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Capital, Interest, and Corporate Finance

CHAPTER

13

© 2003 South-Western/Thomson Learning

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Production, Saving, and TimeSince production takes time, it cannot occur without prior saving

For example, while Jones is waiting for his current crop to grow, he must rely on food saved from prior production

Jones could take some of his time to make a plow which would increase his productivity

However, making the plow is time consuming

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Production, Saving, and TimeIn making the plow, Jones engages in roundabout production

That is, when Jones produces capital he hopes to increase his future productivity

An increased amount of roundabout production in an economy means that more capital accumulates more goods can be produced in the futureAdvanced industrial economies are characterized by much roundabout production capital accumulation

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Production, Saving, and TimeProduction requires saving because both direct and roundabout production requires time

Time during which goods and services are not available from current production

In modern economies, producers need not rely exclusively on their own prior saving by relying on financial intermediaries for funds

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Consumption, Saving, and TimeMost consumers value present consumption more than future consumption they have a positive rate of time preferenceAnother explanation for this positive rate of time preference is uncertaintyBecause present consumption is valued more than future consumption, households must be rewarded to postpone consumption they must be rewarded

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Consumption, Saving, and TimeBy saving a portion of their income in financial institutions, households forgo present consumption for a greater ability to consumer in the future

Interest is the reward offered households for forgoing present consumption

The interest rate is the annual interest as a percentage of the amount saved

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Consumption, Saving, and Time

The higher the interest rate, other things constant, the more consumers are rewarded for saving the more willing they are to save

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Optimal InvestmentIn a market economy characterized by specialization and exchange, firms need not produce their own capital, nor must they rely upon their own saving

They can purchase capital using borrowed funds

Exhibit 1 identifies six pieces of farm machinery that Jones has ranked from most to least productive

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Exhibit 1: Marginal Rate of Return on Investment

The total product of the farm equipment is shown in column (2) and the marginal product of each piece of equipment in column (3).With no equipment, Jones can produce 200 bushels of corn. If he adds the Tractor-Tiller, his production increases to 1,200 the marginal product of the Tractor-Tiller is 1,000 bushels per year; the addition of the combine would contribute an additional 800 bushels, and so on.Suppose Jones sells corn in a perfectly competitive market at $4 per bushel the price is multiplied by the marginal product to yield the marginal revenue product the change in total revenue resulting from adding another piece of farm equipment.For simplicity, suppose each piece of farm equipment costs $10,000 as shown in column (5).

Total Marginal Marginal Marginal Marginal Farm Product Product Revenue Resource Rate ofEquipment (bushels) (bushels) Product Cost Return (1) (2) (3) (4) = (3$4) (5) (6) = (4/5)No equipment 200 - - - -Tractor-Tiller 1,200 1,000 $4,000 $10,000 40%Combine 2,000 800 3,200 10,000 32Irrigator 2,600 600 2,400 10,000 24Harrow 3,000 400 1,600 10,000 16Crop Sprayer 3,200 200 800 10,000 8Post-Hole Digger 3,200 0 0 10,000 0

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Optimal InvestmentSuppose that the equipment is so durable that it lasts indefinitely, and that the price is expected to remain the same in the future

Thus, the farm equipment will increase revenue not only in the first year but every year into the future

The optimal investment requires that Jones take time into consideration

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Optimal InvestmentJones can’t simply equate the marginal resource cost with marginal revenue product

The marginal cost is an outlay this year, whereas the marginal product is an annual amount this year and each year into the future

Markets bridge this time discrepancy with the interest rate

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Optimal InvestmentJones must decide how much to invest

The first task is to compute the marginal rate of return he would earn each year by investing in farm machinery

The marginal rate of return on investment is capital’s marginal revenue product as a percentage of its marginal resource cost

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Optimal InvestmentFor example, the Tractor-Tiller yields a marginal revenue product of $4,000 per year and has a marginal resource cost of $10,000

The rate of return Jones could earn on this investment is $4,000 / $10,000 is 40%

The rates of return for all the pieces of farm equipment are shown in column (6)

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Exhibit 1: Marginal Rate of Return on Investment

Dividing the marginal revenue product of capital in column (4) by the marginal resource cost of that capital in column (5) yields the marginal rate of return in column (6) for each piece of equipment.

Total Marginal Marginal Marginal Marginal Farm Product Product Revenue Resource Rate ofEquipment (bushels) (bushels) Product Cost Return (1) (2) (3) (4) = (3$4) (5) (6) = (4/5)

No equipment 200 - - - -Tractor-Tiller 1,200 1,000 $4,000 $10,000 40%Combine 2,000 800 3,200 10,000 32Irrigator 2,600 600 2,400 10,000 24Harrow 3,000 400 1,600 10,000 16Crop Sprayer 3,200 200 800 10,000 8Post-Hole Digger 3,200 0 0 10,000 0

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Optimal InvestmentGiven the marginal rates of return on each piece of equipment, how much should Jones invest in order to maximize profits?

