Capital, Loanable Funds, Interest Rate

The demand and supply for different types of capital take place in capital markets. In these capital markets, firms are typically demanders of capital, while households are typically suppliers of capital. Households supply capital goods indirectly, by choosing to save a portion of their incomes and lending these savings to banks. Banks, in turn, lend household savings to firms that use these funds to purchase capital goods.

Loanable funds. The term loanable funds is used to describe funds that are available for borrowing. Loanable funds consist of household savings and/or bank loans. Because investment in new capital goods is frequently made with loanable funds, the demand and supply of capital is often discussed in terms of the demand and supply of loanable funds.

Interest rate. The interest rate is the cost of demanding or borrowing loanable funds. Alternatively, the interest rate is the rate of return from supplying or lending loanable funds. The interest rate is typically measured as an annual percentage rate. For example, a firm that borrows $20,000 in funds for one year, at an annual interest rate of 5%, will have to repay the lender $21,000 at the end of the year; this amount includes the $20,000 borrowed plus $1,000 in interest ($20,000 × .05).

If the firm borrows $20,000 for two years at an annual interest rate of 5%, it will have to repay the lender $22,050 at the end of two years. After one year, the firm will owe the lender $21,000 as explained above; however, because the loan is for two years, the firm does not have to repay the lender until the end of the second year. During the second year, the firm is charged compound interest, which means it is charged interest on both the principal of $20,000 and the accumulated unpaid interest of $1,000. It is as though the firm receives a new loan at the beginning of the second year for $21,000. Thus, at the end of the second year, the firm repays the lender $21,000 + (21,000 × .05) = $22,050.

In general, the amount that has to be repaid on a loan of X dollars for t years at an annual interest rate of r is given by the formula 

For example, if X = $20,000, r = .05, and t = 2, the amount repaid is found to be $20,000 × (1.05) ² = $22,050.

Determination of the equilibrium interest rate. The equilibrium interest rate is determined in the loanable funds market. All lenders and borrowers of loanable funds are participants in the loanable funds market. The total amount of funds supplied by lenders makes up the supply of loanable funds, while the total amount of funds demanded by borrowers makes up the demand for loanable funds. The loanable funds market is illustrated in Figure . The demand curve for loanable funds is downward sloping, indicating that at lower interest rates borrowers will demand more funds for investment. The supply curve for loanable funds is upward sloping, indicating that at higher interest rates lenders are willing to lend more funds to investors. The equilibrium interest rate is determined by the intersection of the demand and supply curves for loanable funds, as indicated in Figure .

Rate of return on capital and the demand for loanable funds. The demand for loanable funds takes account of the rate of return on capital. The rate of return on capital is the additional revenue that a firm can earn from its employment of new capital. This additional revenue is usually measured as a percentage rate per unit of time, which is why it is called the rate of return on capital. Firms will demand loanable funds as long as the rate of return on capital is greater than or equal to the interest rate paid on funds borrowed. If capital becomes more productive—that is, if the rate of return on capital increases—the demand curve for loanable funds depicted in Figure will shift out and to the right, causing the equilibrium interest rate to rise, ceteris paribus.

Thriftiness and the supply of loanable funds. The supply of loanable funds reflects the thriftiness of households and other lenders. If households become more thrifty—that is, if households decide to save more—the supply of loanable funds increases. The increase in the supply of loanable funds shifts the supply curve for loanable funds depicted in Figure down and to the right, causing the equilibrium interest rate to fall, ceteris paribus.

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Measures of Capital

 

While labor is measured in terms of the number of workers hired or the number of hours worked, it is difficult to measure capital in terms of physical units because there are so many different types of capital goods. Capital goods, therefore, are simply measured in terms of their market or dollar value.

Capital stock. The market value of capital goods at a given point in time, for example, at the end of a year, is referred to as the capital stock. A firm's capital stock is the market value of its factory, equipment, and other capital goods at a given point in time. A household's capital stock is the market value of its residential structures, human capital, and other capital goods at a given point in time. Firms' and households' capital stocks will vary over time due to investment and depreciation.

Investment. Investment is the addition of new capital goods to a firm's or household's capital stock. Investment is a flow measurement; it represents the market value of new capital purchased or produced per unit of time. For example, if a firm with $90,000 in capital at the end of last year purchases $10,000 in capital during the current year, its investment for this year is $10,000, while its capital stock at the end of the current year is $100,000.

