A construction company is bidding on a project comprising five high$-$rise buildings to be erected one after the other. $$The company considers the use of advanced, hydraulically operated tunnel forming systems to be purchased and used $40$ times on each building over a $1-$yr period of time. $$The tunnel forms cost $$80/$sf$.$No salvage value is expected at the end of the $5-$yr project. $$As the two last buildings to be constructed slightly differ in their design, the forms will have to be modified at the cost of $$12\mathrm{.}5/$sf$.$Periodical maintenance is expected every $80$ uses at a cost of $4\%$ of the purchase cost. $$Consider an annual interest rate of $5\%.$What is the expected average material cost per sf for each use?

Hints:

There is no salvage value.

The average material cost has three components: purchase cost, modification cost, and maintenance cost.

Purchase occurs at the start $=$ year $0.$

Modification occurs at the end of the third year $=$ year $3.$

Maintenance occurs at the end of years $2$ and year $4.$ Since this is a five$-$year project, you cannot use the maintenance formula which assumes unform costs over the life of the forms.$$ Instead, use the modification formula twice: once for year $2$ and once for year $4.$