Question

Shifted cash flow: Revenue from gas wells that have been in production for at least 5 years tends to follow a decreasing geometric gradient. One particular rights holder received royalties of $4000 per year for years 1 through 6 (i.e. six times), but beginning in year 7, income decreased by 15% per year through year 14 (geometric gradient of 15%). What was the future value (year 14) of the income from the well, if all of the income was invested at 10% per year

Answer 1

Hi

Please find the solution below:
Approach:
For year 1 to 6, the amount 4000 was received, while from 7-14 the amount decreased by 15% every year. Hence, in year 7, 4000 * (1-0.15) was received, and so on ftill year 14...

All the amounts received between year 1 to 14 were invested at 10%. Therefore, $4000 received at year 1, was invested for 13 years at 10% p.a. i.e. 4000 (1+0.1)^13 and so on..

The sum of all these investments gives the final value 91.6k
Let me know in case of any queries.

Year	Amount	Invested at 10%
1	4000	13,809.08
2	4000	12,553.71
3	4000	11,412.47
4	4000	10,374.97
5	4000	9,431.79
6	4000	8,574.36
7	3400	6,625.64
8	2890	5,119.81
9	2456.5	3,956.22
10	2088.025	3,057.08
11	1774.821	2,362.29
12	1508.598	1,825.40
13	1282.308	1,410.54
14	1089.962	1,089.96
		91,603.32