Depreciation. Depreciation is also a flow measurement; it measures the reduction in market value of a firm's or household's capital stock per unit of time. Depreciation of the capital stock is caused by normal wear and tear and by the obsolescence of capital goods over time.

When depreciation over a period of time exceeds investment over the same period of time, the capital stock decreases; otherwise, the capital stock increases or remains the same. For example, if the firm with $90,000 in capital at the end of last year purchases $10,000 in new capital during the current year, but experiences $20,000 in depreciation during the current year, its capital stock at the end of the current year will have decreased to $80,000 ($90,000 + $10,000 − $20,000). If depreciation during the current year is only $5,000, instead of $20,000, then the firm's capital stock at the end of the current year will have increased to $95,000.

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Present Value and Investment Decisions

Firms purchase capital goods to increase their future output and income. Income earned in the future is often evaluated in terms of its present value. The present value of future income is the value of having this future income today.

Present value formula. The present value of receiving $20,000 one year from now can be calculated using the present value formula. The formula for finding the present value of X dollars received t years from now at the current market interest rate r is

For example, if X = $20,000, t = 1, and r = .05, the present value of $20,000 received one year from now is 20,000/(1.05)¹ = $19,047.62.

The present value of $20,000 received two years from now at an interest rate of 5% is found by setting X = $20,000, t = 2, and r = .05. The present value in this case is $20,000/(1.05)² = $18,140.59. As you can see from these examples, the present value of the future income is the amount of income that you would need to invest today, at current market interest rates, in order to obtain the same amount of future income at the same future date.

Firm's investment decision. The firm's investment decision is to determine whether to purchase new capital. In determining whether to purchase new capital—for example, new equipment—the firm will take into account the price of the new equipment, the revenue that the new equipment will generate for the firm over time, and the scrap value of the new equipment. The firm will also take into account the interest rate, which represents the firm's opportunity cost of investing in the new equipment. It will use the interest rate to calculate the present value of the future net income that it expects to earn from its purchase of the new capital equipment. If the present value is positive, the firm will choose to purchase the new equipment. If the present value is negative, it is better off forgoing the investment in new equipment.

As an example, consider a restaurant that is trying to decide whether to invest in a new piece of capital equipment—a jukebox. The jukebox costs $7,000 and lasts 4 years. The restaurant estimates that the jukebox will provide it with income of $2,000 per year, net of maintenance costs. After 4 years, the scrap value of the jukebox is estimated at $500. In determining whether to purchase the jukebox, the firm will calculate the net present value of the present and future income that it receives from purchasing the jukebox. The firm's present value calculations are shown in Table for an interest rate of 10%.

The calculation of net present value includes the initial outlay of $7,000 for the jukebox. The present value formula is used to calculate the present value of the $2,000 annual income received in each of the 4 years. In the fourth year, the $500 scrap value is added to the $2,000 in income received from the jukebox. The total net present value of the jukebox turns out to be −$318. Because this amount is negative, the firm will choose to forgo purchasing the jukebox.

As Table reveals, the firm's net present value calculations depend on the interest rate. The higher the interest rate is, the higher the firm's opportunity cost of investing in the jukebox. A higher interest rate lowers the present value of the future income earned from capital, making it less profitable for the firm to invest in new capital; however, if interest rates fall, the opportunity cost of investing in new capital also falls. The lower the interest rate is, the higher the present value of the future income earned from new capital investment, and the more likely it is that firms will invest in new capital.

For example, consider what happens to the firm's net present value calculations for the jukebox when the interest rate falls from 10% to 6%. Table repeats the present value calculations of Table at the lower interest rate of 6%.

At the lower interest rate, the net present value of the jukebox is positive ($326). If the firm can obtain $7,000 in loanable funds at 6% interest, it will choose to purchase the jukebox.

The decision to invest in other types of capital goods can also be made on the basis of present value calculations. For example, the decision to invest in human capital by attending college is based on the present value of the future income that an individual can earn with a college degree. If the present value is positive, the individual will choose to attend college. If the present value is negative, the individual will not attend college and will perhaps take a job instead.

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