Unit 5 Macroeconomic policy: Inflation and unemployment
5.12 Current costs and future benefits: Understanding investment and asset prices
In our model of the business cycle, firms’ investment decisions depend on interest rates and expected future profits. We argued in Unit 3 that if the interest rate rises, firms will reduce their investment spending. In the model, this is how monetary policy affects aggregate demand. Secondly, if firms become more optimistic about future profits, investment spending and hence aggregate demand will increase.
In this section, we will analyse investment in more detail. We use the concept of present value, which enables us to evaluate decisions where the costs and benefits arise at different times. Present value is useful for calculating the value of many different types of assets; we will explain how asset prices also depend on interest rates, providing a second channel through which monetary policy affects the economy.
Investment and present value
Imagine that your employer has asked you to assess whether the company should engage in a major investment project which is expected to earn profits for the company in the future. In practice, these profits might be many years away, and almost invariably could not be guaranteed. But to illustrate the logic of the decision, we will start with an example.
Suppose that the project will last just a single year. Assume that the initial investment will cost $I, and there is no uncertainty: if it invests, the company will receive a return of $X in a year’s time (measured in real terms). Furthermore, suppose that your firm has sufficient funds available from accumulated profits to make the investment if it so chooses.
- opportunity cost
- What you lose when you choose one action rather than the next best alternative. Example: ‘I decided to go on vacation rather than take a summer job. The job was boring and badly paid, so the opportunity cost of going on vacation was low.’
The question you need to consider is whether the return X is sufficiently high that it is worth spending I now, and then waiting for a whole year to obtain it. Are there other ways of using the company’s funds during the year that would leave it in a better position? In other words, what is the opportunity cost of the project?
Assuming that this is the best project available to the firm, you should consider the alternative of investing the funds in the financial markets. Suppose that risk-free financial assets pay a guaranteed real interest rate, r.
In both cases, the firm would pay $I now. Then in a year’s time it would have:
- $X if it invested in the project
- $I(1 + r) if it invested in the risk-free asset.
So you should recommend that the firm undertakes the project if and only if:
\[X>I(1+r)\]This criterion compares the future return from the project, X, with its ‘future costs’: the opportunity cost \(I(1+r)\) is the amount the company would be giving up in a year’s time to obtain the amount, $X.
Remember we assumed that the firm had sufficient funds to finance the investment itself. However, the same criterion would apply if the firm had to borrow the initial cost I—assuming that it could borrow to finance a risk-free project at the risk-free interest rate. In that case \(I(1+r)\) is the amount it would have to pay back at the end of year; so again it should invest provided the repayment is below the return, X.
- present value
- The effective value today of a stream of income or other benefits that will be received in the future. The present value is less that the future value when future income is discounted using an interest rate or the person’s own discount rate. See also: net present value.
- net present value
- The net present value of a project that will generate income at some time in the future is the present value of the stream of income, minus the present value of the associated costs (whether the costs are incurred in the present or the future). See also: present value.
- risk premium
- Risky assets have to offer a higher rate of return than risk-free assets to compensate the buyer for risk. The risk premium is the difference between the return on the risky asset, and the risk-free rate.
- exogenous
- Exogenous means ‘generated outside the model’. In an economic model, a variable is exogenous if its value is set by the modeller, rather than being determined by the workings of the model itself. See also: endogenous.
The criterion above is expressed in ‘future values’. Another way of writing it is:
\[\frac{X}{1+r}-I>0\]We can interpret this as telling us that, if we consider the project from the perspective of the present, its cost is $I, but its benefit is effectively smaller than $X—because it takes a year to arrive. The present value of the return from the project is \(X/(1+r)\). Then we say that the net present value of the project is
\[\text{NPV}=\frac{X}{1+r} - I\]and the project should be undertaken if and only if its net present value is positive.
We can use present values to make comparisons between benefits and costs received at different times. In general, we calculate the present value of a future payment by discounting it: in the example above, where the firm is interested only in maximizing its profit and the project is risk-free, the discount rate is r, the market interest rate on risk-free assets.
But capitalist enterprises are not, typically, engaged in activities that generate risk-free returns. If the project was risky, your discount rate, which we will call d, would be higher. For a risky project with expected (or average) return \({$X^E}\), the investment decision rule is:
\[\text{Invest if and only if} \text{ NPV}>0, \text{where} \text{ NPV}=\frac{X^E}{1+\text{RP}+r} - I\]As before, your discount rate is equal to the interest paid on market assets that have a similar level of risk to your project. But this is higher than the risk-free rate, r: it is
\[d = r + \text{RP}\]where RP is the risk premium (which is strictly greater than 0). Risky assets have to offer a higher level of interest—otherwise buyers would always choose the risk-free alternatives.
How big RP is will depend on both the degree of uncertainty and the nature of the uncertainty of what you expect to get back from the investment. But one key prediction of finance theory is that the size of the risk premium will not reflect individual preferences, but simply reflects the ‘market price of risk’. From the point of view of the firm, the discount rate, d, is therefore exogenous, since it is just set by a combination of financial markets and the central bank.
The investment function
Using the present value criterion for investment, we can now understand why (as we previously assumed) aggregate investment depends on the interest rate, and expected future profits.
First, if expected future profits, \(X^E\), increase for all potential investment projects that firms are considering, more of these projects will satisfy the investment criterion. So aggregate investment will rise.
Now suppose the expected profits, \(X^E\), remain as before, but the market interest rate, r, rises. Then firms’ discount rates are higher, reducing the present value of expected profits, and hence the net present value of all projects. Fewer projects will satisfy the investment criterion, so aggregate investment will fall. This is one of the transmission channels of monetary policy.
In the extension to this section, we model these two effects in more detail.
Present value and asset prices
We can use present value to analyse other problems. Suppose that you are considering buying a share in a company. As a shareholder, you can expect to receive dividend payments from the company in future. If real interest rates fall, then, other things being equal, the present value of any future dividend will increase. Intuitively, if the present value of what the share offers you goes up, it is likely to lead you, and many other investors, to be more willing to buy it. If large numbers of investors are suddenly more willing to buy a given share, its price is highly likely to increase. Demand has risen relative to the fixed supply of shares.
- asset prices
- Asset prices is a general term used to refer to the prices of both financial assets (like shares or bonds) and real assets (such as housing, land, gold, or works of art). See also: asset.
And it is not just the price of shares that will be affected. Similar considerations apply to almost any asset that will generate an income in the future, from financial assets like shares and bonds to real assets like houses or land. As we discuss in the next section, the impact on asset prices is a key element of the transmission of monetary policy.