# What time value of money

### What is the time value of money (TVM)?

Definition:

Time value of money states that money received now is worth more than money received later.
Money can be used to make more money now. t.

## How to figure out the value of money over time

Money has a value over time because it can be used to earn more money. Consider this when comparing payments made or received at different times.
If you could earn 10% interest, \$100 today would be worth \$110 a year.
So, a \$110 payment a year ago is equivalent to a \$100 payment now. The \$10 in interest that \$100 could earn over that time period is its “time value.” Discounting is the process of turning a future payment into money that can be used now.

Example

Imagine that the interest rate at your bank was 10% per year. Assume you owed money to a friend. They offered to pay you back \$1,000 today or \$1,050 a year from today. Since putting that \$1,000 in the bank now would give you \$1,100 next year, you should take the immediate repayment. The time value of \$1,050 in a year is less than \$1,000 today.

### Takeaway

There are things you can do in your 20s that hurt when you are in your 40s. Just try hiking that mountain. The mountain hasn’t changed, but climbing it now requires more effort, agony, and dedication.
In 20 years, a \$100 bill will be worth substantially less due to inflation and interest earned on it.

### Why is the time value of money important?

When deciding whether or not to make an investment, the time value of money is a very important factor. Without taking time value into account, it would be hard to compare opportunities.

### Take this simple example:

You have the chance to buy a \$1,000 bond from a trustworthy company. They give you the option of getting \$1,100 in one year or \$1,200 in two years. Without considering the time value of money, the second option clearly offers a better return on your money (\$200 rather than \$100).

But you might notice that in either case, you get \$100 per year. You increase your return by \$100 by waiting an extra year. But if you bought that one-year bond, you could take the \$1,100 when it matured, buy another \$1,000 one-year bond the next year, and get the same \$100 return on the second year while having \$100 in your pocket. This is much better.

## Account for time value of money

The time value of money is the amount of money that you could earn between today and the time of a future payment. So, if you lend your brother \$2,500 for three years, you don’t just take \$2,500 out of your bank account until you get it back. The money you’re giving up also has a value in terms of time.

### In order to account for the lost earning power, you need three pieces of information.

• The amount of money that you will be giving up. This is how much you are investing or how much money you won’t be able to use for a while.
• how long you plan to give up the money. Compound interest tenfolds money’s time value.
Money’s value over time is high if the time period is more than a few years.
• Having a solid ROI means
The return on another investment with the same risk is a fair discount rate. . If the risk of investing in stocks is about the same as other investments, the average return from the stock market might be a good return. The return on U.S. Treasury bonds might be a good comparison if the investment is less risky. Whatever that other investment with a similar level of risk is, that’s how much money you’re not making while your money is locked up. So, its possible interest rate is a good way to measure how much time is worth. What time value of money

Use this formula to figure out how much your money is worth over time:

Future value = Current value x (1+ annual interest rate) ^ number of years

Let’s say that if your money stayed in your account, it would earn you a 5% return. By putting in the numbers from this example, we can figure out how much your money is worth over time.

Future value = \$2,500 x (1.05)^3 = \$2,894

In other words, over the three years of the loan, your \$2,500 would grow to \$2,894. So, if you only get back \$2,500, you’ve lost the value of that money over time. In this case, that is \$394 (\$2,894 – \$2,500).

## How do you figure out what the value is right now?

You may want to compare the payments you will get at different times in the future. Or, you might want to know how much a payment in the future is worth right now. To do this, you need to do the calculation for the value of money in the future backwards.

Instead of calculating interest on an investment now, you will have to figure how much you would have to invest now to get the same amount of money in the future.

The formula for doing this is:

Present value = Future value / (1+ annual interest rate) ^ number of years

For example, if you were to get a \$500 bond maturity payment in two years and the discount rate was 5%, you could use the present value formula as follows:

Present value = \$500 / (1.05)^2 = \$453.51

So, getting \$500 in two years is the same as putting \$453 in the bank today and earning 5% interest. If the most you could earn is 5% interest, you would make more money by buying the right to that future payment for less than \$453.

