Case Study

A contractor operates a rock crusher and stores the material until needed in an adjacent stockpile area. The stockpile area is unpaved, and some of the stockpiled aggregate is contaminated by the sub$-$grade and cannot be used. The estimated stockpile losses are shown in the Table $1.$ This equates to a combined loss of $8\%$ each year.

The contractor is considering to pave the stockpile area to reduce the loss of aggregate. Paving the stockpile area would reduce the losses due to contamination to about $2\%.$ The crusher produces $250,000$ tons$/$year at a cost of $$1\mathrm{.}50/$ton$.$ The new paving should last $10$ years, and there has no salvage value.

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The paving will cover $4\mathrm{.}56$ acres. The previous stockpile losses will serve as sub$-$grade and base courses for the new surfacing.$$ A $3$ thick surface will require $3700$ tons of asphaltic concrete, which costs $$20/$ton installed. The engineering and site work involve a one$-$time cost of about $$5000.$ The surface requires routine maintenance costing about $$1000/$year$.$

Table $2$ shows the uncertainty $($lower and upper limits$)$ of the data estimated by the contractor to evaluate the feasibility of paving the stockpile area.$$ Assuming the contractor has a minimum accepted rate of return $($MARR$)$ of $12\%,$ answer the following questions $($the use of Microsoft Excel to solve this case study is strongly recommended.$$ Excel charts and functions $($e$.$g$.$RATE$$and$$PV$)$ can speed up your calculations, make your solution more accurate, and facilitate neater submission$)$:

$1.$ Determine the internal rate of return $($IRR$)$ of the stockpile area paving.

$2.$ For each of the $7$ variables in Table $2,$ use IRR to graph NPV vs$.$ the value of this variable, as the variable ranges between the limits you derive from the table $($use $10\%$ intervals$).($hint: for each graph, use estimated values of the other factors, e$.$g$.,$ use values ranging between $5$ to $20$ years for the economic life on x$-$axis versus the NPV on the y$-$axis assuming average values for the other variables$).$

$3.$ Based on your answer to question $2,$ which of the factors in Table $2$ is riskier for the decision about whether to pave the stockpile area? $($hint: examine the variance of NPV between upper and lower limits$)$

$4.$ Estimate the IRR for the $$worst$-$case$$ and $$best$-$case$$ scenarios for all $7$ variables in Table $2.($hint: for the best$-$case scenario assume all variables will have their best possible outcome and vice versa for the worst$-$case scenario$).$

$5.$ What is the NPV of the $$worst$-$case$$ and $$best$-$case$$ scenarios using the contractor$$s MARR?

$6.$ Apply some other analyses, of your choice other than the ones listed above, you deem could help the contractor make their decision about paving the stockpile area.

$7.$ Based on your answers to questions $1$ through $6,$ what is your recommendation for paving the stockpile area? Explain your reasoning.

$$ Table $1$ Current Stockpile Losses Table $2$ Lower and Upper Limits on Estimated Data