Question

A machine purchased 1 year ago for $1055,000 costs more to operate than anticipated. When purchased, the machine was expected to be used for 10 years with annual maintenance costs of $32,000 and a $10,000 salvage value. However, last year, it cost the company $38,000 to maintain it, and these costs are expected to escalate to $40,000 this year and increase by $2,000 each year thereafter. The market value is now estimated to be $105,000 − $15,000k, where k is the number of years since the machine was purchased. It is now estimated that this machine will be useful for a maximum of 5 more years. A replacement study is to be performed now. Determine the value the first cost of this defender to be used in replacement analysis. Assume i = 10% per year.

EOY AOC

0 38000

1 40000

2 42000

3 44000

4 46000

5 48000

Answer 1

Market value of defender = 105000 - 15000 * k

Since machine was purchased one year ago.

First cost of defender to used = 105000 - 15000 * 1 = 90000

Using excel for ESL analysis

Year	Discount factor	O&M cost	PV (O&M)	Cumulative (O&M)	Cumulative (O&M) + Initial Cost	Salvage value	PV (Salvage value)	NPV	(A/P,10%,n)	EUAC
A	B	C	D=C*B	E	F=E+90000	G	H=G*B	I=F-H	J	K = I*J
1	0.909091	40000.00	36363.64	36363.64	126363.64	75000.00	68181.82	58181.82	1.100000	64000.00
2	0.826446	42000.00	34710.74	71074.38	161074.38	60000.00	49586.78	111487.60	0.576190	64238.10
3	0.751315	44000.00	33057.85	104132.23	194132.23	45000.00	33809.17	160323.07	0.402115	64468.28
4	0.683013	46000.00	31418.62	135550.85	225550.85	30000.00	20490.40	205060.45	0.315471	64690.58
5	0.620921	48000.00	29804.22	165355.07	255355.07	15000.00	9313.82	246041.25	0.263797	64905.06
Discount factor	1/(1+0.1)^n
(A/P,i,n)	i((1 + i)^n)/((1 + i)^n-1)

Minimum EUAC is 64000 in year 1, so ESL = 1 yrs

Showing formula in excel

Year	Discount factor	O&M cost	PV (O&M)	Cumulative (O&M)	Cumulative (O&M) + Initial Cost	Salvage value	PV (Salvage value)	NPV	(A/P,10%,n)	EUAC
A	B	C	D=C*B	E	F=E+90000	G	H=G*B	I=F-H	J	K = I*J
1	=1/(1.1)^A17	40000	=C17*B17	=D17	=90000+E17	=105000-15000*2	=G17*B17	=F17-H17	=0.1*((1 + 0.1)^A17)/((1 + 0.1)^A17-1)	=I17*J17
2	=1/(1.1)^A18	=C17+2000	=C18*B18	=E17+D18	=90000+E18	=G17-15000	=G18*B18	=F18-H18	=0.1*((1 + 0.1)^A18)/((1 + 0.1)^A18-1)	=I18*J18
3	=1/(1.1)^A19	=C18+2000	=C19*B19	=E18+D19	=90000+E19	=G18-15000	=G19*B19	=F19-H19	=0.1*((1 + 0.1)^A19)/((1 + 0.1)^A19-1)	=I19*J19
4	=1/(1.1)^A20	=C19+2000	=C20*B20	=E19+D20	=90000+E20	=G19-15000	=G20*B20	=F20-H20	=0.1*((1 + 0.1)^A20)/((1 + 0.1)^A20-1)	=I20*J20
5	=1/(1.1)^A21	=C20+2000	=C21*B21	=E20+D21	=90000+E21	=G20-15000	=G21*B21	=F21-H21	=0.1*((1 + 0.1)^A21)/((1 + 0.1)^A21-1)	=I21*J21
Discount factor	1/(1+0.1)^n
(A/P,i,n)	i((1 + i)^n)/((1 + i)^n-1)