Question

In: Finance

Without using excel pleaseb) Maintenance records of a certain type of machine indicatethat the...

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?

Solutions

Expert Solution

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


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