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erastova [34]
3 years ago
13

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?
Business
1 answer:
valentina_108 [34]3 years ago
7 0

Answer: 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 answer:

<h3><u>1. Calculating the total value of earnings after 15 years</u></h3>

We calculate the Future Value of the investment as follows:

\mathbf{FV = PV * (1+r)^{n}}

FV = 12475000 * (1+0.15)^{15}

\mathbf{FV = 101509843.8}

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

<h3><u>2.Calculating the gradient</u></h3>

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

Year Revenues

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    <u>     250000  + 12x</u>

Total   32,50,000.00  + 78x

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

32,50,000 + 78x = 101509843.8\\

78x = 101509843.8 - 32,50,000.00 = 9,82,59,843.82

x = \frac{9,82,59,843.82}{78}

\mathbf{x = 12,59,741.59}

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