# How do you Understand the Time Value of Money in Cost of Capital?

**What is the Time Value of Money?** If an individual behaves rationally, then he would not equate money in hand today with the same value a year from now. In fact, he would prefer to receive today than receive after one year. The time value of money or TVM is a basic financial concept that holds that money in the present is worth more than the same sum of money to be received in the future. The time value of money is the greater benefit of receiving money now rather than later. It is founded on time preference. **How do you Understand the Time Value of Money in Cost of Capital?**

**Here is explained the Time Value of Money in Cost of Capital.**

**Time value of money (TVM)** is the idea that money that is available at the present time is worth more than the same amount in the future, due to its potential earning capacity. This core principle of finance holds that provided money can earn interest, any amount of money is worth more the sooner it is received. The time value of money explains why interest is paid or earned: Interest, whether it is on a bank deposit or debt, compensates the depositor or lender for the time value of money. It also underlies investment. Investors are willing to forgo spending their money now only if they expect a favorable return on their investment in the future, such that the increased value to be available later is sufficiently high to offset the preference to have money now.

**The reasons cited by him for preferring to have the money today include:**

- The uncertainty of receiving the money later.
- Preference for consumption today.
- Loss of investment opportunities, and.
- The loss in value because of inflation.

The last two reasons are the most sensible ones for looking at the time value of money. There is a ‘risk-free rate of return’ (also called the time preference rate) which is used to compensate for the loss of not being able to invest in any other place. To this, a ‘risk premium’ is added to compensate for the uncertainty of receiving the cash flows.

**The required rate of return = Risk-free rate + Risk premium**

The risk-free rate compensates for the opportunity lost and the risk premium compensates for risk. It can also be called as the ‘opportunity cost of capital’ for investments of comparable risk. To calculate how the firm is going to benefit from the project we need to calculate whether the firm is earning the required rate of return or not. But the problem is that the projects would have different time frames of giving returns. One project may be giving returns in just two months, another may take two years to start yielding returns.

If both the projects are offering the same %age of returns when they start giving returns, one which gives the earnings earlier is preferred. This is a simple case and is easy to solve where both the projects require the same capital investment, but what if the projects required different investments and would give returns over a different period of time? How do we compare them? The solution is not that simple. What we do in this case is bring down the returns of both the projects to the present value and then compare.

*Before we learn about present values, we have to first understand future value.*

**Future Value:**

Future value is the amount that is obtained by enhancing the value of a present payment or a series of payments at the given rate of interest to reflect the time value of money. If we are getting a return of 10 % in one year what is the return we are going to get in two years? 20 %, right. What about the return on 10 % that you are going to get at the end of one year? If we also take that into consideration the interest that we get on this 10 % then we get a return of 10 + 1 = 11 % in the second year making for a total return of 21 %. This is the same as the compound value calculations that you must have learned earlier.

**Future Value = (Investment or Present Value) * (1 + Interest) No. of time Periods**

The compound values can be calculated on a yearly basis, or on a half-yearly basis, or on a monthly basis or on a continuous basis or on any other basis you may so desire. This is because the formula takes into consideration a specific time period and the interest rate for that time period only. To calculate these values would be very tedious and would require scientific calculators. To ease our jobs there are tables developed which can take care of the interest factor calculations so that our **formulas can be written as: **

**Future Value = (Investment or Present Value) * (Future Value Interest Factor n, i)**

where n = no of time periods and i = is the interest rate.

**Present Value:**

When a future payment or series of payments are discounted at the given rate of interest up to the present date to reflect the time value of money, the resulting value is called present value. When we solve for the present value, instead of compounding the cash flows to the future, we discount the future cash flows to the present value to match with the investments that we are making today. **Bringing the values to present serves two purposes:**

- The comparison between the projects become easier as the values of returns of both areas of today, and.
- We can compare the earnings from the future with the investment we are making today to get an idea of whether we are making any profit from the investment or not.

For calculating the present value we need two things, one, the discount rate (or the opportunity cost of capital) and two, the formula. The present value of a lump sum is just the reverse of the **formula of the compound value of the lump sum:**

**Present Value = Feature Value/(1 + i)n**

*Or to use the tables the change would be:*

- Present Value = Future Value * (Present Value Interest Factor n, i).
- where n = no of time periods and i is the interest rate.

**Perpetuity:**

If the annuity is expected to go on forever then it is called perpetuity and then the above formula reduces to:

**Present Value= A/i**

Perpetuities are not very common in financial decision making as no project is expected to last forever but there could be a few instances where the returns are expected to be for a long indeterminable period. Especially when calculating the cost of equity perpetuity concept is very useful.

**For growing perpetuity, the formula changes to:**

**Present Value= A/i – g**

All these calculations take into consideration that the cash flow is coming at the end of the period.

**Present Value of Future Money Formula:**

The formula can also be used to calculate the present value of money to be received in the future. You simply divide the future value rather than multiplying the present value. This can be helpful in considering two varying present and future amounts. In our original example, we considered the options of someone paying your $1,000 today versus $1,100 a year from now. If you could earn 5% on investing the money now, and wanted to know what present value would equal the future value of $1,100 – or how much money you would need in hand now in order to have $1,100 a year from now – the formula would be as follows:

**PV = $1,100 / (1 + (5% / 1) ^ (1 x 1) = $1,047**

The calculation above shows you that, with an available return of 5% annually, you would need to receive $1,047 in the present to equal the future value of $1,100 to be received a year from now. To make things easy for you, there are a number of online calculators to figure the future value or present value of money.

Time value of money principle also applies when comparing the worth of money to be received in future and the worth of money to be received in further future. Time value of money is the concept that the value of a dollar to be received in future is less than the value of a dollar on hand today. One reason is that money received today can be invested thus generating more money. Another reason is that when a person opts to receive a sum of money in future rather than today, he is effectively lending the money and there are risks involved in lending such as default risk and inflation.