Problem $1$

You are an engineer at a manufacturing plant, and you have been asked to lead a study to consider potential energy savings projects. One idea is to convert the overhead lighting from metal halide bulbs to LED.

Currently, there are $150$ bulbs in the plant that are on $24$ hours$/$day$,355$ days$/$year$.$ Each bulb requires $250W$ of electric power. The average cost of electricity is $$\frac{0\mathrm{.}105}{k}Wh.$ These bulbs last an average of $10,000$ hours and cost $$15$ each to replace.

You have received a proposal to convert all $150$ bulbs to LED. The new bulbs required $150W$ of power each. They have a life expectancy average of $50,000$ hours and would cost $$125$ each. The proposal also quotes a one$-$time cost of $$10,000$ to convert the existing light fixtures to work with LED bulbs.

Considering the initial cost of new bulbs and fixture conversion, as well as the difference in annual cost of electricity and bulb replacements, is this project economically justified based on a present value approach?

The company uses a discount rate of $12\%$ and a time horizon of $10$ years on these types of investments. $($Hint: this is a decision to choose the least penalizing equivalent value.$)$

a$)$ Create cash flow diagrams for both scenarios.

b$)$ Determine which option is better and why.

Assume that this project can be implemented at the end of this year and the plant will have already incurred the cost of operating the existing bulbs at the current level this year. All potential gains would start from next year.

Tip: Do not attempt to predict the exact year$($s$)$ of bulb replacement.