Understanding the Time Value 0f Money（理解货币时间的价值）-外文翻译

Understanding the Time Value 0f Money（理解货币时间的价值）-外文翻译 理解货币的时间价值 Norman D. Gardner, Utah Valley State College 摘要 当今社会是一个商品经济社会，企业在激烈的市场竞争中要想生存与发展，就必须考虑到企业价值最大化，也就是企业在投资过程中实现经济效益的同时也要创造社会效益。货币时间价值就是企业长期投资决策必须考虑的一个重要因素，它所揭示的是在一定的时空条件下运动中的货币具有增值性的规律，这一规律普遍适用于当前的商品经济社会，对现代公司理财起重要的作用。 恭喜～你赢得现金大奖～你有两种付款方式: 答:?现在接收10,000元 ?三年接收10,000元 你会选择哪个选项, 时间价值是什么, 如果你像大多数人一样，你会选择现在获得10000美元。毕竟，三年是一个漫长的时间等待。任何理性的人为什么会推迟到未来付款时，他或她可能会产生同样数量的钱呢, 对于大多数人来说，采取本的钱简直是完全出于本能。因此，在最基本的层面上， 货币时间价值表明，所有的事情都是平等的，最好是有钱现在比晚通好。 但是，这是为什么,一个100美元的法案，从现在的100美元的帐单一年相同的值，不是吗,其实，虽然条例草案是一样的，你可以做更多的钱，如果你拥有了它与现在因为随着时间的推移，你可以赚更多的利息你的钱。 回到我们的例子:通过接收10,000元的今天，你正准备增加未来价值一段时间你的钱被一个以上的投资获得的利益。对于选项B中，你没有时间在你身边，并在三年内将收到您的未来价值付款。为了说明这一点，我们提供了一个时间表: 如果你是选择A，你的未来价值将10,000元，另加任何超过三年获得 的利益。对于方案B的未来价值，另一方面，只会10,000元。所以你怎么能计算出到底有多少个选择一个是值得的，比方案B,让我们来看看。 未来价值基础 如果您选择方案A，并投资于一个简单的4.5,，按年率计算的总金额，您的投资在第一年年底未来值是一零四五零美元，这当然是乘以利息10,000元的本金计算率4.5,，然后加利息获得的本金: 未来值在第一年年末投资: =(10,000美元× 0.045)+ $ 10,000 =10450美元 您还可以计算出一个具有上述方程的简便操作的一年，总投资金额: , 原方程:($ 10,000 × 0.045)+ $ 10,000 =10.45美元 , 操纵:10,000美元× [(1 × 0.045)+ 1] =1.045万美元 , 最后的:10,000元×(0.045 + 1)=1045美元 操纵上述公式是单纯的类似变量$ 10,000(本金)10,000元除以整个原始方程清除。 如果一万零四百五美元投资账户中留在第一年年底是左原封不动，你的投资额在4.5,的一年吧，你有多少,要计算这一点，你会采取一十点四五?美元和乘以1.045(0.045 1)一次。在两年后，你会一万零九百二十零美元: 未来值在第二年年底投资: =$10450×(1 +0.045) = $ 10,920.25 上述计算，那么，就等于公式如下: 未来价值= $ 10,000 ×(1 0.045)×(1 0.045) 回想课和指数规则，其中规定，如条件乘法相当于增加他们的指数。在上面的方程，这两个条款相同的是:(1 0.045)，并在每个指数等于1。因此，该方程可以表示如下: 我们可以看到，该指数等于它的年收入的钱是在投资感兴趣的地方。因此，计算三年的投资未来值计算公式是这样的: 这种计算告诉我们，我们并不需要计算一年后的未来价值，那么第二年，那么第三个年头，等等。如果你知道多少年，你想保持在目前的资金投资数额，这一数额的未来值是由下列公式计算: n 未来价值(终值)=P(1+i) 现值基础 如果您收到10,000元的今天，现值的做法，当然现值10,000元，因为你的投资是什么让你现在如果你今天花。如果10000美元，将在一年收到的金额的现值10,000元不会因为你没有在你的手，现在在目前的。若要查找您将收到10,000元在未来的现值，你需要假装10,000美元的总投资金额，你今天的未来价值。换句话说，找到未来的1万美元，我们需要找出多少我们今天要投资，以在将来获得10,000元的现值。 计算其现值，或金额，我们要投资的今天，你必须减去从10,000元(假设的)累计利息。要做到这一点，我们可以打折的未来付款期内利率金额(000美元)。从本质上讲，你正在做的是重新安排上述方程因此未来值，您也许能解决体育的未来值以上方程可重写取代变量与P 的现值 (PV)和操作如下: n 原方程:FV=PV*(1+i) n 操纵:两边都除以(1+i) -n 最终方程:PV=FV*(1+i) 让我们看一下从美元的方案B提供记住万，1万美元将在三年来收到向后是真正的作为一个投资的未来值相同。如果今天我们在两年的标志是，我们会回来的付款折扣一年。在为期一年大关的同时，现值1万美元将在一年内收到的代表作为如下: -1 现值(10,000元支付在未来一年二月底)=$10000*(1+0.045) =$9569.38 请注意，如果今天我们在为期一年的标志是，9,569.38美元以上的将被认为从现在起，我们的投资一年未来的价值。 继续进行，在第一年，我们将期待在两年内获得10 000美元酬金。在一个4.5,的利率，为预期在两年内支付1万美元的现值计算将是如下: -2现值=$10000*(1+0.045)=$9157.3 当然，由于指数的规则，我们不必计算未来价值的投资每年都在数从10,000元，第三年收回投资。我们可以把更简洁的公式，并以此作为公允价值10000美元。所以，这里是如何计算今天的美元从3年收入4.5,的投资预计1.0万现值: -3 现值=$10000*(1+0.045) =$8762.97 因此，未来一万元付款的现值的价值为8,762.97今天，如果利率为4.5,的速度递增。换句话说，选择方案B更像是走$ 8,762.97现在，然后投资了三年。上述公式说明，一个是更好的选择，不仅因为它提供了你的钱，但现在，因为它提供您$ 1,237.03($ 10,000 - $ 8,762.97)现金更多～此外，如果你投资10000美元，您从方案A收到，您的选择给你一个未来的价值是$ 1,411.66($ 11,411.66 - $ 10,000)，比期权的未来价值B.大于 现值的远期付款 让我们添加一些香料公司的投资知识。如果在三年内支付的金额比今天你收到吗,或者说你可以得到15,000元今天或1.8万美元的四年。你会选择哪一个,如果您选择接受15,000元今天的整个投资额，你实际上可能最后得到的现金数额在四年低于18000美元。你可以找到15,000元的未来价值，但由于我们总是生活在现在，让我们找到了18,000元的现值如果利率目前为4,。请记住，对当前值的计算公式如下: -n PV=FV*(1+i) 在上述公式，所有我们正在做的是，扣除投资的未来值。使用以上，在四年付款的现值18,000元的数字可以计算如下: -4 现值= $18000*(1+0.04) =$15386.48 从上面的计算我们现在知道我们的选择与接受$ 15,000或$ 15,386.48今天。当然，我们应该选择推迟了四年付款～ 结论 这些计算结果表明，从字面上时间就是金钱 - 的钱你现在的价值是不一样的，因为它将在未来，反之亦然。因此，重要的是要知道如何计算的金钱，使您 可以区分的投资，为您提供在不同的时间价值时间价值的回报。 Understanding The Time Value Of Money Norman D. Gardner, Utah Valley State College Abstract In today's society is a commodity economy society, the enterprise in the fierce competition in the market to survival and development, it is necessary to consider the maximization of enterprise value, also is the enterprise in the investment process to realize economic benefits while also to create social benefits. The currency time value is enterprise long-term investment decision-making must be considered one of the most important factors, it reveals it is in a certain time-space conditions movement of money has value-added rule, this rule is widely used in the current commodity economy society, modern corporate finance to play an important role. Congratulations!!! You have won a cash prize! You have two payment options: A.Receive $10,000 now