Question

The Tree Top Airline​ (TTA) is a small​ feeder-freight line started with very limited capital to serve the independent petroleum operators in the arid Southwest. All of its planes are​ identical, although they are painted different colors. TTA has been contracting its overhaul work to Alamo Airmotive for ​$35,000 per plane per year. TTA estimates​ that, by building a ​$450,000 maintenance facility with a life of 15 years and a residual​ (market) value of ​$100,000 at the end of its​ life, they could handle their own overhaul at a cost of only ​$25, 000 per plane per year. What is the minimum number of planes they must operate to make it economically feasible to build this​ facility? The MARR is 12​% per year.

Answer 1

Answer:

To make it feasible it will need to operate 7 or more planes.

Explanation:

450,000 maintenance facility

useful life of 15 year

salvage value of 100,000

saving cost per plane:

third party cost - own facility cost = cost savings

           35,000  -          25,000      =    10,000

present value of the salvage value: (present value of a lump sum)

$\frac{salvage }{(1 + rate)^{time} } = PV$  

salvage $ 100,000

time  15 years

Minimum accepter rate of return: 0.12000

$\frac{100000}{(1 + 0.12)^{15} } = PV$  

PV   18,269.6261

present worth of the facility:

450,000- 18,268.63 = 431,731.37

Now we determinate the PMT over a 15 years period to know the cost savings per year to justify the facility:

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV 431,731

time 15

rate 0.12

$431731.37 \div \frac{1-(1+0.12)^{-15} }{0.12} = C$

C  $ 63,388.630

As each plane cost savings are 10,000

63,388.62  / 10,000 = 6.39

the company will need to operate 7 or more planes.