技术经济学英文版演示文稿C2.ppt
《技术经济学英文版演示文稿C2.ppt》由会员分享,可在线阅读,更多相关《技术经济学英文版演示文稿C2.ppt(89页珍藏版)》请在三一文库上搜索。
1、2. TIME VALUE OF MONEY 2.1 Theory of Equivalence 2.2 Equivalence Relationship 2.3 Nominal and Effective Interest Rates 2.4 Continuous Payments 2.5 Gradient Equations for Continuous Payment,2.1 Theory of Equivalence(等值) In any decision making process, we have to account for the benefits and the costs
2、 of a project. In a typical project, the costs occur at the beginning of the project and the benefits accur over a period of time. For example, installation of a waterflood project results in benefits in terms of additional oil recovery over several future years.,However, to install waterflood, we m
3、ay have to incur sufficient costs at the present time. This money has to come from internal capital of a corporation or from a lending institute. Either way, by using internal capital or by borrowing money, we will either lose the opportunity to invest the money somewhere else or we will have to pay
4、 interest to the lending institution.,That is, instead of investing the money in a waterflooding project, we could have earned interest from a bank by investing that money in the bank; or, if we have borrowed the money to invest in this project, we have to pay interest on the borrowed amount. This l
5、ost opportunity (opportunity cost) or the interest payment has to be accounted for in our cost benefit analysis. One way to do this is through the understanding of the time value of money.,Money is a valuable commodity. People will pay you to use your money. You will have to pay someone to use their
6、 money. The cost of money is established and measured by an interest rate. Interest rate is periodically applied and added to(额外的) the amount (the principal) over a specific period of time.,For example, depositing $100 in the bank for one year may generate an interest of $6 at the end of the year. T
7、hat is, the bank has paid you 6% interest to use your money. In the same vane, the bank will turn around and lend that money to another individual and charge 10% interest. The borrower will have to pay back $110 at the end of one year. We can also say that, for you, $100 today is equivalent to $106
8、one year from now. For the bank, $100 today is equivalent to $110 one year from now. This principal is called a theory of equivalence.,This simple example clearly illustrates that money has an earning power. Just like any other commodity, money can be put to work and earn more money for its owner. B
9、ecause of this, a dollar received today is worth more than a dollar received one year from now. Todays dollar can be invested to earn more than one dollar one year from now.,2. l Theory of Equivalence Once we know that money is a valuable commodity and it has an earning power, we need to establish a
10、 method to compare the monies collected at different times. For example, if you have the option of receiving $100 today or $110 one year from now, what would you prefer? If you can only invest $100 in a bank at 5% interest rate, you can only earn $5 one year from now. That will total up to $100 + $5
11、 = $105 one year from now. Obviously, $105 is less than $110 you could receive one year from now. Therefore, you would prefer $110 one year from now.,The economic equivalence is also affected by the time. Consider the extension of the previous example. If some one offers you $100 today, $110 one yea
12、r from now or $121 two years from now, which one would you prefer? As before, It depends on what you can do with the $100 you will have today. If you invest it at 5% interest rate, after one year you will have $100 + $100(.05) = $105 After two years, you will have $105+ $105(.05) = $110.25 Since $11
13、0.25 is smaller than $121, you would prefer $121 two years from today. On the other hand, if you can earn 25% interest rate, you will have, after one year $100 + $100(0.25) = $125 and after two years $125 + $125(0.25) = $156.25,Think about why this principle is so important. When conducting the cost
14、 benefit analysis of any project, if the benefits are received in the future, we cannot directly compare the present costs to the future benefits unless we can convert the future benefits to equivalent present benefits; or, in the alternative, we will have to convert the present cost to equivalent f
15、uture costs. In this chapter, we will learn how we can accomplish this task.,2.2 Equivalence Relationships To understand the theory of equivalence in a more rigorous way, we need to establish certain relationships starting from some basic parameters. We can define these parameters as: P = present su
16、m of money F = future sum of money A = end of period cash payment or receipt i = interest rate per period n = number of periods,In addition to defining the necessary parameters, we will also define the cash flow diagrams we will be using in this book. The cash flow diagram represents the cash flow p
17、rofile during the life of the project. For example, after investing $10,000 at the beginning of the project, if we receive $3,000 each year in benefits for five years, we can draw the cash diagram as in Figure 2.1.,In this cash flow diagram, the horizontal line represents the time scale; the arrows
18、signify cash flows and are placed at the end of period. Upward arrows represent cash receipts (benefits), whereas the downward arrows represent expenses (costs). Note that cash flow diagram is a function of whose point of view it represents.,0 1 2 3 4 5,2.2.1 Relationship Between P and F The cash fl
19、ow diagram for establishing the relationship between the present sum and the future sum can be drawn as in Figure 2.4.,0 1 2 3 n-1 n,P,F,Figure 2.4: Relationship Between P and F,(1) P, i, n-F=? after one period P+Pi=P(1+i) If we continue to invest the new principal, p(l + i), for another period , af
20、ter n periods, (2.1),(2) F, i, n- P =?,0 1 2 3 n-1 n,P,F,Figure Relationship Between P and F,Example 2.2 If you need $10,000 after 5 years, how much should you invest today at an interest rate of 10%? Solution Given: F = $10.000, n = 5 years, i = 10% Find: P,Eq. 2. I can also be written as,Using Eq.
21、 2.2, You need to invest $6,209 today.,Example 2.3 If you invest $4,000 in a bank at an interest rate 6.25%,the money would you have at the end of three years? Solution Given: P = $4,000, n = 3 years, i = 6.25%, Find: F Using Eq. 2.1 You will have $4,798 after three years.,Example 2.4 If you want to
22、 invest $3,000 at an interest rate of 7%, how long will it take to double the initial investment? Solution Given: P = $3,000, F = $6,000, i = 7% Find: n Using Eq. 2.1, Taking log on both sides The amount will double in 10.2 years.,Thumb of rule (rule of 72),2.2.2 Relationship Between A and F Let us
23、extend the previous relationships to a case where a payment is made at the end of each period. We would like to calculate the future value of these payments at the end of the total period. Cash flow diagram for this arrangement is shown in Fig. 2.5.,Figure 2.5: Periodic Payments,F n,0 1 2 3 n-1,A A
24、A A A,(3) A, i, n-F=? Considering that for the first payment, we earned interest for (n - l) periods (see Fig. 2.6), and for the last payment we earned no interest, using Eq. 2.l, we can write, (2 3) multiplying Eq. 2.3 by (l + i), (2.4) subtracting Eq. 2.3 from Eq. 2.4 and rearranging, we obtain,Th
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- 技术 经济学 英文 演示 文稿 C2
链接地址:https://www.31doc.com/p-2643306.html