TUTORIAL 6 no. 7 . Would you please explain why are you not multiplying the cash flow of a possible raise in annual salary by V^5 ?, because the raise is only possible after 5 years. thank you

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If she moves to Cape Town, the benefit (salary) she will receive will either be:

\(\rightarrow\) A starting salary of R150 000 per year for 15 years until she retires at age 60. There is a 70% chance that this is the case (There is a 70% chance she doesn't get a promotion)

\(\rightarrow\) R150 000 per year for 5 years and 2×R150 000= R300 000 for the 10 years after that if she gets a promotion. There is a 30% chance of this happening.

In both instances, the salary is going to increase by 10% per year.

So the expected present value of the benefit is :

$$0.7 × 150 000(v + 1.1v^2 + 1.1^2 v^3 +. . . + 1.1^{14}v^{15}) + \\0.3 × 150 000(v + 1.1v^2 + 1.1^2v^3 + 1.1^3v^4 + 1.1^4v^5) +\\ 0.3 × (2 ×150 000) (1.1^5v^6 + 1.1^6v^7 + . . . + 1.1^{14}v^{15}) $$

I suspect that the last line of the summation is what is you need clarity on. This last line $$0.3 × (2 ×150 000) (1.1^5v^6 + 1.1^6v^7 + . . . + 1.1^{14}v^{15})$$ can also be written as: $$0.3 × (2 ×150 000) × v^5 ×(1.1^5v + 1.1^6v^2 + . . . + 1.1^{14}v^{10})$$ if you take out a common factor of \(v^5\) and so the cash flow is being multiplied by a present value factor of \(v^5\).

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