[ Music ] >> Next we're going to use the notion of the time value of money to calculate net present value. The main approach here is the discounting of cash flows, both inflows and outflows, to their present current day value. This ultimately facilitates comparability across multiple investment alternatives. But we'll just use the numerical example that we started with, Hogarth bottling machine, for which they are investing $23,000 now and enjoying cash savings over the next four years. Adding to this example we'll talk about Hogarth using a required rate of return of 16% in its capital budgeting decisions. Again upper management has just decided that that is the legitimate threshold to make investments worthwhile. Again influenced by a variety of factors. And we'll assume that all cash flows occur at the end of the year, except for the initial investment amounts. In that case the $23,000 is expended immediately. So let's calculate the net present value. The generic formula for net present value is the dollar amount times the factor, where the factor is equal to 1 over 1 plus the rate raised to the time, or number of years that we are discounting the dollars. So for the inflow associated with the end of year one that amount was $10,000. The rate, or factor, that we would use to adjust this dollar amount to create a present value of a future amount and to current day terms would be 1 over 1 plus point 16. That's our firm's cost of capital and we're using that as the discount rate, raised to the first power. The first power being because this is only discounting one year. So that equates to $10,000 multiplied by, with some rounding, point 862. That means that the $10,000 that we will earn at the end of year one, in today's value terms, is $8,620. Now let's take a look at the cash savings that occur at the end of year two. That amount is $8,000. And the factor we would use to discount it would be 1 over 1 plus point 16 squared. Squared because we're talking about discounting via that rate for two years' worth of time. That is equal to $8,000 times point 743, again with some rounding involved there. And so the $8,000 received at the end of year two, in today's value, is equal to $5,944. When I do the same process for years three and four I calculate the $6,000 savings that we earn at the end of year three to be $3,846 in today's terms. And the $5,000 cash flow that I earn at the end of year four translates into $2,760 in today's dollars. All four of these inflows have now been translated into current day value taking into account the time value of money. So when I combine the value of all of these inflows I'm summing them up. 8,620; 5,944; 3,846; and 2,760 amount to $21,170. This is the value of all our future inflows associated with this project in today's terms. Now I compare that versus the $23,000 that it takes to invest in this project. And when I've converted all of my future inflows into today's dollar terms it doesn't seem as though it's worthwhile compared to the $23,000 in today's dollars that I have to expend. In other words the net present value of this project is negative; $1,830. And absent other considerations that is adopting just the financial perspective this investment does not look all that favorable from the net present value perspective. So let's talk about some of the advantages and disadvantages of the net present value method. The advantages are that it takes into account the time value of money. And the longer the project the more important this factor is. So it's more realistic, more accurate in terms of measuring the benefits and the costs of a capital investment. It's also focused on cash flows, which may be very important to managers, especially when determining the feasibility of a project. And it allows for comparability. No matter when the timing of the inflows and outflows are, as well as their amounts and this lifespan of the projects everything can be compared in today's terms. That allows for a very powerful tool, especially when considering different opportunities. Disadvantages include that there are some assumptions at the heart of the net present value method, specifically something about the timing of the cash flows and the cash flows being immediately invested our necessary assumptions to rely on this methodology. It's also subject to uncertainty. You're not quite sure what the appropriate discount rate or rate of return should be and so to the extent that there are multiple options there you might be making a decision under one right that might be different compared to other assumptions. Ultimately the net present value carries a lot of advantages and we'll turn to a brother or a sister method in internal rate of return next.