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|
Project No. 1 |
Project No. 2 |
Project No. 3 |
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|
Original Data |
Future Value in 5 Years |
Original Data |
Future Value in 5 Years |
Original Data |
Future Value in 5 Years |
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Row |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
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|
1 |
Amount of investment |
1.0 |
1.6 |
1.0 |
1.6 |
1.0 |
1.6 |
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|
2 |
Income: End of Year1 |
0.3 |
0.44 |
0.4 |
0.59 |
0.5 |
0.73 |
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|
3 |
End of Year 2 |
0.4 |
0.53 |
0.4 |
0.53 |
0.4 |
0.53 |
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|
4 |
End of Year 3 |
0.3 |
0.36 |
0.3 |
0.36 |
0.1 |
0.12 |
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|
5 |
End of Year 4 |
0.3 |
0.33 |
0.3 |
0.33 |
|
|
||
|
6 |
End of Year 5 |
0.1 |
0.10 |
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|
|
|
||
|
7 |
End of Year 6 |
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|
|
|
|
|
||
|
8 |
Future value of flow of income (at the end of five years) |
|
1.76 |
|
1.81 |
|
1.39 |
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|
9 |
Future profit (row 8 minus row 1) |
|
0.16 |
|
0.21 |
|
-0.21 |
||
|
10 |
Rate of future profit on the investment |
|
10% |
|
13% |
|
-13% |
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Explanation of the tableColumns 3, 5, and 7 display the future value five years from now. The amounts written in these columns are the results of a calculation based on the following assumptions:
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We receive 10% annual interest rate from the bank for each installment we deposit.
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We raise the $1 million investment, The amount from the loan, which we return at the end of five years, and which bears 10% annual interest.
Row 9 shows the future profit – The future profit is obtained by subtracting row 1 from row 8.
Row 10 shows the future profit rate – The rate of future profit is obtained by dividing row 9 by row 1.
More Realistic Assumptions:
The assumption in the table that the interest we will pay on the loan will be equal to the interest we receive on deposits (10%) is not realistic. It is more reasonable that we will have to pay higher interest on the loan. Assume that this rate is 15%. The new results are displayed in the table.
Table 2.8 (Sums in millions of $)
In the table, the future value of the amount of the investment is $2 million, compared with $1.6 million as in the previous example.
In this situation where a 15% interest rate is charged to borrow and a 10% interest is earned for deposits, only Project 2 is profitable.
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|
Project No. 1 |
Project No. 2 |
Project No. 3 |
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|
|
Original Data |
Future Value in 5 Years |
Original Data |
Future Value in 5 Years |
Original Data |
Future Value in 5 Years |
|||
|
Row |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
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|
1 |
Amount of investment |
1.0 |
2.0 |
1.0 |
2.0 |
1.0 |
2.0 |
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|
2 |
Income: End of Year 1 |
0.3 |
0.52 |
0.4 |
0.70 |
0.5 |
0.88 |
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|
3 |
End of Year 2 |
0.4 |
0.61 |
0.4 |
0.61 |
0.4 |
0.61 |
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|
4 |
End of Year 3 |
0.3 |
0.40 |
0.3 |
0.40 |
0.1 |
0.13 |
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|
5 |
End of Year 4 |
0.3 |
0.35 |
0.3 |
0.35 |
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|
||
|
6 |
End of Year 5 |
0.1 |
0.10 |
|
|
|
|
||
|
7 |
End of Year 6 |
|
|
|
|
|
|
||
|
8 |
Future value of flow of income |
|
1.97 |
|
2.05 |
|
1.61 |
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|
9 |
Future profit (row 8 minus row 1) |
|
-0.03 |
|
0.05 |
|
-0.39 |
||
|
10 |
Rate of future profit on the investment (row 9 divided by row 1) |
|
-1.5% |
|
2.5% |
|
-19.5% |
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The Distinction Between Savers and Debtors in Calculating Future Value
We will examine this distinction through an example.
The parents of two brothers, one a saver and one a debtor, offer each of them money according to two alternatives:
-
Alternative 1 – receiving $100k now.
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Alternative 2 – receiving $150k five years from now.
According to alternative 1, they will behave as follows:
The saver will deposit the money in a savings plan in the bank at 5% annual interest.
The debtor will repay debts, thereby saving annual interest payments of 15%.
The situation five years from now will be as follows:
The saver: If he chooses alternative 1, he will have $128k (rounded-off) five years from now. If he chooses alternative 2, he will have $150k five years from now. In this case, alternative 2 is preferable
The debtor: If he chooses alternative 1, his debts will be $201k (rounded-off) less five years from now (as compared with a situation in which he does not pay back his debts). If he chooses alternative 2, his debts will be $150k less five years from now.
Alternative 1 is preferable.
