Interest as the Return to Capital

So far, we have discussed interest as the price of loanable funds. Interest may also be viewed as the return that goes to capital as a factor of production. In other words, interest is the return to capital as a productive input in the circular flow model of the economy.

If an entrepreneur buys a machine for $100 and makes $25 a year by using it in production, the entrepreneur earns 25 percent interest on the investment in the machine. Using this concept of interest, we can show how the market for capital equipment works in Figure 2.

Figure 2. Return on Investment in Capital Goods

D is the derived demand curve for capital goods. S₁ and S₂ are short-run fixed supply curves for capital goods. Investment in new plant and equipment will take place if the interest earned on such investment (i₁ and i₂) exceeds the interest rate on loanable funds. New investment shifts the supply curve of capital goods from S₁ to S₂.

The demand curve, D, is the marginal revenue product curve of capital. It represents the entrepreneur's estimate of how much each unit of capital equipment will add to the firm's revenue. In effect, D is the derived demand curve for capital equipment. We assume that the short-run supply of physical capital — machines, building, tools, and the like — is fixed and cannot be augmented except over the long run. S₁ and S₂ are therefore drawn as vertical straight lines in Figure 2. The point where demand and supply intersect determines the rate of interest that entrepreneurs earn on each level of fixed capital investment.

Generally, there is a tendency for the rate of return on capital goods to fall over time and for an associated decline to exist in the demand for loanable funds. Offsetting this tendency in the economy are forces such as technological change that increase the productivity of capital goods and shift the demand curve for capital goods to the right.

 

The Nature of Returns to Owners of Capital

 

We have seen that individuals invest in capital goods because they expect to make a rate of return in excess of the cost of capital.

The elements of this rate of return can be broken down into three categories:

- pure interest;

- risk;

- profits and losses.

Pure Interest

Pure interest: The interest obtained from a risk-free loan.

Summarizing, the rate of return to capital investment embodies three components: a pure interest return, a premium for bearing risk, and a residual component reflecting unexpected changes in the value of capital goods. Each of these components has an important allocative function in the economy. Pure interest induces people to save. The risk premium leads individuals to invest in risky but valuable ventures. Economic profits are the spur to entrepreneurship and innovation in the economy.

 

The Present Value of Future Income

Present value: Today's value of a payment received in the future; future income discounted by the rate of interest.

The present value of any amount at any time in the future can be computed. The formula for doing this is:

PV = A_n

(1 + r)^n,

where A_n is the actual amount anticipated in a particular year in the future;

r is the rate of interest;

n refers to the particular year in the future.

Note two aspects of present value computations.

1. The lower the rate of interest used in making these computations, the higher will be the present value attributed to any given amount of income to be made in the future. Table 1 illustrates this point clearly. The present value of $100 one year from now is $97.10 at a 3 percent interest rate and $89.30 at a 12 percent interest rate.

2. The present value of a given amount to be received in the future declines as the date of receipt advances further into the future. In Table 1, for any given interest rate the present value of $100 is less the further it is to be received in the future. To see this relation, simply read down any column in the table. The point is that the present value of future revenues or costs is inversely related to the rate of interest and the distance of the date in the future when payment will be received.

Table 1

The Present Value of $100 at Various Yean in the Future

Years in the Future	3%	5%	7%	10%	12%
	$97.10	95.20	93.50	90.90	89.30
	94.30	90.70	87.30	82.60	79.70
	91.50	86.40	81.60	75.10	71.10
	88.80	82.30	76.30	68.30	63.60
	86.30	78.40	71.30	62.00	56.70
	83.70	74.60	66.60	56.40	50.70
	81.30	41.10	62.30	51.30	45.20
	78.90	67.70	58.20	46.60	40.40
	76.60	64.50	54.40	42.40	36.00
	74.40	61.40	50.80	38.50	32.20
.	.	.	.	.	.
.	.	.	.	.	.
.	.	.	.	.	.
	64.20	48.10	36.20	23.90	18.30
.	.	.	.	.	.
.	.	.	.	.	.
.	.	.	.	.	.
	22.80	8.70	2.13	.85	.35

The further in the future the $100 is received, reading vertically down the table at any interest rate, the less it is worth now Reading horizontally across the table, the higher the interest rate the less is the value of $100 at any year in the future.

 

Investment Decisions

The estimation of present value is important to firms because investment decisions involve current expenditures for plant and equipment in the expectation of future revenues from the goods and services produced by the plant and equipment. Two aspects of investment decision making are paramount.

1. The future revenues that an investment project will yield are estimated and converted to present value terms. This process provides the firm with an estimate of how much a project is worth now.

2. The firm must know what its cost of loanable funds is; that is, it must know on what terms it can borrow or lend money. This cost is the interest rate that the firm will apply to investment decisions. A simple decision rule follows from these two steps: If the estimated present value of a project exceeds the cost of loanable funds, a profit-maximizing firm will undertake the project. If not, it will turn down the project.

Discount rate: The interest rate that a firm uses to determine the present value of an investment in a capital good; the best interest rate that a firm can obtain on its savings.

By taking the appropriate rate of interest, commonly called the discount rate when used in investment planning, from Table 1 and applying it to the estimated future revenue at the end of each year, we derive in the last column of Table 2 how much the flow of future income from the machine for each year is worth today. As you can see, the total present value of the estimated future income produced by the piece of equipment is $41,200 (the sum of the figures in the last column). This total present value is considerably less than the cost of the machine ($50,000), and so the firm will rationally reject this investment proposal.

Table 2

The Discounted Present Value of $10,000 for Six Years

Year	Estimated Future Revenue (received at year-end)	Discounted Value (12% rate)	Present Value of Income
	$10,000	0.89	$8,900
	10,000	0.80	8,000
	10,000	0.71	7,100
	10,000	0.64	6,400
	10,000	0.57	5,700
	10,000	0.51	5,100
	Total $60,000		Total $41,200