Question

Determine the value of x, for a company’s two investment alternatives to be equivalent at an interest rate of 15% per year:

Option 1. Invest $3 at the end of the first year. Starting from the end of 9th year, the company gets sales of $x for 4 years, followed by $2.7x for 7 years, and $x for 4 years.

Option 2. Invest $35 at year 0, and the company starts to get sales $35 at the end of year 7, increment by 1 cumulatively until at the end of year 13 (e.g., at end of year 8 is 36).

Answer 1

The present value of option 1 can be expressed as

Now, calculating the present worth of option 2

Now, equate the two values

The value of x = $ 10.81

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