Finance

Future Value - Evaluation of Investment Profitability


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.

Future Value - Evaluation of Investment Profitability596Future Value - Evaluation of Investment Profitability