Economics: Analyzing Capital Markets

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Capital refers to any good that's used to produce other goods. When we talk about a firm's capital stock, we're talking about the tools that are available to that firm to produce its final goods and services that it sells to customers. So, one example of capital is the factory that the firm produces output in. Another example would be the equipment that's in that factory - drill presses, lathes, automatic sanders, painting machines - any tools that are used to produce goods and services.
When a firm is trying to decide how much capital to employ, it uses a logic that's very similar to the logic it uses in its labor decision - that is, should we hire an extra worker? And the answer depends on the revenue that that worker adds and the cost of getting that worker to work in your factory. A firm continues to employ labor until the extra revenue is equal to the extra cost, or the marginal revenue product is equal to the wage.
The decision that the firm uses in employing capital is quite similar. Capital has a special property, and that is, it is durable. If you buy a factory, you can use it year after year; if you put a machine to work, it's going to be producing output for you for many periods to come. Now, of course, a certain amount of that capital is going to wear out each year. We call that depreciation. And because of depreciation, you've got to repair your factory from time to time, you've got to spend money to service your machines, and so forth. But, for the most part, capital is defined by its durability. It is a tool that lasts; it is an investment; it is an asset that creates profits for the firm into the future. So when we consider the firm's decision about how much capital to put to work, we're thinking about an investment decision. How much should we pay for a particular asset, given the returns that we expect to get from it in the future?
Let me lay out this problem systematically. If our firm under consideration - suppose a television manufacturer - is considering buying another assembly plant, what kind of logic will it work through to decide whether or not to buy the factory? Well, the factory's got a price tag sticking on it, and the firm can pay the price or it can let this factory go. If it pays the price, it has gained access to an opportunity to earn profits. Well, how much profit? The firm is going to sit down, look at the capital, consider different strategies for using that to make television sets, decide how much labor it would have to hire to man the factory floor, and it's going to come up with a calculation for the number of television sets that it can produce in this factory - say 1,000 television sets a year. One thousand television sets a year multiplied by the price of $100.00 per television set is $100,000.00 worth of revenue that this factory will be creating.
Well, we've got to subtract from that revenue the cost of making those television sets in the factory, and that's going to depend on how much we have to pay the workers who are going to be doing that task. Let's suppose we add up wages times workers employed, and we find that the total labor bill for cranking out those 1,000 television sets is $90,000.00. That means $100,000.00 worth of revenue minus $90,000.00 worth of variable costs equals $10,000.00 worth of profit each year from this asset.
Well, $10,000.00 a year worth of profit is a stream that's going to persist into the future. Maybe that also includes the cost of offsetting the depreciation of the capital asset if we had to throw in a little money to fix windows and grease the wheels from time to time. But any way you look at it, you've got an income stream now that you expect if you buy this asset. And here I'm writing down this income stream - benefit minus cost, or the revenue you get from producing and selling those television sets minus the money that you have to spend on variable inputs and depreciation to make those television sets come out the other side. What you do is you take each year's profit and you discount it by 1 plus the interest rate.
So what you're doing here is calculating the present discounted value of the stream of profits that you expect if you own this factory and employ it in the production of television sets. So the first year you discount profits by 1 plus the interest rate. The second year you discount the profits by 1 plus the interest rate squared, and so forth, all the way up to the Nth year - which could be way out towards infinity - in which you discount the profits earned by 1 plus the interest rate, raised to the power of N - this is the present value of the profit stream.
Now, if you know the interest rate, then you can plug the interest rate in here and calculate present value. Alternatively, you can think about this problem from a different angle. Suppose what we know is not the interest rate, but we know the price that we have to pay to acquire the asset. If we write here the price of that factory - and suppose the price of that factory is $200,000.00 - then $200,000.00 is the price. We take annual profits from this factory of $10,000.00, and we can solve this complicated equation in terms of R. That is, what is the interest rate that would make $200,000.00 - the price of the factory - equal to the present discounted value of the profit streams that the factory is going to generate whenever we stock it with workers and make TV sets?
