A small company purchased now for ?50,000 will lose ?9,600 each year for the first 4 years

Economics Nov 11, 2020

A small company purchased now for ?50,000 will lose ?9,600 each year for the first 4 years. An additional investment of ?30,000 in the company will be required at the end of the 4th year. After 15 years, the company can be sold for ?70,000. What should be the profit each year from 5th through the 15th year to obtain a rate of return of 25%?

Expert Solution

This question needs to be solved in two steps:

Step 1: The amount of money that is invested by the end of year 4 including the required return on it

= 50000*(1+25%)^4+9600*1.25^3+9600*1.25^2+9600*1.25+9600+30000

= 207420

Step 2: This is teh PV of annuity with X that needs to be recovered over 11 years (year 5 to year 15, both inclusive) with a rate of 25%

207420 = X*((1-(1+25%)^-11)/0.25) = P*3.6564

P = 207420/3.6564 = P56728 is the amount of profit required annually from Y5 to Y15

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