Question 1188615: CONTEXT:
You need to invest in an air conditioner (A/C). You have two choices.
1. A/C, regular
2. A/C, with inverter
You are assuming that the A/C with inverter will be the better choice in the long run.
QUESTION: WHEN will it be the better choice?
DATA:
1. A/C, regular
Price: PhP 24,000
Down Payment: PhP 8,000
(12) Monthly Installments: PhP 1,375
2. A/C, with inverter
Price: PhP 35,000
Down Payment: PhP 13,500
(12) Monthly Installments: PhP 1,890
TASKS:
1. Create a model of the data you have by letting the down payment be the
y-intercept and the monthly payment as the slope.
2. What is the graph of the system?
3. Compute for the solution by using substitution.
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! to keep this as simple as posible, i think you are trying to compare two options so that you can find the break even point.
without taking into consideration cost of money, inflation, economic life of equipment, taxes and any real world considerations, i think what you can do is what i'm going to show you below.
you have two options and you want to find the break even point.
your cost for plan A is 13500 + 1890 * x
your cost for plan B is 8000 + 1375 * x
these are capital costs only (down payment for equipment plus amortized monthly cost for equipment).
to find the break even point, you would set them equal to each other.
you would get 13500 + 1890 * x = 8000 + 1375 * x.
subtract 8000 from both sides of the equation and subtract 1890 * x from both sides of the equation to get:
13500 - 8000 = 1375 * x - 1890 * x
combine like terms to get:
5500 = -515 * x
solve for x to get:
x = 5500 / -515 = -10.67961165 months.
the number of months is negative because there is no break even point.
with just the capital costs that you showed, plan A is more expensive and will always be more expensive over time.
those two equations can be graphed as shown below:
as you can see, there is no break even point.
you need to add in operational cost savings to get a break even point.
in order to get a break even point, the operational costs for the air conditioner without inverter must be greater than the operational costs for the air conditioner with inverter.
from what i get on the internet, the electricity costs for the air conditioner with inverter are 30% to 50% less than the electricity costs for the air conditioner without inverter.
outside of that, i think the operational costs will probably be the same unless you can determine other operational cost differences between the two plans.
for demonstration purposes, i assumed 1000 dollars per month electricity costs for the air conditioner with inverter plan and 2000 dollars per month electricity costs for the air conditioner without inverter plan.
the costs for the air conditioner with inverter plan becomes 13500 + 1890 * x + 1000 * x = 13500 + 2890 * x.
the costs for the air conditioner without inverter plan becomes 8000 + 1375 * x + 2000 * x = 8000 + 3375 * x.
to find the break even point, set them equal to each other to get:
13500 + 2890 * x = 8000 + 3375 * x
subtract 8000 from both sides of the equation and subtract 2890 from both sides of the equation to get:
13500 - 8000 = 3375 * x - 2890 * x
combine like terms to get:
5500 = 485 * x
solve for x to get:
x = 5500 / 4856 = 11.34020619 months.
round to two decimal places to get 11.34 months.
those two equations can be graphed as shown below:
as you can see, the break even points is in 11.34 months.
a more sophisticated analysis would need to take into account the other factors i mentioned above.
the graphical analysis would not be possible without going through a cash flow analysis and then manually plotting the points on the graph.
the costs for electricity were just taken off the top of my head to show you the impact that they might have.
the real study would have to determine the actual costs for electricity between the two options to determine if there is a cut off point and where it would.
the real study would probably have to go out more months than are shown here because the real break even point may be further out than shown by my made up figures.
also you would have to keep in mind that the amortization costs are for 12 months so that any more months would not include them, but only include the electricity and other operational costs.
as i said before, i kept this very simple, but a real analysis would need to be a cash flow analysis taking into account other factors not taken into account here.
i hope this helps.
solving this as solving a system of equations by substitution is not the way this type of problem would be solved, as best i can determine.
let me know if you have any quetions.
theo
Answer by ikleyn(52786)  (Show Source):
You can put this solution on YOUR website! .
Please consider my post as an INDEPENDENT OPINION.
From my point of view, the task which you posted to the forum is a BAD STYLE nonsense.
/\/\/\/\/\/\/\/
Do you know the tale by Hans Christian Andersen " The Emperor's New Clothes " ?
Everybody applauded, except only one little boy, who said " . . . but the king is naked . . . "
https://andersen.sdu.dk/vaerk/hersholt/TheEmperorsNewClothes_e.html
https://en.wikipedia.org/wiki/The_Emperor%27s_New_Clothes
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