**In this lesson, you’re expected to learn about:**

– the time value of money

– calculating present and future values

– discounted cash flows

Money has a tendency to change in value over time. Thus, a constant quantity of money tends to be worth less as you hold onto it for longer periods of time.

The two primary causes for this decrease in value are * inflation *and

*. A number of variables influence these rates but these two forces are the most direct causes.*

**interest rates**In their ability to change the value of money over time, inflation and interest rates play an important role in how companies manage their liquid assets and their investments.

Thus, the ** time value of money** is an important concept that you need to understand in corporate finance.

**Time Value of Money**

https://www.youtube.com/watch?v=gkoEAPAW7eg

**Losing value over time**

**1) Nominal Value **

Nominal value is a measure of the number of units of currency that you have, i.e. the volume of money. For example, $10 has a nominal value of $10.

* 2) Real Value*Measures the ability of money to be exchanged in real terms for other things. Therefore, real value refers to the purchasing power of money, which includes nominal value plus inflation.

This distinction is important, as the goal of companies is to ensure that their nominal value increases faster than the real value of each unit of currency decreases. In other words, they want to make money faster than the money they have loses value.

**Nominal and Real Value of Money**

http://www.managementstudyguide.com/nominal-and-real-value-of-money.htm

*Let’s now look at the two main factors that cause money to change real value over time – the*

**inflation rate**and**interest rates**.**Inflation**

Inflation is when a currency’s ability to purchase goods (purchasing power) is diminished – when its purchasing power decreases, causing people to spend more units of currency to acquire an equal quantity of goods.

*So what impact does inflation have on finances after it has already occurred? *In essence, it’s quite simple. Let’s use an example.

Also, if inflation is 2% per year and you hold onto $100, over the course of 10 years, that $100 loses 20% of its value as measured by its ability to purchase goods.

**Deflation**Deflation occurs when money increases in value, meaning that it’s able to purchase more goods at an equivalent price. Being able to buy more with your money is always good however low levels of inflation are needed to ensure that enough money is going around the system for growth.

**Interest Rate**

Interest rate is the rate of return you make on an interest-bearing asset or the rate you pay when you borrow money. So when you have a bank account that generates 1% per year, you’ll have 1% more money in that account next year than you have this year, assuming that you leave that money in the account untouched during that period.

If interest rates are increasing the amount of money you have at exactly the same rate that inflation is decreasing the value of each unit of currency, you can continually purchase the same amount of goods using the money in that bank account.

As you may recall, opportunity cost measures the loss of forgoing the next best option. Opportunity cost becomes a problem when the next best investment is better than the one you choose.

For instance, if you buy an investment that makes a fixed 2% per year and then the next day the interest rate on that investment increases to 3%, you’re generating less nominal value on your investment than the market is offering to investors by taking it now. In other words, you’re losing 1% per year.

**Predicting Future Value**

Future value calculations are simply a matter of determining how much revenue an investment is going to generate over a period of time at the interest rate offered by that particular investment.

Two of the most commonly used future value equations in corporate finance involve interest rates – simple and compound interest. We’ll look at these in detail in the upcoming sections.

**FV = PV (1 + r.t)**

*Let’s look at an example of how to calculate future value using the equation above. *

FV = 100 (1 + 0.01 x 10)

= 100 (1.1)

= $110

Thus, the total amount of increase in nominal value that the interest earns over 10 years is $10.

**Compound Interest**Compound interest is similar to simple interest except that investments earning compound interest generate interest on the interest earned rather than just on the principal balance.

Although this difference adds some complexity to the equation used to calculate the future value, the basic components are still the same.

**FV = PV [(1 + r)^t] **

Say that you buy an investment for $100 that pays 10% each year and you plan on holding the investment for five years.

FV = 100 [(1 + 0.1)^5] = 100 x 1.6105 = $161.05

**Future Value**

http://financeformulas.net/Future_Value.html

**Calculating Present Value**

This ability to estimate the value of something today that’s going to change value over time is essential not only when buying and selling assets, but also as a critical element of tracking the progress and efficiency of capital assets within an organization.

This approach is especially important if you plan to sell that item of capital, when you’re buying used capital or if you deal with any sort of other investments such as bonds or derivatives.

For example, you can apply present value to bond investments in which investors know exactly how much money they’re going to earn nominally and when they’ll receive that money. In cases like this, you can determine how much of the future value you’ve already accumulated at any given point by using the following equation:

**PV = FV / (1 + r.t) **

PV = 100 / (1 + 0.05 x 1)

= 100 / 1.05 = 95.24

Another way of looking at present value is that the more interest you earn or pay on future cash flows, by way of higher interest or longer-term investments, the less the present value is going to be. In the case of higher interest, the present value increases at a much faster rate over time, whereas longer-term investments increase at the same rate but simply take longer to mature fully.

*Importance of determining present value*Being able to determine the present value of each potential investment, purchase or cash flow before committing to it helps you and your company to make the best possible decisions.

For instance, in making a large purchase that may include several installments, you can calculate whether your company would be better off paying for the item outright or making monthly payments with interest while keeping the remaining funds in an interest-bearing account of some sort.

**Discounted Cash Flows**

Discount value is another term for present value and comes from the fact that you’re taking a known future value and discounting it at the interest rate in question. The reason for the distinction in terms is that discount rate and discounted cash flows are easier to refer to than present value calculation rate or present value rate of future cash flows.

Beyond that, no difference exists in the meaning of the two terms. The only functional difference from present value is that we’re talking specifically about exchanges in cash instead of simply value generated. In other words, we mean cash flows instead of value.

For example, when your company purchases a large item, each cash payment the firm makes is considered a cash flow. If you purchase a machine for producing goods for resale, both the future costs of buying and operating that machine and the value of the goods created by the machine in the future are measured as discounted cash flows, with each individual cash flow discounted to its present value.

Even though each cash flow is likely to have the same interest rate, each one is going to have a different present value because each one is paid at a different point in time.

Discounted cash flow equation:

**DCF = [CF1 / (1 + r.t)1] + [CFn / (1 + r.t)n]**

**Net Present Value (NPV)**In this case, you add up all the present values of future cash flows to determine the value of discounted cash flows, also known as the net present value (NPV). In other words, NPV is the total value of all the discounted cash flows of a particular account, investment or loan.

In the real world, it can get a bit more complicated because the size of those cash flows will also be impacted by inflation so, in reality, companies often do a range of calculations showing that NPVs the outcome might range between.

*We’ll be looking at NPV in more detail later.*