Suppose he borrows the money, paying the market interest rate Jones will buy more capital as long as its marginal rate of return exceeds the market interest rate he will stop before capital’s marginal rate of return falls below the market rate of interest

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Optimal Investment

If the market rate of interest is 20%, Jones would invest in the first three pieces of equipment $30,000

Conversely, if the market rate of interest falls to 10%, he will invest in the Harrow as well and at 6% he will invest in the Crop Sprayer

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Exhibit 1: Marginal Rate of Return on Investment

Jones should increase his investment as long as the marginal rate of return on that investment exceeds the market rate of interest

The data in column (6) provide the information for the step-like curve where the solid lines reflect the amount Jones will invest at each interest rate

For example, if the market interest rate is between 32% and 40%,, Jones should invest in the first piece of equipment

This step-like curve represents the farmer’s demand for investment. It is a derived demand, based on each additional piece of equipment’s marginal productivity.

The curve steps down to reflect diminishing marginal productivity of capital

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Optimal Investment

The results would not change if Jones used his own funds so long as he could save at the market interest rate

That is, whether Jones borrows the money or uses savings on hand, the market interest rate represents his opportunity cost of investing

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Summary of StepsFirst, compute the marginal revenue product of capitalNext divide the marginal revenue product by the marginal resource cost to determine the marginal rate of return the firm’s demand curve for investmentThe market interest rate is the opportunity cost of investingFirm should invest more as long as the marginal rate of return on capital exceeds the market interest rate

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Market for Loanable FundsThe major demanders of loans are firms that borrow to invest in physical capitalAt any time, each firm has a variety of investment opportunities they rank their opportunities from highest to lowest, based on their expected marginal rates of returnFirms will increase their investment until their expected marginal rate of return just equals the market interest rate

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Market for Loanable FundsFirms are not the only demanders of loansHouseholds are often willing to pay extra to consume now rather than later and one way to ensure that these goods and services are available now is to borrow for present consumptionHousehold demand curve for loans also slopes reflecting consumers’ greater willingness and ability to borrow at lower interest rates, other things constant

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Market for Loanable FundsBanks play the role of financial intermediaries in the market for loanable funds

The loanable funds market brings together savers, or suppliers of loanable funds, and borrowers, or demanders of loanable funds, to determine the market rate of interest

The higher the interest rate, other things constant, the greater the reward for saving the larger the quantity of loanable funds

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Exhibit 2: Market for Loanable Funds

S

Loanable funds per year (billions of dollars) 0

8

D

Inte

res

t ra

te (

per

cen

t)

100

The supply of loanable funds curve shows the positive relationship between the market interest rate and the quantity of savings supplied, other things constant the upward sloping supply curve shown as S.

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Demand for Loanable FundsFor the economy as a whole, if the amount of other resources and the level of technology are fixed, diminishing marginal productivity causes the marginal rate of return curve, which is the demand curve for investment to slope downward

The demand for loanable funds is based on the expected marginal rate of return these borrowed funds yield when invested in capital

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Demand for Loanable FundsEach firm has a downward-sloping demand curve for loanable funds, reflecting a declining marginal rate of return on investment

With some qualifications, the demand for loanable funds by each firm can be summed horizontally to yield the demand for loanable funds by all firms as seen by D in Exhibit 2

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Exhibit 2: Market for Loanable Funds The demand for loanable funds by all firms is shown as D. Factors assumed constant along the demand curve include the prices of resources, the level of technology, and the tax laws.

The demand and supply for loanable funds determine the market interest rate which in our example is 8% and the equilibrium quantity of loanable funds is $100 billion per year.

S

Loanable funds per year (billions of dollars) 0

8

D

Inte

res

t ra

te (

per

cen

t)

100

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Exhibit 2: Market for Loanable Funds

Any change in the demand or supply for loanable funds will change the market interest rate. For example a major technological breakthrough that increases the productivity of capital will increase its marginal rate of return demand for loanable funds shifts from D to D' a higher interest rate and an increase in the quantity of loanable funds

S

Loanable funds per year (billions of dollars) 0

8

D

Inte

res

t ra

te (

per

cen

t)

100

9

D'

115

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Why Interest Rates DifferThus far, we have been talking about the market rate of interest, implying that only one interest rate prevails in the loanable funds market

At any particular time, however, a range of interest rates coexist in the economy

Why do interest rates differ?Risk some borrowers are more likely than others to default

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Why Interest Rates DifferDuration of the loan• Since the future is uncertain, and the further

into the future a loan is to be repaid, the more uncertain that repayment becomes lenders require a higher interest rate

• Term structure of interest rates is the relationship between the duration of the loan and the interest rate charge

Cost of administration• Costs of executing the loan agreement,

monitoring the loan, and collecting the payments

• These costs, as a proportion of the total amount of the loan, decrease as the size of the loan increases

Tax treatment• Lower the tax rate, the lower the interest rate

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Present Value and DiscountingBecause present consumption is valued more than future consumption, present and future consumption can’t be directly compared

