JAMES WESTON: Hi, welcome back to finance for non-finance professionals. I'd like to do one more example with you. It's sort of a capstone example using our discounted cash flows compounding and discounting that we've been doing in the last few lectures. This capstone example is going to incorporate a lot of the different tools that we've been using across the different videos over the last week. So let's say-- and this is a little bit more foreshadowing in what we're going to do in week two, which is a little bit more using these tools to make capital budgeting decisions inside the firm-- here I'm going to give you a choice. You've got a choice between three different options. You can take $1,000 in cash right now. You can receive $2,000 at the end of three years. Or you can wait 10 years and receive $3,000. So let's think about using our present value and future value technology. Let's think about putting those things together and thinking about which one of those is the best. Which one of those has the highest value. If the discount rate is 10%, and then we'll think about how that answer might change if discount rates were different-- maybe if they were 5%. So let's move over to the spreadsheet and build a model to solve this problem. All right, in this example we've got three choices. And we need to decide which of these choices is the best one. We've got $1,000 today, $2,000 3 years from now, or $3,000 10 years from now. What we're going to do is use discounted cash flows to put all those choices into the same time period so we can compare apples to apples. Let's think about the first choice. We have $1,000 today. How much is that worth to us today? Well, it's $1,000 cash in hand, so there's no discounting to do. It's just $1,000. The second choice though, has $2,000 coming in three years from now. So how much is that worth to us today when you're going to have to discount it one, two, three periods into the present. How are we going to do that? Let's say equals. Let's go grab and grab that cell. And we're going to discount it by saying over 1 plus r, the discount rate, raised to the-- the little carrot is the exponent-- third power. Hit Return. Boom, $1,503-- that's how much that $2,000 is worth to us today if discount rates are 10%. We've got one more option, we could wait 10 years to get $3,000. How much is that worth to us today? Again, we can say equals-- let's go and grab that cell, $3,000, and discount it 1 plus 10% raised to the 10th power-- discounting that $3,000 back 10 periods at 10%, that gives us an answer of $1,157. So which of these options is the best? Option two, $1,503. Now, let's think a little bit about that answer. That answer reflects a trade off between discount rates and how far those cash flows are in the future. If the discount rate had only been 5%, let's think about whether that answer would change. In fact, it does. The answer now is option three is the highest, $1,842. Why? Because we lowered the discount rate, which means we were more willing to be patient. We were charging less for time. As we charge less for time, that $3,000 10 years from now becomes more attractive. In fact, if I go only 2% discounted or 1% discounted, that $3,000 in the future becomes more and more attractive as I'm more and more willing to be patient. Now of course if I'm less willing to be patient, let's say discount rates were 15%, the answer would change back to option two. But if I discounted really hard, let's say at 50%, the answer changes again, and the answer is no option 1. The more I'm charging for time-- 50% is a really high discount rate-- that means I'm not even willing to wait three years for the $2,000. The best option is $1,000 right now. The higher the discount rate, the less patient I'm willing to be. The lower the discount rate, the more patient I'm willing to be. And we see that the answer changes depending on the discount rate. But at our 10% initial discount rate, the answer was option two with a value of $1,503. All right, what we saw from that spreadsheet model was that the best option of those three that we had was option two that gave us about $1,500. The best option was waiting a couple of years to get the $2,000. That was better than $1,000 today, or waiting 10 years for the $3,000. The other thing that we realized from that example was-- and this sort of wraps up the week for us-- that that answer was really dependent on the discount rate. When we made the discount rate really low, it was worth it to be patient. And the answer changed to let's wait 10 years for the $3,000. And when we amped up the discount rate all way up to 50%, the answer changed again. It came back to I don't want to wait at all. I don't want to wait two years for $2,000. Forget about 10 years, I want the money today. So the answers of the financial valuation, and that trade off between making decisions between money today versus money tomorrow, depends critically on how much money's coming in, when that money's coming in, and how hard are we discounting it. And that's a good way to wrap up week one, which was all about the basics of valuation, compounding, and discounting. In week two, we're going to take those tools and apply them to the capital budgeting process inside the firm.