[ Music ] >> While the payback period and accounting rate of return methods have their share of advantages, there is one more disadvantage that needs to be discussed. Specifically, both ignore the time value of money. Now what is the time value of money? Well, ask yourself this question. Would you rather receive $1,000 today or one year from now? Presumably your answer is now. Why? Because you can use the $1,000 during the coming year if you were to receive it today. Whereas in if you had to wait until the end of the year you wouldn't get to use it. It wouldn't earn interest or some other return for you. And when we consider multiple tiers the time value of money can become quite important. So let's take a look at our hypothetical comparison that we've kept on the backburner until now. Again, we had two projects: A and B. [ Pause ] For project A in year zero the initial outflow was $100,000. And for project B, if we were to pursue that, the initial outflow was substantially higher. $250,000. The cash savings or inflows between the two projects are quite different, especially when considering their behavior over time. Project A's cash savings occur quite regularly throughout years 1 through 6. Project B's cash inflows occur relatively small in the early years, but substantial in the later years, especially in that year 6. Now without taking into account the time value of money you can see that project A's net flow is $140,000, and project B's is higher at $167,000. But if the time value of money is an important consideration in here it might be that waiting for that big outflow over in project B is not worth it. We have to wait that long to receive that much cash. It may be that the regular cash inflows associated with project A given the effect of the time value of money are more valuable to us as an investor, or as the firm. So let's talk about discounting cash flows. Specifically we need to calculate the present value of future cash flows and that involves the following parameters. First of all, we need the amounts. In our hypothetical example when do these inflows and outflows occur and how much are they? We need to understand the notion of time. Are the two projects or the projects spanned over multiple years far into the future or is it relatively near? And, finally, we need to understand the discount rate. That's the rate in which we discount money received in the future compared to what we receive currently. The time and the discount rate yield a factor that allows for the calculation of the present value of a dollar received in the future. The present value factor is 1 divided by a denominator of 1 plus the rate raised to the power of time. So in essence if we had a 3 year window and the discount rate was 10% our factor would be 1 divided by 1 plus .10, our 10% discount rate, raised to the third power for the fact that we're talking about 3 years. [ Pause ] We'll next turn to some numerical examples to talk about how the time value of money allows us to calculate alternative measures for capital budgeting.