现值是什么？

What is the present value?

<!-- @@@ -->

Present value (PV) is the current value of a future sum of money or series of cash flows. Its calculation is based on discounting future value at an estimated rate of return. The discount rate represents the rate of return that would have been earned had the money been invested. Present value calculations are of great significance in both investment and corporate strategic planning.

Key Points

• Present value (PV) is based on the concept that a certain amount of money today will tend to be more valuable than the same amount in the future because it can be invested and earn a profit in the meantime.
• Present value calculations require an estimate of the potential rate of return, which is called the discount rate.
• Since the discount rate can only be estimated, if the estimate is inaccurate, the present value calculation results will also be wrong.
• Investors can also calculate future value (FV) by applying the estimated rate of return to today's value.

Understand present value

The concept of present value holds that a specific amount of money today is usually worth more than the same amount in the future. This is called the time value of money. On the contrary, the current value of a certain amount receivable in the future is usually lower than this amount.

For example, $1,000 today should be worth more than$1,000 five years from now because $1,000 today can be invested and earn a return over those five years. Assuming an annual return of 5$1,000 will turn into approximately $1,276 in five years based on annual compound interest.

The present value calculation works in reverse. Assume you will receive $1,000 in five years (future value FV). How much is that money worth today? Based on the same annual return of 5$784. In this formula, the rate of return is called the discount rate. The term "discount" means converting future value into present value.

Present value formula and calculation

The formula for calculating the present value of a future sum of money is as follows:

<!-- @@@ -->

To calculate the present value of a series of future cash flows, you repeat this formula for each cash flow and then sum them. Fortunately, these days you can easily do this using software or an online calculator instead of having to do the calculations manually.

Determine the discount rate

As mentioned earlier, the discount rate is the rate of return used to make present value calculations. It represents the rate of return you give up if you choose to receive an amount in the future rather than the same amount today. The discount rate is highly subjective because it is only an estimate of the return you might earn over a period of time on money invested today.

In many cases, investors often choose the risk-free rate of return as the discount rate. This usually refers to the interest rate on U.S. Treasury bonds, as these are considered to be virtually risk-free because they are backed by the U.S. government.

The higher the discount rate you choose, the lower the present value will be because you are assuming a higher return on your money.

Benefits of Present Value

• Present value can clarify whether the expected rate of return on an investment is sufficient to make it worth pursuing. Businesses and investors often set a hurdle rate that represents the minimum rate of return they need to achieve.
• Present value helps investors and companies choose between different investments.

Limitations of present value

• Present value requires assumptions about discount rates, which may not be accurate.
• Because of these assumptions, present value calculations can also be manipulated by those who support a particular investment, such as corporate managers promoting older projects.

Note: You can also incorporate the potential effects of inflation into the present value formula by using what is called a real interest rate rather than a nominal interest rate.

Present value example

As a simple example, let's say you have the choice of receiving $2,000 today or$2,200 one year from now. You can expect to safely invest the $2,000 and earn a 3% return. Which option is better?

In this case, $2200 is the future value (FV), so the present value (PV) is calculated as 2200 ÷ (1 + 0.03)1. The result is$2135.92. So if you want to receive your payment now, you'd need to get at least $2,135.92 (not just$2,000) to break even.

Calculate future value and present value

In the present value formula above, we assume that you know the future value and need to calculate the present value.

When you know the present value, you can also calculate the future value, using the following formula: FV = PV x (1 + r)n.

Plug in the same numbers from the above example:

FV= 2000 × 1.03 = $2060.

From the calculation of present value and future value, $2,200 in one year will be more cost-effective than$2,000 now.

Of course, the results of both calculations also depend on the accuracy of the rate of return you choose.

How to calculate present value?

Present value is calculated using three data points: the expected future value, the interest rate likely to be earned on the investment, and the number of payment periods, such as 1 in the case of a one-year investment without compound interest.

Using the above information, you can calculate the present value using the formula:

<!-- @@@ -->

Present value example

Consider a scenario where you expect to receive a one-time payment of $5,000 in five years. If the discount rate is 8.25$3363.80.

Importance of present value

The importance of present value is that it allows investors and businesses to judge whether certain future outcomes are worth investing in today. This is particularly important when selecting potential investments, especially investments that are expected to pay off at various times in the future.

Conclusion

Present value is a way of expressing the current value of future funds or cash flows. While it's useful, it relies on making good assumptions about future returns, which can become particularly complex over longer periods of time.

References

[1] Investor.gov. "Compound Interest Calculator."

[2] Calculator.net. "Present Value Calculator."

[3] Investor.gov. "Treasury Securities."

[4] Calculator.net. "Present Value Calculator."

