# Cost Calculations

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Cost calculations appear everywhere in construction, from estimating the cost of building materials for a domestic renovation, to managing the budget for a large commercial project. Typically, the mathematics used at the end of a cost calculation is just basic arithmetic, but there is often complexity involved from a project management perspective in deciding what needs to be calculated and how this should be done -- e.g. in setting accounting assumptions or interpreting regulatory requirements.

### Example Problem

It is estimated that the construction of a metropolitan apartment complex requires a team of contract plumbers whose total work commitment will be $235$ hours. A commercial plumbing firm can provide such a team at a rate of $\$110$per hour without GST. The director of the plumbing firm advises that if the number of hours is increased to$250$, the team can be provided at a discount rate of$\$105$ per hour without GST. By calculating the total cost (including a GST of $10\%$) of the required number of hours at the undiscounted rate and $250$ hours at the discounted rate, decide which is the better offer in terms of cost.

### Solution

The cost (including GST) of hiring a team of plumbers for the required number of hours is
$$235\times (110+10\%\ctext{ of }110) = 235\times (110+0.1\times 110) = 235\times 121 = \28435,$$
and the cost of hiring a team of plumbers at the discounted rate for $250$ hours
$$250\times (105+10\%\ctext{ of }105) = 250\times (105+0.1\times 105) = 250\times 115.5 = \28875.$$
Hence the cheaper option is $235$ hours. Note, however, that this might not be the best option from a project management point of view. The difference between the costs of service at $250$ and $235$ hours is $\$440 = \$28875-\$28435$. And this would purchase an extra$15$hours. These `cheap hours', which would cost approximately$\$29$, might be useful as a contingency.

More information can be found from chapter 3 of this Maths Quest site.