Capital and Rental Cost

We want to talk about economic growth. However, first we need to introduce some of the standard concepts used by economists. This lesson looks at capital and related concepts.

Josh plans to have a lawn-mowing business during the five-month mowing season. There are plenty of people willing to pay \$25 each time their lawn is mowed. Josh needs a lawnmower and also a pickup truck to haul the lawnmower to the jobs. The lawnmower and the pickup truck are capital goods. Capital goods include office buildings, factory equipment, airplanes, and other durable (long-lived) goods. Capital goods are contrasted with consumer goods and services, such as food, haircuts, and movie tickets. Some of the differences are listed in the table below.

Consumer Goods and ServicesCapital Goods
Provide immediate, direct enjoymentCan be used to produce other goods and services
Can only be used for a short period of timeCan be used for years
Bought primarily by consumersBought primarily by businesses

There are 100 days in the lawn mowing season. Josh can mow 8 lawns a day. So his total revenue will be (\$25 per lawn)(8 lawns per day)(100 days) = \$20,000.

A new lawnmower costs \$600 and a new pickup truck costs \$25,000. But Josh still thinks he can make money.

Josh can lease the pickup truck for the mowing season for \$3,000, and he can lease the lawnmower for \$300. The total lease cost of \$3300 is the rental cost of capital for Josh's lawn-mowing business.

(We used the term "simple interest rate" to be distinct from "compound interest." If interest compounds, then the borrower pays "interest on the interest." Here is how simple interest and compound interest differ, if you borrow \$600 at an interest rate of 1 percent.)

MonthSimple Interest CalculationCompound Interest Calculation
First(.01)(\$600) = \$6(.01)(\$600) = \$6
Second(.01)(\$600) = \$6(.01)(\$600 + \$6) = \$6.06
Third(.01)(\$600) = \$6(.01)(\$600 + \$6 + \$6.06) = \$6.12
Fourth(.01)(\$600) = \$6(.01)(\$600 + \$6 + \$6.06 + \$6.12) = \$6.18
Fifth(.01)(\$600) = \$6(.01)(\$600 + \$6 + \$6.06 + \$6.12 + \$6.18) = \$6.24
Total Due\$630\$630.60

Why does it cost \$300 to lease the lawnmower? Because leasing the lawnmower is like borrowing money to buy it and then selling it after five months.

Suppose that Josh borrowed \$600 at a simple interest rate of 1 percent per month for five months. That means that after five months, Josh would owe 5 percent in interest, or \$30 in interest, in addition to the \$600 principal. That is, a bank lends Josh \$600 today, and he has to pay back \$630 in five months.

What if Josh does not borrow the \$600? Instead, he takes the money out of a savings account, where it could earn interest at the rate of one percent a month. Either way, the interest cost of the money is \$30. This is true whether Josh pays the interest on a loan or foregoes the interest on a savings account.

To Think About: Is the interest rate at which Josh can borrow likely to be higher than the rate that he can earn on savings? Why? Does that mean that it is cheaper for Josh to finance his lawnmower with savings than with borrowing?

Depreciation

When Josh sells the lawnmower in five months, he can get \$330 for it. The difference between the purchase price of \$600 and the \$330 he can get for the lawnmower after five months of use is called depreciation. Capital goods depreciate because of physical wear and tear. Another type of depreciation comes from technological change. As newer models come out (think of computers), older models become less valuable. For a lawnmower, most of the depreciation reflects wear and tear, rather than technological change.

If Josh gets his lawnmower by borrowing, buying, and selling, then he pays \$630 (principal plus interest) and gets back \$330, for a net cost of \$300. This happens to be the same cost as leasing the lawnmower. If the leasing cost were \$200, then it would be cheaper for Josh to lease. Conversely, if the leasing cost were \$400, Josh would find it cheaper to buy a lawnmower and then sell it.

1. Suppose that the lawnmower only depreciates by \$200, so that Josh could sell it for \$400 after five months. Would he be better off leasing the lawnmower for \$300 or borrowing to buy a lawnmower and then selling it?

2. Suppose that the interest rate is 1 percent per month, simple interest. Suppose that the price of a lawnmower is \$1200 and the resale price at the end of five months is \$660. What is the cost to Josh of borrowing to buy the lawnmower and then re-sell it? What do you think the leasing cost should be?

3. If the interest rate goes up to 2 percent per month, does this raise or lower the cost of capital?

4. Summarize the factors that affect the cost of capital.

5. Suppose that to buy the pickup truck Josh borrowed \$25,000 at a simple monthly interest rate of 1 percent. What is the total interest cost (five months of interest at one percent per month)? For how much would he need to be able to re-sell the pickup truck in order to make this transaction equivalent to the \$3000 cost of leasing?