In this chapter I want to talk about one of the six kinds of capital - business capital and specifically about business decisions, investing in new factories, equipment or research and development, that is covered by the patent system, for example. In other words, I want to talk about profit oriented investment and get a simple principle, that is the basic metric for a business manager on whether a particular investment should or should not be made. The core idea is that a business manager, working on behalf of the owners of a company, essentially undertakes to maximize the value of the company. To maximize the shareholder value, if this is a share company with the owners by equity, for example as in the corporate sector. And so the idea here is that, investment decisions are evaluated on a basic condition - will this investment raise the value of the firm, thereby the wealth of the shareholders who have put their money into this enterprise, to maximize their wealth? When it comes to investment - we're talking about buying a new factory, or buy new machinery that's going to last over time, and in fact the benefits from that investment might not be seen for two or three or four years in the future, and may be increments to profitability for many years after that. Just like saving decisions, investment decisions are inherently intertemporal decisions. It won't surprise you to know that our main conclusion, therefore is that the interest rate which is the return on saving, or the cost of borrowing between periods of time therefore plays a crucial role in the investment decision. When we looked at the balance of saving and investment in the economy, we assumed that saving was an increasing function of the interest rate and investment was a decreasing function of the interest rate, and the market equilibrium is found where the interest rate equalizes the flow of saving and the flow of investment. We're going to look at that relationship with a little bit more care. The starting point if one wants to know how to maximize the value of a business, is to ask what is the value of a business. Broadly speaking the value of a business is the discounted flow of earnings of that business. Investors invest by buying shares, based on the expected future profitability of the business. A simple expression of this relationship is shown here, where I say that the market value of the business which I denote V, is equal to the earnings today which I call E 1, that means the earnings in the first period minus outlays that are made for investments today in order to build business capital in the future, plus the earnings in the second period but expressed in present value terms. In other words, if a company is going to earn a million dollars next year but the interest rate is 10%, then the present value of that million dollars recall, is 1 million divided by 1.1 so less than a million dollars in present value terms today. If the business owns capital, part of the value of the firm will be the capital that remains after use, in the second period. So if a company is investing today and it's going to build capital, and part of the capital will depreciate, that capital will have its own market value perhaps in future use by the company or resale value to the market as the company sells a used piece of machinery and buys a new one through yet another round of investment. Let's consider this investment decision. You're the manager and you want to examine whether to make an investment I 1, in today's period in order to raise the capital for period 2, you're going to resell the capital at the end of period 2 to the marketplace and the question - is is an incremental investment going to raise the value of the company? So in order to study that question, we specify that today the company has a capital stock business capital K1. By next year some of that capital today, whether it's the factories or the machinery will have depreciated basically we'll have worn out or lost some of its productivity so it's convenient to say that if the rate of depreciation is given by a parameter d, little d, the amount of today's capital that will still be with us next year in the company is K 1 times 1 minus d, so if little d is 0.02, 2% rate of depreciation. If you have $100 of capital today, it would be a hundred times 1 minus 0.02 or 0.98 meaning 98 dollars worth of capital next period. But next year's capital depends not only on what remains of the existing stock of capital, but the amount of new investment undertaken today to build the capital for next period. So this leads to an equation or a relationship that says K 2 the amount of capital available for production in your factory in period 2 is equal to K 1 times 1 minus D, plus I 1. Let's suppose that next period’s capital has a certain productivity, meaning that it adds to the production of output in the economy. And we'll say that this marginal productivity, meaning the extra output from an extra unit of capital. That means that if I add to the capital stock next year one unit, how much extra output will I get next year MPK which is some number, times one unit. If I add 10 units of capital how much extra output would I get next year? Well in this simple framework, it would be the value represented by MPK, the marginal product of capital times ten units of capital. So I can now express algebraically, the value of next year's earnings. This means that E 2 is equal to MPK times this year's capital, net of depreciation plus new investment, plus the amount of that new investment that will be resold after it's used next year. And if I stick that level of earnings back into the share valuation expression, because remember the value