In: Finance
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?
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