### What’s the difference between annual and perpetual compounding

How quickly the interest on an investment builds up will depend on how often it earns interest. One method that is often used is to figure out interest once a year. The interest rate is added to the balance at the end of the year. When you keep the account open for another year, you earn interest not only on the original deposit but also on the interest that is still in the account.

Interest may be due every six months, every three months, every month, or even every day. When interest is applied more often, the amount earned grows faster. The formula for figuring out these more frequent periods of compounding is:

Future Value = Present value * (1 + (annual interest rate / number of periods in the year)) ^ (number of years * number of periods in the year)

Compare the following table, which shows how a simple interest rate of 12% is calculated when compounded once a year and four times a year: It’s important to know that each interest payment is 3% (12% divided by 4 quarters).

 Annual Quarterly 1Q 2020 \$100.00 \$100.00 2Q 2020 \$100.00 \$103.00 3Q 2020 \$100.00 \$106.09 4Q 2020 \$100.00 \$109.27 1Q 2021 \$112.00 \$112.55 2Q 2021 \$112.00 \$115.93 3Q 2021 \$112.00 \$119.41 4Q 2021 \$112.00 \$122.99 1Q 2022 \$125.44 \$126.68 2Q 2022 \$125.44 \$130.48 3Q 2022 \$125.44 \$134.39 4Q 2022 \$125.44 \$138.42 1Q 2023 \$131.71 \$142.58

## What does “net present value” mean?

After taking into account the time value of money, the net present value (NPV) is the amount of money that a future stream of payments is worth in the present. It is also the amount of money you would have to invest today at a certain interest rate to get the same stream of payments in the future.

When trying to compare different income streams with different sizes and times, NPV is an important calculation. By putting both possible investments into the same unit of measure, they can be compared directly. What time value of money

### Here are two examples of payment plans:

 Option 1 Option 2 Year 1 \$100 \$500 Year 2 \$200 \$400 Year 3 \$300 \$300 Year 4 \$400 \$200 Year 5 \$500 \$100 Total \$1,500 \$1,500

### Both options provide the same amount of money over the same period of time.

But they are not of equal value. We can reveal the difference by calculating the NPV, which highlights the time value of money. To do so, calculate the present value of each payment, then sum them up. We used a 5% discount rate here.

 Option 1 (present values) Option 2 (present values) Year 1 \$100 \$500 Year 2 \$190 \$381 Year 3 \$272 \$272 Year 4 \$346 \$173 Year 5 \$411 \$82 NPV \$1,319 __\$1,408 __

Because the payments are bigger at the beginning of the series, option 2 is worth more than option 1. You can get a bigger return on your money if you reinvest those payments.

The net present value (NPV) is the amount of money you would need now to make all the payments in the table.If you pay the \$500 in the second year, you have less time to make money on the initial balance. So, you need to start with more money if you want to make those early payments that are bigger. What time value of money

In theory, the NPV is the most money that someone should be willing to pay for the income stream in question. When a business’s revenue stream is its future cash flow, this is often called the discounted cash flow (DCF).

## How do you choose the right rate of discount?

The amount of money’s earning power and how its buying power changes over time are directly related to its “time value.”The opportunity cost of that money is the best discount rate

The weighted average cost of capital is the proper discount rate for borrowing to invest (WACC).
As you pay to utilize money over time, you should use the cost of borrowing money as its value.

In simple analyses, round numbers like 10% are often used. As the discount rate, people often also use the prime rate, the average rate of return on stocks, or the current yield on U.S. Treasury bonds.

In other situations, a business might use a standard discount rate to compare different investments. When comparing different ways to spend money, it is important to use the same discount rate.

### When it comes to public finances

Discount rates are tougher to calculate.
People trade-off for the present, resulting in discount rates far higher than investments. Most of the time, a social discount rate is very low or even zero. What time value of money

People tend to have very high discount rates for themselves. Because people desire to live in the now, they have to make trade-offs that mean discount rates much greater than any investment could earn

For instance,, a person might choose to get \$100 now instead of \$200 in a year. That would mean that the person’s own discount rate is higher than 100%. This could be true for many reasons. The most important thing to note is that the need to meet current needs may be stronger than almost any interest rate could make up for.

There is no right answer to the question of which discount rate to use. That number depends on who is doing the analysis and what their specific situation is.

We will be happy to hear your thoughts