OR B. Receive $10,000 in three years Which option would you choose? What Is Time Value? If you're like most people, you would choose to receive the $10,000 now. After all, three years is a long time to wait. Why would any rational person defer payment into the future when he or she could have the same amount of money now? For most of us, taking the money in the present is just plain instinctive. So at the most basic level, the time value of money demonstrates that, all things being equal, it is better to have money now rather than later. But why is this? A $100 bill has the same value as a $100 bill one year from now, doesn't it? Actually, although the bill is the same, you can do much more with the money if you have it now because over time you can earn more interest on your money. Back to our example: by receiving $10,000 today, you are poised to increase the future value of your money by investing and gaining interest over a period of time. For Option B, you don't have time on your side, and the payment received in three years would be your future value. To illustrate, we have provided a timeline: If you are choosing Option A, your future value will be $10,000 plus any interest acquired over the three years. The future value for Option B, on the other hand, would only be $10,000. So how can you calculate exactly how much more Option A is worth, compared to Option B? Let's take a look. Future Value Basics If you choose Option A and invest the total amount at a simple annual rate of 4.5%, the future value of your investment at the end of the first year is $10,450, which of course is calculated by multiplying the principal amount of $10,000 by the interest rate of 4.5% and then adding the interest gained to the principal amount: Future value of investment at end of first year: = ($10,000 x 0.045) + $10,000 = $10,450 You can also calculate the total amount of a one-year investment with a simple manipulation of the above equation: , Original equation: ($10,000 x 0.045) + $10,000 = $10,450 , Manipulation: $10,000 x [(1 x 0.045) + 1] = $10,450 , Final equation: $10,000 x (0.045 + 1) = $10,450 The manipulated equation above is simply a removal of the like-variable $10,000 (the principal amount) by dividing the entire original equation by $10,000. If the $10,450 left in your investment account at the end of the first year is left untouched and you invested it at 4.5% for another year, how much would you have? To calculate this, you would take the $10,450 and multiply it again by 1.045 (0.045 +1). At the end of two years, you would have $10,920: Future value of investment at end of second year: = $10,450 x (1+0.045) = $10,920.25 The above calculation, then, is equivalent to the following equation: Future Value = $10,000 x (1+0.045) x (1+0.045) Think back to math class and the rule of exponents, which states that the multiplication of like terms is equivalent to adding their exponents. In the above equation, the two like terms are (1+0.045), and the exponent on each is equal to 1. Therefore, the equation can be represented as the following: We can see that the exponent is equal to the number of years for which the money is earning interest in an investment. So, the equation for calculating the three-year future value of the investment would look like this: This calculation shows us that we don't need to calculate the future value after the first year, then the second year, then the third year, and so on. If you know how many years you would like to hold a present amount of money in an investment, the future value of that amount is calculated by the following equation: Present Value Basics If you received $10,000 today, the present value would of course be $10,000 because present value is what your investment gives you now if you were to spend it today. If $10,000 were to be received in a year, the present value of the amount would not be $10,000 because you do not have it in your hand now, in the present. To find the present value of the $10,000 you will receive in the future, you need to pretend that