Question

To produce a certain product, there are two competing processes under consideration. Process A requires acquisition of a new machine that is estimated to have an initial cost of $30,000 and a salvage value of $12,000 at the end of its useful life of 6 years. In addition, the process requires a fixed cost of $47,000 per year and a variable cost of $250 per day. Alternatively, Process B requires the use of human labor. The process will need 6 workers, each earning $100 per day and will have a fixed cost of $20,000 per year and additional variable costs of $200 per day.

a) Draw the cash flow diagrams of each alternative process.

b) Discuss which equivalent worth method(s) may be appropriate to use in the solution of the problem. Express the assumption(s) you should make.

c) State the factor of interest to consider for this problem.

d) Determine the minimum number of days per year required for the two processes to break even at an interest rate of 2% per year. Note that you should explicitly write down your formulation using engineering formulations.

  

  

e) If company predicts to produce this product no more than 90 days a year, which process to choose do you recommend to the company? Explain.

Answer 1

A.

Assumption of no of days in a year to be =365

Process A	0	1	2	3	4	5	6
Machine	30000
Salvage value							12000
Fixed cost		47000	47000	47000	47000	47000	47000
VC		91250	91250	91250	91250	91250	91250
Net CF	-30000	-138250	-138250	-138250	-138250	-138250	-126250

Process B
FC	20000	per year
VC	200	per day
Workers	6
Wage	100	per day
Net CF	-312000	Yearly

B. We can use present worth method, as it adjust every cash for inflation and interest rate for the futture years. And make it comparable in current year.

C. We should use Minimun acceptable rate of return (MARR) or discount rate (R) that tells the opportunity cost.

D.

E. With 90 days working we find the PW of both the process.

Process A	0	1	2	3	4	5	6
Machine	30000
Salvage value							12000
Fixed cost		47000	47000	47000	47000	47000	47000
VC		22500	22500	22500	22500	22500	22500
Net CF	30000	69500	69500	69500	69500	69500	57500
Discounted CF	30000	68137.25	66801.23	65491.4	64207.26	62948.29	51058.35
PW	408643.8(Outflow)
No. of days	90

Process B	1	2	3	4	5	6
FC	20000	per year
VC	200	per day
Workers	6
Wage	100	per day
Net CF	147000	147000	147000	147000	147000	147000
Discounted CF	144117.6	141291.8	138521.4	135805.3	133142.4	130531.8
PW	823410.3(Outflow)

As Process A has less cost compared to process B. we go with Process A.