
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:

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

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 (roundedoff) 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 (roundedoff) 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.