the $10,000 is the total future value of an amount that you invested today. In other words, to find the present value of the future $10,000, we need to find out how much we would have to invest today in order to receive that $10,000 in the future. To calculate present value, or the amount that we would have to invest today, you must subtract the (hypothetical) accumulated interest from the $10,000. To achieve this, we can discount the future payment amount ($10,000) by the interest rate for the period. In essence, all you are doing is rearranging the future value equation above so that you may solve for P. The above future value equation can be rewritten by replacing the P variable with present value (PV) and manipulated as follows: Let's walk backwards from the $10,000 offered in Option B. Remember, the $10,000 to be received in three years is really the same as the future value of an investment. If today we were at the two-year mark, we would discount the payment back one year. At the two-year mark, the present value of the $10,000 to be received in one year is represented as the following: Present value of future payment of $10,000 at end of year two: Note that if today we were at the one-year mark, the above $9,569.38 would be considered the future value of our investment one year from now. Continuing on, at the end of the first year we would be expecting to receive the payment of $10,000 in two years. At an interest rate of 4.5%, the calculation for the present value of a $10,000 payment expected in two years would be the following: Present value of $10,000 in one year: Of course, because of the rule of exponents, we don't have to calculate the future value of the investment every year counting back from the $10,000 investment at the third year. We could put the equation more concisely and use the $10,000 as FV. So, here is how you can calculate today's present value of the $10,000 expected from a three-year investment earning 4.5%: So the present value of a future payment of $10,000 is worth $8,762.97 today if interest rates are 4.5% per year. In other words, choosing Option B is like taking $8,762.97 now and then investing it for three years. The equations above illustrate that Option A is better not only because it offers you money right now but because it offers you $1,237.03 ($10,000 - $8,762.97) more in cash! Furthermore, if you invest the $10,000 that you receive from Option A, your choice gives you a future value that is $1,411.66 ($11,411.66 - $10,000) greater than the future value of Option B. Present Value of a Future Payment Let's add a little spice to our investment knowledge. What if the payment in three years is more than the amount you'd receive today? Say you could receive either $15,000 today or $18,000 in four years. Which would you choose? The decision is now more difficult. If you choose to receive $15,000 today and invest the entire amount, you may actually end up with an amount of cash in four years that is less than $18,000. You could find the future value of $15,000, but since we are always living in the present, let's find the present value of $18,000 if interest rates are currently 4%. Remember that the equation for present value is the following: In the equation above, all we are doing is discounting the future value of an investment. Using the numbers above, the present value of an $18,000 payment in four years would be calculated as the following: Present Value From the above calculation we now know our choice is between receiving $15,000 or $15,386.48 today. Of course we should choose to postpone payment for four years! (For related reading, see Anything But Ordinary: Calculating The Present And Future Value Of Annuities.) Conclusion These calculations demonstrate that time literally is money - the value of the money you have now is not the same as it will be in the future and vice versa. So, it is important to know how to calculate the time value of money so that you can distinguish between the worth of investments that offer you returns at different times.