About TheQuantHackers

TheQuantHackers is a cutting-edge community composed of a group of people from the world's top universities and quantitative finance practitioners, dedicated to exploring the infinite possibilities in the fields of artificial intelligence (AI) and quantification (Quant). Our team members come from world-renowned universities such as the University of Cambridge, Oxford University, Harvard University, ETH Zurich, Peking University, and the University of Science and Technology of China. Our external consultants come from first-class companies such as Microsoft, HSBC, Citadel, Man Group, Citi, Jump Trading, and top domestic private equity companies.$\begin{aligned} &\text{现值} = \dfrac{\text{未来价值}}{(1+r)^n}\\ &\textbf{其中：}\\ &\text{未来价值} = \text{FV}\\ &r = \text{回报率}\\ &n = \text{时间周期数}\\ \end{aligned}$

若要计算未来一系列现金流的现值，需要对每笔现金流重复这一公式，然后将其总和。幸运的是，如今你可以使用软件或在线计算器轻松实现，而不必手动计算。

确定折现率

如前所述，折现率是进行现值计算所用的回报率。它表示如果你选择在未来接受一笔金额而不是今天的同样金额，那么你所放弃的回报率。折现率具有高度主观性，因为它仅是你在一段时间内投资今天的资金可能获得的回报率的估算。

在许多情况下，投资者通常会选择无风险回报率作为折现率。这通常是指美国国债的利率，因为这些国债被认为几乎没有风险，因为它们由美国政府背书。

你选择的折现率越高，现值就越低，因为你假设能够从资金中获得更高的回报。

现值的好处

• 现值可以明确某项投资的预计回报率是否足以使其值得追求。企业和投资者通常会设定一个障碍率，表示他们所需达到的最低回报率。
• 现值有助于投资者和公司在不同投资之间进行选择。

现值的局限性

• 现值需要对折现率作出假设，而这些假设可能并不准确。
• 由于这些假设的存在，现值计算也可能受到那些支持某项特定投资的人的操控，例如推动老项目的企业管理者。

注意： 通过使用所谓的实际利率而不是名义利率，你还可以将通货膨胀的潜在影响纳入现值公式中。

现值示例

作为一个简单的例子，假设你可以选择今天收到2000美元或者一年后收到2200美元。你预计可以安全地将这2000美元投资并获得3%的回报。哪个选项更好？

在这种情况下，2200美元是未来价值（FV），因此现值（PV）的计算公式为2200 ÷ (1 + 0.03)1。结果为2135.92美元。因此，如果你想现在收到款项，你至少需要获得2135.92美元（而不仅仅是2000美元）才能持平。

计算未来价值与现值

在上述现值公式中，我们假设你知道未来价值并需要计算现值。

当你知道现值时，也可以计算未来价值，使用如下公式：FV = PV x (1 + r)n。

将上述示例中的相同数字代入：

FV= 2000 × 1.03 = 2060美元。

从现值和未来价值的计算结果来看，等到一年后的2200美元会比现在的2000美元更划算。

当然，这两种计算的结果同样依赖于你选择的回报率是否准确。

如何计算现值？

现值是通过三个数据点进行计算的：预期的未来价值、投资时可能获得的利率，以及支付期数，例如在一年期的无复利投资情况下即为1。

利用上述信息，你可以使用公式计算现值：

$\begin{aligned} &\text{现值} = \dfrac{\text{未来价值}}{(1+r)^n}\\ &\textbf{其中：}\\ &\text{未来价值} = \text{FV}\\ &r = \text{回报率}\\ &n = \text{时间周期数}\\ \end{aligned}$ 现值（PV）是未来一笔资金或一系列现金流的当前价值。其计算基于将未来价值按estimated rate of return进行折现。如果这笔资金被投资，折现率代表了其可能获得的收益率。现值计算在投资和企业战略规划中均具有重要意义。

关键要点

• 现值（PV）基于一个概念：今天的一定数量的钱，往往会比未来的同样数量更有价值，因为它可以在此期间被投资并获得收益。
• 现值计算需要对潜在回报率进行估算，这被称为折现率。
• 由于折现率只能估计，如果估算不准确，现值计算结果也会出错。
• 投资者还可以通过将估计的回报率应用于今天的价值来计算未来价值（FV）。

理解现值

现值的概念认为，现今的一笔特定资金的价值通常会高于未来的同样金额，这被称作货币的时间价值。而反之，未来应收的一定金额，其当下价值通常低于这一金额。

例如，今天的1000美元应该比五年后的1000美元更有价值，因为今天的1000美元可以在这五年内进行投资并获得回报。假设年回报率为5%，按年复利计算，这1000美元在五年后大约能变成1276美元。

现值的计算则是反向的。假设你将在五年后收到1000美元（未来价值FV），那么今天这笔钱值多少呢？按照同样的年回报率5%计算，答案大约为784美元。在此公式中，回报率被称为折现率。"折现"一词表示将未来价值折算为现值。

现值公式及计算

计算未来一笔资金的现值的公式如下：