In this lecture, we're going to go through a detailed example, so that you can see some of what we talked about put into work. Let's suppose that a company is considering purchasing a new machine, and that new machine is going to save costs associated with the production of a product they sell. Let's suppose that that machine is going to cost them $200 million. Further, let's assume that it's going to save $50 million in production costs in each of the next five years. Then finally, let's assume that the division manager thinks that they'll be able to sell that machine at the end of five years for $20 million. In order to make this simple, let's assume that there's no working capital effects associated with this, so we're going to ignore that in this particular example. We're also assuming that the revenues of the companies are unaffected. So essentially, we're not going to change the product price even though we're reducing our production costs. So this $50 million is essentially going to increase our income by $50 million because we're not going to affect the revenues. So let's ignore taxes for now, and let's ask should we purchase the machine if the discount rate is 10 percent? Well, this is relatively straightforward given what I've laid out. So here's our timeline. You can see at time zero, we have a $200 million cash outflow, and then for years one through five, we're going to get $50 million in production savings. Then in the fifth year, we're going to get an additional $20 million when we sell the machine. So in the fifth year, we're actually going to get $70 million. Fifty million dollars of it comes from the savings, and $20 million comes from selling the machine. So we go to calculate the present value and you can see the present value formula there, and when you calculate the net present value, you can see that the net present value this project is almost $2 million. It's $1.96 million. So what would you do? Well, in this case, it's a positive net present value project. You would accept the project because it's adding roughly $2 million of value to the company. Well, that was simple. Well, let's complicate it a little bit, and the way to complicated is to just to make one additional assumption. That's, let's assume that the tax rate is 40 percent. Because remember what we're interested in estimating always is, how did the after-tax cash flows of the organization change because of the project? So let's see what happens. So what happens to the initial investment? Think about that for a minute. What do we know about that initial investment? It was the purchase of a machine. What kind of an expenditure is a purchase of a machine? It's capital investment, right? It's capitalized. What kind of a tax break do you get when it's capitalized? You don't get any tax break, because it's capitalized. So the initial investments still stays at minus $200 million, because it's still a capitalized cost. So whether we had taxes or no taxes, it doesn't make any difference. The after-tax outflow here remains minus $200 million. Now, let's think about what the annual cash flows are going to be for years one through five, and we're going to ignore the $20 million and salvage value for now. We're going to analyze that separately. You'll see here there's two columns. There's a column that says tax return, and there's a column that says cash flows. So let's look at the tax return column. What's going to happen on our tax return? Well remember, the machine is going to reduce our production costs by $50 million, so we're going to get savings of $50 million. What's that going to do? That's going to increase our taxable income by $50 million. But remember on the tax return, we're now going to get to depreciate the machine that we bought. For simplicity, let's assume that we're going to use straight line depreciation with a five-year life, and let's just assume, so you can see something about gains and losses when we sell the machine. Let's assume when the company depreciated the machine, they assumed that the salvage value was going to be zero. So what's the annual depreciation going to be then? They're going to take the 200, subtract off a zero salvage value, divided by five, and you're going to get $40 million a year. So what that means is that the taxable income is going to go up by 10 on the tax return. We said the tax rate was 40 percent, and what that means is the taxes are going to go up by four. Now let's look at the cash flow column. What are the things from the tax return column that belong in the cash flow column? Well, the cash savings belongs over there because our production costs went down, so our cash expenditures went down by $50 million. But remember, the depreciation is not a cash flow. So that doesn't belong over in the cash flow column. It reduced the taxes that the company paid because you can see instead of paying taxes on $50 million of cash savings, we only had to pay taxes on 10 because of the $40 million of depreciation. But it doesn't belong in the cash flow column. The other thing that belongs in the cash flow column is the increase in the taxes associated with this project, and those were four. So what we see now, is that the annual cash flows are 46. Well, what's the salvage value at the end of year five? Well, the original cost of the project, of the equipment, was $200 million, and when we get to the end of year five, what's the total amount of depreciation that we will have taken on that piece of equipment? That's what we often refer to as the accumulated depreciation, which is how much depreciation have we taken in total. So at $40 million a year depreciation times five years, what that means is that the accumulated depreciation will be $200 million. That means we will have completely written off that piece of equipment by the end of year five. So it'll be sitting on our tax books, because we're assuming we're using straight line for tax purposes here. It'll be sitting on our tax books at a value of zero. Well, what's going to happen then? We're going to sell that machine for $20 million. But the government's going to say, "Hey wait a minute, you just sold this machine for $20 million. You already wrote off the entire amount of the machine. It's sitting on your books for zero. You've got a gain." So they're going to tax us based on that gain. So we're going to multiply the 40 percent tax rate times the gain of 20, and we're going to find out our taxes are going to go up by eight. So what's the salvage value that we're actually going to get? The salvage value that we're going to get is the cash proceeds of 20, less the increase on the taxes because of the gain of eight, and that means that the net salvage value is going to be 12. So now let's see with taxes, what's happened to the net present value of our project. So we're going to do the same calculation that we did before as far as the discounting is concerned. But instead of having $50 million a year of savings, we only have $46 million after taxes, and instead of having a $20 million salvage value, we only have $12 million salvage value. Look at that net present value. It's minus $18.2 million. Do we want to take that project? No. That's a negative net present value project. We take that project, it'll destroy value. Notice the impact that the taxes had. We went from a project that was positive NPV by roughly $2 million to one that is negative NPV by roughly $18 million. This is why we calculate the after tax cash flows associated with projects, because taxes can have an enormous impact on the value that we're seeing. Let's do an alternative scenario. Just so you can see what happens, let's suppose for sake of argument, that the accumulated depreciation was only a $150 at the end of year five. Let's figure out what happens to the salvage value now. So if the accumulated depreciation was a 150 at the end of year five. We bought the machine for $200 million, that means that machine is sitting on our books for 50. When we sell that machine for 20 guess what we have? We have a loss of 30 because now we're selling that machine for 20 when it's sitting on our books for 50. So we have a loss of 30. So the government say, "Okay, you had a loss. That's going to reduce your taxable income. We multiply that loss by 40 percent." So our taxes are going to go down by 12, because of the loss associated with that. What that means is that the salvage value, is now the proceeds from the sale of 20 plus the reduction in the taxes of 12, and so our after-tax salvage value is now 32. Well, that sounds like a good deal. We had 12 before. Now, we have 32. Well this sounds like a good deal. But wait. Think for a minute. What else has to change if the accumulated depreciation is only a 150 at the end of year five? Something else had to happen, and the other thing that had to happen was that the annual depreciation that we got every year had to only be 30 a year. So what that means is that we were only taking $30 million a year in depreciation if we only wound up with accumulated depreciation of a 150. Well, what's the impact of that? Well, what that's going to do, is it's going to increase our taxable income in years one to five. So now we're going to have taxes that we have to pay of eight, and so the annual cash flows associated with the savings are now going to be 42, instead of the 46 that we calculated before. So what do you think is going to happen? Do you think the project is going to look better or do you think the project is going to look worse? Well, think about what we did. We reduced the cash flows from 46 to 42 in the first five years, and then in the fifth year, what did we do? We increased the cash flows to 32 from 12 on the salvage value. So what we did, was we pushed the cash flows farther away, and if you're with me, you know that that's going to reduce the net present value. So when now when you calculate the net present value, the net present value is actually worse than it was before. Because we've postpone the cash flows, we pushed the cash flows further away, which of course reduces their net present value. So now the net present value is almost minus $21 million.