of the company is equal to the present value of today's earnings plus future earnings. I now as a manager have an important tool, that I can use to ask the question - should I undertake that investment? By the way that's what your CFO will do, your chief financial officer will get all these data together, if this extra million dollars is undertaken and it's going to be worth in resale value maybe $950,000 next year but it's going to produce an extra $100,000 of profitability next year and the interest rate is 10%, should that investment be made in order to raise the market value of the company? And she's going to calculate all of that, and then bring it to the CEO or to the board with the recommendation that that is absolutely an investment that should be made because it's going to raise V, the value of the company or it's going to lower the value of the company, so don't make it the returns are not good enough. If you do the algebra with these simple assumptions that I've made, and ask the question - would a higher level of investment today raise the value of the firm? Turns out we can see in the algebra a simple result. And that is yes, if MPK meaning the marginal productivity of capital is high enough. Well, how high does it have to be? Turns out, a pretty basic expression is the marginal productivity of capital, net of the rate of depreciation greater than or less than the market interest rate. Well even though I've given a very, very simple framework in this two period illustration, this expression though dressed up a bit is really the expression that CFOs and CEOs and boards use to analyze an investment. They ask - what is the marginal productivity of this investment? Basically the incremental value that will come from an added amount of investment. Maybe they have to add it not just in next year, but in many years to come so they add up the present value of those increments over time. They look at the depreciation rates of capital, and then they look at the cost of borrowing and in our simple illustration the cost that this business would pay to borrow is the interest rate. And while we are using the phrase interest rate, a CFO would use the term the cost of capital. That's a little bit different from the interest rate, essentially in economic concept the same variable that we can say, that the decision on investment depends on comparing the marginal productivity of investment net of depreciation, with the market interest rate or the market cost of capital. The amount of investment undertaken in the economy will be a negative function, a declining function of the rate of interest. Because as the rate of interest goes higher, the number of investments in the economy that are going to meet this investment criterion are going to be fewer. Since we can say that profit maximizing businesses are going to be using this investment criterion because they're trying to maximize the value of the company, we end up deriving what we assumed earlier a downward sloping investment schedule in which investment is a negative function of the interest rate. This simple explanation that I've offered in this chapter gives us a little bit more depth, it explains that in a profit oriented economy such as most in the world, investment decisions are taken to maximize shareholder value. In order to do that the marginal productivity of capital is compared with the market interest rate and that leads to this negative relationship. Of course in the real world of investment decision-making, there are many added considerations. Investments are not for one period there for many periods. There are, of course, multiple kinds of capital and firms also pay taxes on their income. So just as we had to elaborate the consumer or the household consumption and saving relationship by adding in taxation, a full understanding of business investment would involve a more complicated expression that essentially would say that what counts is the marginal productivity of capital, net of taxation compared to the cost of capital. This means that tax policy can affect investment decisions and thereby affect economic growth. Tax design is not only about how much revenue to collect, but what kind of incentives are put in the economy for investment and for economic growth. And that consideration also needs to balance the considerations of fairness and environmental sustainability as well. This is a brief look at business investment, but it is given us what we need. An investment demand function in which the investment in the economy is a negative function of the interest rate - that helps us to understand the balance of saving and investment. It also gives us insight into stabilization policy, because one way that governments seek to stimulate the economy, to boost aggregate demand remember which is C + I + G + (X - M) is to boost I. And since I is a negative function of the market interest rate, one way to boost I in principle, is to reduce the interest rate and one way to do that at least in principle is through central bank monetary policy. So the dependency of investment on the interest rate, is an invitation to explore how the central bank can or perhaps cannot influence the market interest rate, and that of course is discussed in detail in another module.
The Basic Theory of Business Investment
From SDG Academy 20 August, 2019
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From SDG Academy 20 August, 2019 |
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From SDG Academy 23 August, 2019 |
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From SDG Academy 20 August, 2019 |
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From SDG Academy 20 August, 2019 |