Northwestern energy estimates that the present worth now of income from an investment in renewable energy sources is $12,475,000. there will be no income in years 1 and 2, but in year 3 income will be $250,000, and thereafter it will increase linearly through year 15. what is the required gradient of income growth, if interest rate is 15% per year?

The gradient of income growth is $12,59,741.59. This means that income must rise by $12,59,741.59 each year.

We follow these steps to arrive at the

We calculate the Future Value of the investment as follows:

This represents the total of revenues earned over 15 years from the investment.

Since income increases linearly over 15 years, we can consider year 3 earnings as the base. Let the income increase in year 4 by x. Since income increases yearly, we can calculate income in each year as follows

YearRevenues

1              0

2              0

3         250000

4         250000  + x

5         250000  + 2x

6         250000  + 3x

7         250000  +4x

8         250000  + 5x

9         250000  + 6x

10         250000  + 7x

11         250000  + 8x

12         250000  + 9x

13         250000  + 10x

14         250000  + 11x

15         250000  + 12x

Total   32,50,000.00  + 78x

Now we equate the values in steps 1 and above to find 'x' the gradient