The interest rate that solves this problem is called the "internal rate of return" on this factory. That is, if this factory were a bank account, and you put $200,000.00 into it, what would the interest rate have to be that would allow you to take out $10,000.00 each year, the same way that this factory allows you to earn $10,000.00 in profits? The answer, if this problem stretches on out towards infinity, is about 5%. So at an interest rate of 5%, an annual profit of $10,000.00 has a present discounted value of $200,000.00. So, if the actual interest rate in the market - that is, if the opportunity cost of capital, the rate of return that you could earn by taking that same $200,000.00 and using it to purchase a bond, or to put it right into your bank account - if the interest rate is 7%, then you would do better to take the money that you were going to spend on that factory and invest it somewhere else. Put it in the bank, or buy a bond, earn 7%; don't put it in this factory and get a rate of return of only 5%.
On the other hand, if the interest rate in the market is only 3%, then this factory looks awfully good by comparison; the internal rate of return is high relative to the opportunity cost of capital. In fact, it even pays you as an entrepreneur to go out and borrow money at 3%, buy this factory for $200,000.00, and get an annual rate of return of 5%; borrow money at 3%, earn 5% on it, and there's your profit on the capital.
So the rule for a firm is: Borrow money as long as the market's interest rate is less than the internal rate of return on the projects you're considering. If the internal rate of return is lower than the market interest rate, then you would do better to forego the investment opportunity and invest any surplus funds you may have in the bank or in other bonds. By all means, don't borrow money at an interest rate that's higher than the internal rate of return on the project you're considering.
So how can we turn this logic into a demand curve for capital? Well, here's what we can do. We write the opportunity cost of capital on the vertical axis - this is the interest rate - and on the horizontal axis, we write the amount of capital that the firm is going to acquire in a given period of time. Now, capital is kind of a hard thing to measure. I mean, what is the unit in which you measure capital? I mean, some capital is factory building, some of it is tools, some of it is equipment, some of it may be patents, and other intellectual properties.
So the way we're going to measure capital is in total dollars that the firm spends on capital - that is, the firm's capital stock will be measured in terms of dollars invested. So let's suppose that a firm can earn an internal rate of return of say 10% on a project that costs $200,000.00. So at 10% interest rate, the firm would be willing to invest in that $200,000.00 project. When the rate of return drops down to 8% - that is, when the market rate is 8% - the firm finds it profitable to invest in a project that has an internal rate of return at 8%. And let's suppose that project costs $300,000.00. So add $300,000.00 to the $200,000.00 that you'd spend on the 10% project to the total amount of investment spending of $500,000.00. Then keep going down. Look at projects with internal rates of return that are lower. Here's one with an internal rate of return of 7% that costs $100,000.00. Here's one with an internal rate of 6% that costs $400,000.00. And at each internal rate of return, add on those projects that have that internal rate of return.
So here we go - eventually we can connect the dots, and this gives us the firm's demand curve for capital - how much money the firm wants to spend on investment projects as a function of the market interest rate. When the market interest rate is very high, then there aren't very many projects that are worth undertaking, because the internal rate of return on most projects is going to be lower than the market price of capital.
So when the market price of capital is high, the total amount of investment spending that the firm wants to do, the total amount of capital that it wants to acquire, is low. On the other hand, at a low interest rate, there are lots of projects whose internal rate of return exceeds the opportunity cost of capital. And, therefore, the firm is going to be doing a lot of investment spending, it's going to be acquiring a lot of capital.
So here you have it - the demand curve for capital. Firms make a comparison between the internal rate of return on an investment project, like buying a factory, and the amount of interest they would have to pay on the money they borrowed to get into that project. When the interest rate is high, few projects are profitable. When the interest rate is low, lots of projects have internal rates of return that are above the opportunity cost of capital, and firms acquire more.
Resource Markets
Capital Markets
Analyzing Capital Markets Page [2 of 2]