Question

You work for a famous architectural firm. Your supervisor asked you to evaluate two alternatives for improving the facade of the firm’s building. The building can be completely painted at a cost of SR 6.5K. The paint is expected to remain attractive for 4 years, at which time repainting will be necessary. Every time the building is repainted, the cost will be 20% higher than the previous time. Alternatively, the building can be sandblasted now and every 6 years at a cost 40% greater than the previous time. If the company’s MARR is 10% per year, what is the maximum amount that could be spent now on the sandblasting alternative that would render the two alternatives indifferent over a study period of 12 years?

Answer 1

Lets first design the cashflows. Lets say that the sandblasting would cost X. Then the cashflow would look like the following-

The alternatives would be equal when their NPVs are equal. We know that NPV is given by

So, using the formula above, we get

Cashflow of alternative 1=-6500-7800/1.1⁴-9360/1.1⁸-11232/1.1¹²

Cashflow of alternative 2=-x-1.4x/1.1⁶-1.96x/1.1¹²

Equating these cashflows, we get

-6500-7800/1.1⁴-9360/1.1⁸-11232/1.1¹²=-x-1.4x/1.1⁶-1.96x/1.1¹²

Solving for x, we get

x=8188.27

So, at a sandblasting cost of 8188.27 these two alternatives would be equal.