In this lesson, we're going to look at the concept of present value. Let us use a simple example in this lesson to illustrate the concepts. Let's say I promised to pay you $10 each year forever, and ask you what you would pay me today. For the right to receive that continuous and endless stream of payments in the future, you would first need to evaluate the risk of the investment opportunity. You need to look at such things as how creditworthy I am by my ability to make good on my promise to pay you $10 forever, but you will also need to consider inflation rates and interest rates and any other types of risks that could impact your rate of return. Let's say after this evaluation, you determine that you need a 10% rate of return to compensate you for the risks of making this investment.

You now have enough information to calculate the value of this opportunity to you using what is called a discounted cash flow analysis. discounting is a method that is often used in finance to determine the value of a future stream of cash flow. The concept of time value of money is at the very heart of discounting, which is to say $1 received today is worth more than $1 received a year from now, which is worth more than $1 received two years from now and so on and so forth. The reason this statement is true is that you can take the $1 received today, invest it and earn a return giving you more than $1 a year from now. The expected rate of return becomes our discount factor. financial analysts have all sorts of ways that They can do a present value calculation.

And it doesn't matter what method is used, the answer will always be the same, you could use a present value table, which tells you the discount factor by lining up your discount rate with a number of periods. You can also use a formula to calculate the discount factor, which is the same as the PV if the present value interest factor, which is calculated as one divided by one plus the discount rate to the exponent of the number of periods that you're investing for. And then finally, you can use Excel and use a function in Excel called present value. Any one of these three approaches will result in the same answer. So let's put this into a spreadsheet so that you can see visually what I'm talking about. Let's put our years across To talk and call them 12345, and so on, this goes on for forever to the right of your screen, by the way, because I made a forever promise.

Next, let's put our $10 of cash flow under each of the years. Next, let's put our 10% discount rate into cell B seven, and calculate our discount factor using the formula on the previous slide. Notice how the discount factor the PV if is getting smaller and smaller, the further to the right we go, which makes sense because $1 12 years from now is not going to be worth a whole lot to me today. In fact, it's worth 32 cents. Next, multiply the cash flow the $10 by the discount factor to come up with or arrive at the discounted cash flow. Finally, add up The discounted cash flows to calculate a present value.

The result when rounded is $100. In fact, if you were to add up all the columns to the right, you would get precisely $100 $100 represents the value of this investment opportunity, and you should be willing to pay me $100 for this promise, you might think all these columns are kind of crazy, and there must be a better way. Well, it's your lucky day, because there is let's take the value of the investment opportunity, the $100 and divide it by the annual cash flow of $10. This two equals 10. Now, finance people call this a multiple and you will see multiples quoted all over the place in finance media, from earnings multiples, to cash flow multiples, to even the book value multiples that we saw in our last lesson, when we were comparing Microsoft ofs market capitalization to its book value of equity. If you know the income, and you know the multiple, you literally multiply the two together to determine value.

But this multiple also ties back to our rate of return. When you have a constant and infinite life cash flow stream, you can take your discount rate and divide it into one to determine your multiple. In other words, one divided by 10% equals the same 10 times multiple $10 of income times the multiple of 10 gives us our very same $100 of value. Let's do this using a different set of assumptions that are a little messier to work with. If I promised you $6 a year forever, and your required rate of return was 15%. How much is this investment opportunity worth?

If you Got $40 you would be correct, calculated as six times one divided by your discount rate of 15%. Or even more simply $6 divided by 15% equals the $40. Got it? Let's change our original scenario ever so slightly, and instead, assume that the cash flows grow at a constant rate. How does that change our analysis? Let's model this out in Excel.

Notice how the cash flow is growing by 2% each year. Once again these cells will reach as far as the eye can see to the right of your screen. The sum of the discounted cash flows is $125 which is to say we get $100 of value from our initial $10 and an incremental $25 of present value from the growth in the cash flow. Now a shortcut method still works. However, we need to adjust that denominator by subtracting the expected growth rate from our discount rate, we change our original formula to read $10 divided by 10% minus 2%. The value of this opportunity is the very same $125, implying a multiple of 12 and a half times.

Always remember that smaller discount rates will increase present value. What if the cash flows were expected to instead decreased by 2% per year, say in the situation of a declining business? Well, instead of subtracting 2% from the discount rate, we add it and as a result, the value is now at $3 and our multiple decreases to 8.3 times. still with me, let's try another variation. What if instead, I promised to pay you $10 for only the next five years and not forever, like I did in the previous example, how much is this worth? We call this an annuity.

When the cash flow forecast only occurs for five years, we need to look up the discount factor in a different table or use a different formula. We call this the discount factor of an annuity or the present value interest factor of an annuity they mean the same thing. Let me just show you something that will help you conceptualize what this formula represents. The present value interest factor table for a lump sum is on the left. The table for the annuity is on the right. You can add up the five separate discount factors from the table on the left hand came up with the same discount factor supplied on the table on the right When you think about what an annuity represents, this makes sense.

So whether you do it the long way by discounting each $10 cash flow for five years, or use the alternative table or a formula to calculate the discount factor, your answer is the same. In this case, we take the 3.791 discount factor from the table and multiply it by the $10 annual cash flow to determine a present value of $37 and 91 cents. That is what you should be willing to pay me for this investment opportunity. Let me see if I can really fool you now by offering you an investment opportunity that has cash flows that are both finite and uneven. What are you going to pay me for this? I promised to pay you $5 in the first year $10 in the second $7 in the third $8 in the fourth and $11 in the fifth year, at which point it's over.

Many business opportunities experience uneven cash flows like this. So how are you going to handle it? When this is the situation, there are no shortcuts, you sit down with a spreadsheet and you input the assumptions. Let's do that now. This screen illustrates the approach and is consistent with what was shown earlier years across the top cash flows on row five. The discount factor has been calculated on row seven and the discounted cash flow on row nine, you can add up the discounted cash flows to determine the present value of this opportunity.

This gives us $30 and 36 cents. This is what those five cash payments over the next five years are worth in today's dollars. The basis of what you've just learned in this lesson are the foundation for so many types of financial analysis. As we illustrated in this lesson, we can determine the value of something, it could be a business and investment or securities like stocks or bonds. All of these types of opportunities come with a stream of cash flow and a discount rate, which you can use to determine value. A more advanced extension of this idea is for capital budgeting, capital budgeting is deciding about whether or not to invest capital in a new long term project, such as opening a new plant or purchasing a competitor's business.

The process you use a similar forecast the future cash flow, determining discount rate, calculate present value and then subtract off the upfront investment. The results give you what is called net present value because present value of cash flow is subtracted from the investment required to obtain them. If the resulting number is positive, the opportunity Create shareholder value, and if it's negative, it dilutes it and the project should not be pursued. So now you have learned a little something about how to calculate present value. In this lesson, we learned three really important things. First of all, present value determines the value today of a future stream of cash flow.

Secondly, to determine value, you need a cash forecast and a discount rate. The discount rate is set based on an expectation of return. And thirdly, we learned about three different approaches to calculating value, depending on the characteristics of the stream of cash flow. In our next lesson, let's flip this around and look at future value.