A way of standardizing the discussion is to measure all consumption in terms of its present value

Present value is the current value of a payment or payments that will be received in the future

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Present Value One Year Hence

Suppose the market interest rate is 10%, so you can either lend or borrow at that rate

One way to determine how much you would pay for the opportunity to receive $100 one year from now is to ask how much you would have to save now, at the market interest rate, to end up with $100 one year from now

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Present Value One Year HenceThat is, what amount of money, if saved at a rate of interest of 10%, will accumulate to $100 one year from now

We can calculate the answer with the following formula

present value x 1.10 = $100, orpresent value = ($100/1.10) = $90.91That is, if the interest rate is 10%, $90.91 is the present value of receiving $100 one year from now

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Present Value One Year HenceThe procedure of dividing the future payment by 1 plus the prevailing interest rate in order to express it in today’s dollars is called discounting

The interest rate used to discount future payments is called the discount rate

Thus, the present value of $100 to be received one year from now depends on the interest or discount rate

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Present Value One Year HenceThe more that present consumption is preferred to future consumption, the higher the interest rate that must be offered savers to defer consumption

That is, the higher the interest rate, or discount rate, the more the future payment is discounted and the lower its present value

Alternatively, the higher the interest rate, the less you need to save now to yield a given amount in the future

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Present Value One Year Hence

Conversely, the less present consumption is preferred to future consumption, the less savers need to be paid to defer consumption and the lower the interest rate

The lower the interest rate, or discount rate, the less the future income is discounted and the greater its present valueA lower interest rate means that individuals must save more now to yield a given amount in the future

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Present Value One Year Hence

As a general rule, the present value of receiving an amount one year from now is:

Example: when the interest rate is 5%, the present value of receiving $100 one year from now is: $100/ 1.05 = $95.24

rateinterest 1now fromyear one receivedamount PV

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Present Value in Later YearsNow consider the present value of receiving $100 two years from now what amount of money, if deposited at the market rate of interest of 5%, would yield $100 two years from now?

At the end of the first year, the value would be the present value x 1.05, which would then earn the market interest rate during the second year the following equation

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Present Value in Later Years

Present value x 1.05 x 1.05 = present value x (1.05)2 = $100

70.90$1025.1100$

(1.05)$100 PV

2

tiMPV

)1(

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Present Value in Later Years

Because (1 + i) is greater than 1, the more times it is multiplied by itself (as determined by t), the smaller the present value

Thus, the present value of a given payment will be smaller the further into the future that payment is to be received

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Present Value of an Income Stream

The previous method is used to compute the present value of a single sum to be paid at some point in the futureMore investments, however, yield a stream of income over timeIn cases where the income is received over a period of years, the present value of each receipt can be computed individually and the results summed to yield the present value of the entire income stream

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Present Value of an AnnuityA given sum of money received each year for a specified number of years is called an annuitySuch an income stream is called a perpetuity if it continues indefinitely into the futureAs a practical matter, the present value of receiving a particular amount forever is not much more than that of receiving it for, say 20 years, because of discounting

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Corporate Stock and Retained Earnings

Corporations acquire funds for investment in three ways

Issuing stockRetaining some of their profitsborrowing

An entrepreneur is a profit-seeking decision-maker who organizes an enterprise and assumes the risk of operation

Pays resource owners for the opportunity to use those resources in the firm

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Corporate Stock and Retained Earnings

The initial sale of stock to the public is called an initial public offering, or an IPOA share of corporate stock

Represents a claim on the net income and assets of a corporation, andThe right to vote on corporate directors and on other important mattersOne share of stock leads to one vote

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Corporate Stock and Retained Earnings

Corporations must pay corporate income taxes on any profit

After-tax profit is either paid as Dividends to shareholdersReinvested profit is called retained earnings and allows the firm to finance expansion

Corporations are not required to pay dividends

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Corporate BondsA bond is the corporation’s promise to pay back the holder a fixed sum of money on the designated maturity date plus make annual interest payments until that date

The payment stream for bonds is more predictable than that for stocks

Unless the corporation goes bankrupt, it is obliged to pay bondholders the promised amounts less risky

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Securities Exchanges

Once stocks and bonds have been issued and sold, owners of these securities are free to resell them on security exchanges

There are seven security exchanges in the U.S. with the two largest being the New York Stock Exchange and the Nasdaq

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Securities ExchangesInstitutional investors, such as banks, insurance companies and mutual funds account for over half the trading volume on major exchanges

By providing a secondary market for securities, exchanges enhance the liquidity of these securities

The secondary markets for stocks also determine the current market value of the corporation

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Securities Exchanges

The share price reflects the present value of the discounted stream of expected profit

Security prices give the firm’s management some indication of the wisdom of raising investment funds through retained earnings, new stock issues, or new bond issues

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Securities ExchangesThe greater a corporation’s expected profit, other things constant, the higher the value of shares on the stock market and the lower the interest rate that would have to be paid on new bond issues

Thus, securities markets allocate funds more readily to successful firms than to firms in financial difficulty