The first table gives the present value of $1 at the end of different time perio

Question

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

Table 13.4 Present Value of $1 to Be Received at the End of Each Period for a Given Number of Periods

QUESTION: Remember Carol Stein’s tractor? We saw that at an interest rate of 7%, a decision to purchase the tractor would pay off; its net present value is positive. Suppose the tractor is still expected to yield $20,000 in net revenue per year for each of the next 5 years and to sell at the end of 5 years for $22,000; and the purchase price of the tractor still equals $95,000. Use Tables (a) and (b) to compute the net present value of the tractor at an interest rate of 8%.

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

Explanation / Answer

The cash flow you will receive (10 terms of $12,000 = 4% x $300,000 and the capital payment of $300,000) has to be discounted by 6% a year, then added up.

For instance, the interest after 3 years is discounted by 1.06^3 and it's present value is only $10,075.

Here is a table

year: payment: DCF:

0,5 12000 11,655.43

1,0 12000 11,320.75

1,5 12000 10,995.69

2,0 12000 10,679.96

2,5 12000 10,373.29

3,0 12000 10,075.43

3,5 12000 9,786.12

4,0 12000 9,505.12

4,5 12000 9,232.19

5,0 12000 8,967.1

5,0 300000 224,177.45

Sum of values in the last column: $326,768.54

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