的时间价值更高，而较短的时间则意味着货币的时间价值较低。
货币时间价值英语PPT演示文稿
0
1
2
3
4
5
F V 2 1 0 0 1 0 .1 0 1 0 .1 0 1 2 1
or
F V 2 1 0 0 1 0 .1 0 2 1 2 1
7
Generalizing the Future Value
• Recognizing the pattern that is developing, we can generalize the future value calculations as follows:
• In other words, the amount of interest earned each year is increasing
– Year 1: $10 – Year 2: $11 – Year 3: $12.10
• The reason for the increase is that each year you are earning interest on the interest that was earned in previous years in addition to the interest on the original principle amount
10
The Magic of Compounding
F V N P V 1 iN
If you extended the investment for a third year, you would have:
F V 3 1 0 0 1 0 .1 0 3 1 3 3 .1 0
8
Compound Interest
• Note from the example that the future value is increasing at an increasing rate
Lecture 5 - The Time Value of Money - Making Investment Decisions I
Substituting:
Tt ( Rt Et Dt )
Into:
X t Rt Et It Tt
Yields the following expression for the firm’s cash flow in period t:
X t (1 )( Rt Et ) Dt It
When calculating depreciation, important to note that:
•
it
is
•
Sales tax, delivery charges and installation are treated as being part of the cost of equipment and are added to the cost of the asset for the purpose of calculating depreciation; In some jurisdictions it is possible to depreciate an asset down to zero even if it has a salvage value. However, in this course, if the equipment has a salvage value at the end of its useful life, the asset is depreciated down to this value. Consider the following example:
If an asset costs $20,000, has an estimated salvage value of $5,000 and a useful life of 5 years, the annual straight-line depreciation charge is calculated as:
Lecture 2 The time value of money
Time value
How
much one dollar today can earn during the year，in a economic activity?
interest interest rate
Composing of interest rate
With
a Compound interest i, which of the followings would prefer?
$C at 0; $C (1+i)n at n.
Remarks
at 0 is equivalent to $ C (1+i)n at n; Or $C/ (1+i)n at 0 is equivalent to $ C at n; or $1/ (1+i)n at 0 is equivalent to $ 1 at n.
What is An?
Simple interest
? years
1 2 …… n
Capital + interest
A1=C+Ci =C（1+i） A2=C+2Ci =C（1+2i） …… An=C+nCi =C（1+ni）
interest
Ci 2Ci …… nCi
The future value of $1 today is linear to the length of time under simple interest rate
Simple interest： simple interest can not earn further interest.
高一英语经济理论单选题50题
高一英语经济理论单选题50题1.The main difference between GDP and GNP is that GDP measures the value of goods and services produced within a country's borders,while GNP measures the value of goods and services produced by a country's residents,regardless of where they are located.Which one is more focused on domestic economic activity?A.GDPB.GNP答案：A。
GDP 是国内生产总值，衡量的是一国境内生产的产品和服务的价值，更侧重于国内的经济活动。
GNP 是国民生产总值，衡量的是一国居民生产的产品和服务的价值，不论其在何处生产。
2.Inflation and deflation are two economic phenomena.Which one is characterized by a general increase in prices?A.InflationB.Deflation答案：A。
Inflation 通货膨胀的特点是物价普遍上涨。
Deflation 通货紧缩的特点是物价普遍下降。
3.The supply and demand determine the price of goods.Which one refers to the amount of a good that producers are willing and able to sell?A.SupplyB.Demand答案：A。
Supply 供给是指生产者愿意并且能够出售的商品数量。
Demand 需求是指消费者愿意并且能够购买的商品数量。
Lecture-Options(1)
Portfolios A S(t)
Value at time t V(t)
Value at at time T V(T) S(T)
期权的分类：按期权买者的权利划分
A call option (看涨期权) gives its holder the right to purchase an asset for a specified price, on or before some specified expiration date.
Specification of Options
Expiration date Underlying asset Strike price European or American Call or Put
Opt bought the option is said to be in the long position (多头头寸), the party who sold (or wrote) the option is said to be in short position (空 头头寸).
Calls: An Arbitrage Opportunity?
Suppose that c=3 T=1 K = 18
S0 = 20 r = 10% D=0
Is there an arbitrage opportunity?
Bounds for European Call Option Prices; No Dividends
Profit from buying an IBM European put option: option premium = $7, strike price = $70
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1 2.
3.
消费价格指数
index) （或者生活成本指标）
例如，假设在某一年，名义利率是7%，消费
例子：
为
Assumed Number of Yuan Purchasing Annualized 单利
复利
5、贴现（几种特殊的现金流Perpetuity Growing Perpetuity Annuity
到期收益率6. 6.1 息，每次支付的利息为，债券的价P m C
三种国库券分别称为年到期，在到期日，投资者获得元。
同样地，债券B 两年到期，在到期日，投资者获得r A %
7=r
到期收益率。
价格
500
6.2
即期利率(spot rate)是零息债券的到期收
债券A：即期利率是满足下面方程的的值
本金一次性支付。
这个投资过程所获得的利率即为即期利率。
一般来说，如果以年为计()t
t
S +
1
远期利率6.3 ()2
和即期利率
7.
券的种类太少（事实上，没有真正严格意义上的长期
限的零息债券），所以，这种方法并不切实可行。
例：零息收益曲线的确定
例子
例子：折现因子
期限
例子即期利率与将来每一年的利率
即期利率与将来每一年的利率Observed Long-Term Rates 例子中的远期利率
在第一年的持有期收益率
的关系利率期限结构的不同形态。