Question

13-41 The total marginal cost data for a grouping of defender machines over the next 5 years is: Year 1 Marginal Cost $120,000 100,000 50,000 80,000 250,000 4 What replacement technique is recommended if a challenger is being considered to replace the defender machine grouping. Why? What is the economic life and minimum EUAC of the machine group? Use an interest rate of 12% If the challenger has a minimum EUAC of $110,000, what is your recommendation? a. b. c.

Answer 1

a. We need to calculated economic service life and minimum EUAC of the defender and challenger machines. As machine as different cost in each year, we need to determine the minimum equivalent cost for each year of operation and its economic service life.

b. MARR = 12%

Using excel to calculate Economic service life and Minimum EUAC

Year	Discount factor	O&M cost	PV (O&M)	Cumulative (O&M)	Cumulative (O&M) + Initial Cost	(A/P,12%,n)	EUAC
A	B	C	D=C*B	E	F=E+0	J	K = J*F
1	0.89286	120000.00	107142.86	107142.86	107142.86	1.12000	120000.00
2	0.79719	100000.00	79719.39	186862.24	186862.24	0.59170	110566.04
3	0.71178	50000.00	35589.01	222451.26	222451.26	0.41635	92617.35
4	0.63552	80000.00	50841.45	273292.70	273292.70	0.32923	89977.37
5	0.56743	250000.00	141856.71	415149.42	415149.42	0.27741	115166.49
Discount factor	1/(1+0.12)^n
(A/P,i,n)	i((1 + i)^n)/((1 + i)^n-1)

Minimum EUAC is 8997737 at 4 years, so economic life is 4 years

c. If the challenger has minimum EUAC of 110000, the defender should be replaced only after 4 yrs as minimum EUAC of Defender is less than minimum EUAC of the challenger for 4 yrs

Showing formula in excel

Year	Discount factor	O&M cost	PV (O&M)	Cumulative (O&M)	Cumulative (O&M) + Initial Cost	(A/P,12%,n)	EUAC
A	B	C	D=C*B	E	F=E+0	J	K = J*F
1	=1/(1.12)^N17	120000	=P17*O17	=Q17	=R17	=0.12*((1 + 0.12)^N17)/((1 + 0.12)^N17-1)	=S17*T17
2	=1/(1.12)^N18	100000	=P18*O18	=R17+Q18	=R18	=0.12*((1 + 0.12)^N18)/((1 + 0.12)^N18-1)	=S18*T18
3	=1/(1.12)^N19	50000	=P19*O19	=R18+Q19	=R19	=0.12*((1 + 0.12)^N19)/((1 + 0.12)^N19-1)	=S19*T19
4	=1/(1.12)^N20	80000	=P20*O20	=R19+Q20	=R20	=0.12*((1 + 0.12)^N20)/((1 + 0.12)^N20-1)	=S20*T20
5	=1/(1.12)^N21	250000	=P21*O21	=R20+Q21	=R21	=0.12*((1 + 0.12)^N21)/((1 + 0.12)^N21-1)	=S21*T21
Discount factor	1/(1+0.12)^n
(A/P,i,n)	i((1 + i)^n)/((1 + i)^n-1)