Project No. 1 Project No. 2 Project No. 3 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 1 Amount of investment 1.0 1.6 1.0 1.6 1.0 1.6 2 Income: End of Year1 0.3 0.44 0.4 0.59 0.5 0.73 3 End of Year 2 0.4 0.53 0.4 0.53 0.4 0.53 4 End of Year 3 0.3 0.36 0.3 0.36 0.1 0.12 5 End of Year 4 0.3 0.33 0.3 0.33 6 End of Year 5 0.1 0.10 7 End of Year 6 8 Future value of flow of income (at the end of five years) 1.76 1.81 1.39 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%

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:

1. We receive 10% annual interest rate from the bank for each installment we deposit.

2. 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.

 Project No. 1 Project No. 2 Project No. 3 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 1 Amount of investment 1.0 2.0 1.0 2.0 1.0 2.0 2 Income: End of Year 1 0.3 0.52 0.4 0.70 0.5 0.88 3 End of Year 2 0.4 0.61 0.4 0.61 0.4 0.61 4 End of Year 3 0.3 0.40 0.3 0.40 0.1 0.13 5 End of Year 4 0.3 0.35 0.3 0.35 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 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%

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.

• 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.