The share of national income accruing to capital is more substantial than commonly recognized. National income in Canada is divided 60-40, favoring labour. This leaves a very large component going to the owners of capital. The stock of physical capital includes assembly-line machinery, rail lines, dwellings, consumer durables, school buildings and so forth. It is the stock of produced goods used as inputs to the production of other goods and services.
Physical capital is the stock of produced goods that are inputs in the production of other goods and services.
Physical capital is distinct from land in that the former is produced, whereas land is not. These in turn differ from financial wealth, which is not an input to production. We add to the capital stock by undertaking investment. But, because capital depreciates, investment in new capital goods is required merely to stand still. Depreciation accounts for the difference between gross and net investment.
Gross investment is the production of new capital goods and the improvement of existing capital goods.
Net investment is gross investment minus depreciation of the existing capital stock.
Depreciation is the annual change in the value of a physical asset.
Since capital is a stock of productive assets we must distinguish between the value of services that flow from capital and the value of capital assets themselves.
A stock is the quantity of an asset at a point in time.
A flow is the stream of services an asset provides during a period of time.
When a car is rented it provides the driver with a service; the car is the asset, or stock of capital, and the driving, or ability to move from place to place, is the service that flows from the use of the asset. When a photocopier is leased it provides a stream of services to the user. The copier is the asset; it represents a stock of physical capital. The printed products result from the service the copier provides per unit of time.
The price of an asset is what a purchaser pays for the asset. The owner then obtains the future stream of capital services it provides. Buying a car for $30,000 entitles the owner to a stream of future transport services. The term rental rate defines the cost of the services from capital.
Capital services are the production inputs generated by capital assets.
The rental rate is the cost of using capital services.
The price of an asset is the financial sum for which the asset can be purchased.
But what determines the price of a productive asset? The price must reflect the value of future services that the capital provides. But we cannot simply add up these future values, because a dollar today is more valuable than a dollar several years from now. The key to valuing an asset lies in understanding how to compute the present value of a future income stream.
Present values and discounting
When capital is purchased it generates a stream of dollar values (returns) in the future. A critical question is: How is the price that should be paid for capital today related to the benefits that capital will bring in the future? Consider the simplest of examples: A business is contemplating buying a computer. This business has a two-year horizon. It believes that the purchase of the computer will yield a return of $500 in the first year (today), $500 in the second year (one period into the future), and have a scrap value of $200. What is the maximum price the entrepreneur should pay for the computer? The answer is obtained by discounting the future returns to the present. Since a dollar today is worth more than a dollar tomorrow, we cannot simply add the dollar values from different time periods.
The value today of $500 received a year from now is less than $500, because if you had this amount today you could invest it at the going rate of interest and end up with more than $500 tomorrow. For example, if the rate of interest is 10% (= 0.1), then $500 today is worth $550 next period. By the same reasoning, $500 tomorrow is worth less than $500 today. Formally, the value next period of any amount is that amount plus the interest earned; in this case the value next period of $500 today is 
, where r is the interest rate. It follows that if we multiply a given sum by (1+r) to obtain its value next period, then we must divide a sum received next period to obtain its value today. Hence the value today of $500 next period is simply 
. To see that this must be true, note that if you have $454.54 today you can invest it and obtain $500 next period if the interest rate is 10%. In general:
This rule carries over to any number of future periods. The value of a sum of money today two periods into the future is obtained by multiplying the today value by 
twice. Or the value of a sum of money today that will be received two periods from now is that sum divided by twice. And so on, for any number of time periods. So if the amount is received twenty years into the future, its value today would be obtained by dividing that sum by twenty times; if received 'n' periods into the future it must be divided by 'n' times.
Two features of this discounting are to be noted: First, if the interest rate is high, the value today of future sums is smaller than if the interest rate is low. Second, sums received far in the future are worth much less than sums received in the near future.
Let us return to our initial example, assuming the interest rate is 0.1 (or 10%). The value of the year 1 return is $500. The value of the year 2 return today is $454.54, and the scrap value in today's terms is $181.81. The value of all returns discounted to today is thus $1,136.35.
Table 12.3 Present value of an asset (
)
| Year |
Annual return |
Scrap value |
Discounted values |
| Year 1 |
500 |
|
500 |
| Year 2 |
500 |
200 |
454.54 + 181.81 |
| Asset value today |
|
|
1,136.35 |
The present value of a stream of future earnings is the sum of each year's earnings divided by one plus the interest rate 'n' times, where 'n' is the number of years in the future when the amount will be received.
We are now in a position to determine how much the buyer should be willing to pay for the computer. Clearly if the value of the computer today, measured in terms of future returns to the entrepreneur's business, is $1,136.35, then the potential buyer should be willing to pay any sum less than that amount. Paying more makes no economic sense.
Discounting is a technique used in countless applications. It underlies the prices we are willing to pay for corporate stocks: Analysts make estimates of future earnings of corporations; they then discount those earnings back to the present, and suggest that we not pay more for a unit of stock than indicated by the present value of future earnings.
