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Time is the complicating factor when we analyze capital and natural resources. Because current choices affect the future stocks of both resources, we must take those future consequences into account. And because a payment in the future is worth less than an equal payment today, we need to convert the dollar value of future consequences to present value. We determine the present value of a future payment by dividing the amount of that payment by (1 + r)^{n}, where r is the interest rate and n is the number of years until the payment will occur. The present value of a given future value is smaller at higher values of n and at higher interest rates.
Interest rates are determined in the market for loanable funds. The demand for loanable funds is derived from the demand for capital. At lower interest rates, the quantity of capital demanded increases. This, in turn, leads to an increase in the demand for loanable funds. In the aggregate, the supply curve of loanable funds is likely to be upward-sloping.
We assume that firms determine whether to acquire an additional unit of capital by (NPV) of the asset. When NPV equals zero, the present value of capital’s marginal revenue product equals the present value of its marginal factor cost. The demand curve for capital shows the quantity of capital demanded at each interest rate. Among the factors that shift the demand curve for capital are changes in expectations, new technology, change in demands for goods and services, and change in relative factor prices.
Markets for natural resources are distinguished according to whether the resources are exhaustible or renewable. Owners of natural resources have an incentive to consider future as well as present demands for these resources. Land, when it has a vertical supply curve, generates a return that consists entirely of rent. In general, economic rent is return to a resource in excess of the minimum price necessary to make that resource available.
How would each of the following events affect the demand curve for capital?
Use the tables below to answer Problems 1–5. The first table gives the present value of $1 at the end of different time periods, given different interest rates. For example, at an interest rate of 10%, the present value of $1 to be paid in 20 years is $0.149. At 10% interest, the present value of $1,000 to be paid in 20 years equals $1,000 times 0.149, or $149. The second table gives the present value of a stream of payments of $1 to be made at the end of each period for a given number of periods. For example, at 10% interest, the present value of a series of $1 payments, made at the end of each year for the next 10 years, is $6.145. Using that same interest rate, the present value of a series of 10 payments of $1,000 each is $1,000 times 6.145, or $6,145.
Table 13.3 Present Value of $1 to Be Received at the End of a Given Number of Periods
Percent Interest | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
Period | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 |
1 | 0.980 | 0.962 | 0.943 | 0.926 | 0.909 | 0.893 | 0.877 | 0.862 | 0.847 | 0.833 |
2 | 0.961 | 0.925 | 0.890 | 0.857 | 0.826 | 0.797 | 0.769 | 0.743 | 0.718 | 0.694 |
3 | 0.942 | 0.889 | 0.840 | 0.794 | 0.751 | 0.712 | 0.675 | 0.641 | 0.609 | 0.579 |
4 | 0.924 | 0.855 | 0.792 | 0.735 | 0.683 | 0.636 | 0.592 | 0.552 | 0.515 | 0.442 |
5 | 0.906 | 0.822 | 0.747 | 0.681 | 0.621 | 0.567 | 0.519 | 0.476 | 0.437 | 0.402 |
10 | 0.820 | 0.676 | 0.558 | 0.463 | 0.386 | 0.322 | 0.270 | 0.227 | 0.191 | 0.162 |
15 | 0.743 | 0.555 | 0.417 | 0.315 | 0.239 | 0.183 | 0.140 | 0.180 | 0.084 | 0.065 |
20 | 0.673 | 0.456 | 0.312 | 0.215 | 0.149 | 0.104 | 0.073 | 0.051 | 0.037 | 0.026 |
25 | 0.610 | 0.375 | 0.233 | 0.146 | 0.092 | 0.059 | 0.038 | 0.024 | 0.016 | 0.010 |
40 | 0.453 | 0.208 | 0.097 | 0.046 | 0.022 | 0.011 | 0.005 | 0.003 | 0.001 | 0.001 |
50 | 0.372 | 0.141 | 0.054 | 0.021 | 0.009 | 0.003 | 0.001 | 0.001 | 0 | 0 |
Table 13.4 Present Value of $1 to Be Received at the End of Each Period for a Given Number of Periods
Percent Interest | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
Period | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 |
1 | 0.980 | 0.962 | 0.943 | 0.926 | 0.909 | 0.893 | 0.877 | 0.862 | 0.847 | 0.833 |
2 | 1.942 | 1.886 | 1.833 | 1.783 | 1.736 | 1.690 | 1.647 | 1.605 | 1.566 | 1.528 |
3 | 2.884 | 2.775 | 2.673 | 2.577 | 2.487 | 2.402 | 2.322 | 2.246 | 2.174 | 2.106 |
4 | 3.808 | 3.630 | 3.465 | 3.312 | 3.170 | 3.037 | 2.910 | 2.798 | 2.690 | 2.589 |
5 | 4.713 | 4.452 | 4.212 | 3.993 | 3.791 | 3.605 | 3.433 | 3.274 | 3.127 | 2.991 |
10 | 8.983 | 8.111 | 7.360 | 6.710 | 6.145 | 5.650 | 5.216 | 4.833 | 4.494 | 4.192 |
15 | 12.849 | 11.718 | 9.712 | 8.559 | 7.606 | 6.811 | 6.142 | 5.575 | 5.092 | 4.675 |
20 | 16.351 | 13.590 | 11.470 | 9.818 | 8.514 | 7.469 | 6.623 | 5.929 | 5.353 | 4.870 |
25 | 19.523 | 15.622 | 12.783 | 10.675 | 9.077 | 7.843 | 6.873 | 6.097 | 5.467 | 4.948 |
30 | 22.396 | 17.292 | 13.765 | 11.258 | 9.427 | 8.055 | 7.003 | 6.177 | 5.517 | 4.979 |
40 | 27.355 | 19.793 | 15.046 | 11.925 | 9.779 | 8.244 | 7.105 | 6.233 | 5.548 | 4.997 |
50 | 31.424 | 21.482 | 15.762 | 12.233 | 9.915 | 8.304 | 7.133 | 6.246 | 5.554 | 4.999 |
Mark Jones is thinking about going to college. If he goes, he will earn nothing for the next four years and, in addition, will have to pay tuition and fees totaling $10,000 per year. He also would not earn the $25,000 per year he could make by working full time during the next four years. After his four years of college, he expects that his income, both while working and in retirement, will be $20,000 per year more, over the next 50 years, than it would have been had he not attended college. Should he go to college? Assume that each payment for college and dollar of income earned occur at the end of the years in which they occur. Ignore possible income taxes in making your calculations. Decide whether you should attend college, assuming each of the following interest rates:
A new health club has just opened up in your town. Struggling to bring in money now, the club is offering 10-year memberships for a one-time payment now of $800. You cannot be sure that you will still be in town for the next 10 years, but you expect that you will be. You anticipate that your benefit of belonging to the club will be $10 per month (think of this as an annual benefit of $120). Decide whether you should join at each of the following interest rates:
You have just purchased a new home. No money was required as a down payment; you will be making payments of $2,000 per month (think of these as annual payments of $24,000) for the next 30 years. Determine the present value of your future payments at each of the following interest rates: