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Income from the sale of application software (apps) is usually constant for several years and then decreases quite rapidly as the market gets close to saturation
Income from the sale of application software (apps) is usually constant for several years and then decreases quite rapidly as the market gets close to saturation. Income from one smart phone app was $40,000 in years 1 through 5 and then decreased geometrically by 4% per year through year 7. Determine the equivalent annual income in years 1 through 7, using an interest rate of 8% per year.
Expert Solution
Interest rate = 8% per years
Income from year 1 was $40,000 through year 1 to 5 which decreases by 4 in year 6 and 7
Present value of cash flow: [Cash flow / (1 + Interest rate)^Year]
| Year | Income | Present value of Income |
| 1 | $ 40,000 | $ 37,037.04 |
| 2 | $ 40,000 | $ 34,293.55 |
| 3 | $ 40,000 | $ 31,753.29 |
| 4 | $ 40,000 | $ 29,401.19 |
| 5 | $ 40,000 | $ 27,223.33 |
| 6 | $ 38,400 | $ 24,198.51 |
| 7 | $ 36,864 | $ 21,509.79 |
| $ 205,416.71 |
Present value of Income is $205,416.71
Annual equivalent income: Present value of Income / {[1 - (1 + r)^-n[ / r} = 205,416.71 / {[1 - (1 + 0.08)^-7[ / 0.08} = 39,454.88
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