PPD CASE STUDY Question from Ncarb
Why they are not using total costs for proposed system / cost savings per year which should be 340625/18750? It doesn't make sense to me to use only "initial cost of proposed system/cost saving per year". Can someone please explain ?

Howdy,
340625/18750 = (initial cost of the proposed system + 1 year of maintenance and operation of that system) / 1 year savings between the two systems. It is incorrect to use this because it is assuming 1 years time when the question is asking us to solve for the number of years.Perhaps viewing this question as an income VS debt statement that you're trying to balance would be helpful.
Consider the annual operational and maintenance costs of the proposed system as income since this is where the church will save money and the initial cost of the proposed system is an expense (debt).
The income ($18,750 per year) will be used to pay off the debt ($312,500)
The question is asking how many years it will take for the proposed system to show cost savings over the existing system or in other words, break even from the initial cost of the proposed system (debt) and realize the income from cost savings as profit.So the debt (initial cost of the proposed system $312,500), is the known variable that we are calculating towards to find our answer in number of years...
$312,500 = $18,750/year X (# of years) ..... $312,500/$18,750 = # of years ..... 16.67 = # of years
Typically factoring in the initial cost of the system with the annual operational and maintenance cost is done when solving for a lifecycle analysis type question or for income VS debt questions where the number of years is provided.
For example, if this question asked "In 20 years time, how much will the church save by switching to the proposed system?" Then you would include the initial cost of the proposed system in your calculation like so... ($18,750 per year X 20 years)  $312,500 = $62,500 
The system is going to cost $312,500, which is the $25/sf x 12,500 sf.
The system is going to save $1.50/sf per year, which is $3.75  $2.25 (the existing maintenance cost  new maintenance cost).
$1.50/sf x 12,500sf = $18,750 in savings per year.
To find the payoff # of years you divided the cost to install is $312,500 ÷ $18,750 (annual savings/year) = 16.6 years.
They said to round it to the nearest year, so that's 17 years.
Hope this helps!
Rebekka O'Melia, Registered Architect, NCARB, B. Arch, M. Ed, Step UP, Step UP ARE 5.0 Courses
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