Question

4) The total expenditure for installation of plumbing system with 10 years life period pump in a residential building is 5000 OMR. The initial cost of the pump without installation charge is bought through bank loan (CI) with fixed interest rate in a year 4% and payback period is 48 months, installation cost of pump is 200 OMR, operating cost is 2000 Baiza /Week, and Maintenance cost is 5 OMR/month, labor cost is 20 OMR/year and two time pump part replacement cost in life period is 30 OMR/Replacement, the final cost to exchange the system after 10 years is 10% of Initial cost. What is the initial purchase cost and final cost of the pump system? (5 marks)

Answer 1

Note: Everything in this question becomes over-simplified if we focus on each and every word of the question. Calculation is then just the final touch to the solution.

(Also, 1 OMR = 1000 Baiza)

Point of view (just to simplify the explanation): We are a resident and we want to install plumbing/pump system.

And to install the system, we need to give 5000 OMR on the site(On the spot) when the service provider comes and installs the system at our residence.

Now, 200 OMR is included in this OMR 5000, because 200 OMR is the installation cost of pump. And OMR 5000(or Total expenditure for installation of plumbing system) should obviously include the Installation cost of the pump(or 200 OMR).

Now, the question says: "The initial cost of the pump without installation charge is bought through bank loan..."

And we have to find this initial purchase cost. So let this initial purchase cost be x OMR.

So, we ask bank to give us x OMR.
Now, x + 200 = 5000, so x = 4800

(i)Therefore, the initial purchase cost = 4800 OMR

(ii)To find the final cost of the pump system:

We now assume that 10 years have passed. We have taken the benefit of the pump system. And we had to bear the operating(, labor, maintenance, etc) costs all this while. And even got replaced pump part 2 times. And when the system got exhausted, we got back the money by exchanging the system after these 10 years.

Now, we are interested in finding the net cost that we had to give while using it for its lifetime.

To calculate all cost that we have to bear in these 10 years:

(a) Compound Interest:
Principal = 4800
Rate = 4% per annum
Time period = 48 months = 4 years
Compounded Annually
C.I.=Amount-Principal=4800(1+0.04)⁴ - 4800 = ((1.04)⁴)4800 - 4800 = (1.16985856)4800 - 4800 = 5615.321088 - 4800 = 815.321088

(b) Operating cost for 10 years:
Number of weeks in 10 years = 521.429
=(2000/1000)*521.429 = 1042.858

(c) Maintenance cost:
=5*12*10 = 600

(d) Labor Cost:
=20*10=200

(e) Replacement cost:
=30*2=60

(f) Cost received after exchanging the system:
For simplicity, we can assume that when the system was exhausted after its life period(10 years), we gave it up and got the cost for giving it up.
(The service provider may refurbish/recycle our exhausted plumbing system)

=10% of Initial Cost that we had to give (excluding pump installation cost)
=10% of 4800
=480

Final Cost of the pump system, for us, now = 5000 + (a) +(b) + (c) + (d) + (e) - (f)
= 5000 + 815.321088 + 1042.858 + 600 + 200 + 60 - 480
(As we had to give up (a),(b),(c),(d),(e) from our pocket but we got (f) into our pocket))
=5000 + 2238.179088
=7238.179088 OMR