Question

Maintenance records of a certain type of machine indicate that the first-year

maintenance cost of $80 increases by $30 per year over the 10-year replacement
period of the machine. Answer the following if the maintenance cost is considered to
occur at the end of the year and the firm’s interest rate is 12%:
a) What equal annual payments could the firm make to a service organization to carry out the maintenance for 20 machines?
b) How much additional could be paid for a new type of machine with the same service life that required no maintenance during its life?

Answer 1

a)

EMI = P*i*[(1+i)^n]/[{(1+i)^n}-1]

Where,

P = Principal = 1059.64

i = Interest Rate = 0.12

n = Number of periods = 10

Therefore, EMI = 1059.64*0.12*[(1+0.12)^10]/[{(1+0.12)^10}-1]

= 127.1568*(3.105848)/[3.105848-1] = $187.54

Equal Maintenance per year for 20 Machines = EMI as abive*20 = 187.54*20 = $3750.79

b)

Year	Discounting Factor [1/(1.12^year)]	Cash Flow [Previous Year's Cash Flow]	PV of Cash Flows (cash flow*discounting factor)
1	0.892857143	80	71.42857143
2	0.797193878	110	87.69132653
3	0.711780248	140	99.64923469
4	0.635518078	170	108.0380733
5	0.567426856	200	113.4853711
6	0.506631121	230	116.5251579
7	0.452349215	260	117.610796
8	0.403883228	290	117.1261361
9	0.360610025	320	115.395208
10	0.321973237	350	112.6906328
		NPV = Sum of PVs	1059.640508

Therefore,  Additional that can be paid for new machine = Net Present Valaue of All Years' Maintenance Costs of Old Machines = $1059.64