Question

It is necessary to pump twice as much water as can be handled by an existing small pump, which is now 5 years old. This pump can be sold now for $1200 or kept for 5 years, after which it will have zero salvage value. Operating expenses are $2500 per year.

If the pump is kept, a similar extra one must be purchased for $3500, with operating costs of $2000 per year; its salvage values after 5 and 10 years are the same as for the original (existing) pump.

A large pump, equal in capacity to two of the smaller pumps, costs $6200, with operating expenses of $4200 per year.

New machines have economic lives of 10 years with 1800 and zero salvage values at year 5 and year 10 respectively. Determine the best course of action if the MARR is 10%.

Answer 1

In first case we need to install another pump to meet the demand and in Second case we are replacing the existing pump with a new large pump. In first case, Even though we install another pump having 10 years of economic life to meet the demad the existing pump has only 5 years of economic life left. So comparison need to done at the end of 5 years from the installation of additonal pump.

Case 1 ( Installing additional pump)

Cost of pump = $3500 Salvage value at the end of 5th year = $1200

operating cost = $2000 as we continue the old pump for further 5 years its operating cost =$2500

Total operating cost = $4500

Using Annual Equivalent to determine the best alternative

Annual equivalent = -4500-3500(A/P,i,n)+1200(A/F,i,n)

(A/P,i,n) is equal payment capital recovery factor and (A/F,i,n) is equal payment sinking fund factor

= i =10%, n=5

= -4500- 3500*0.263+1200*0.163 ( salvage is what we get at the end of 5 years therefore positive)

= $-5226.73 ( Negative indicated we need to spend)

In case 1 we need to spend $5226.73

Case 2 ( Installing a single large pump)

Cost of pump = $6200 salvage at the end of 5 years =$1800

operating cost = $4200

If we are installing a single large pump we will sell the already existing small pump and its salvage is $1200 so we will get this money.

Effective cost of pump = 6200-1200 = $5000

Annual equivalent = i=10% and n = 5

  =

=-4200-5000(0.263)+1800(0.163)

=$-5224.15 ( negative indicates spending)

In case 2 we need to spend $5224.15

case 2 is better as spending is less than case 1

Case 2 that is installing a new large pump is better than two small pumps