Question

A machine costing Rs 2 lacs has an effective life of 7 years and its scrap value is Rs 30000. What amount (in lacs) should the company put into a sinking fund earning 5% per annum so that it can replace the machine after its useful life? Assume that a new machine will cost Rs 3 lacs after 7 years.
A) 30161.35
B) 33101.35
C) 33161.35
D) 33111.35

Answer 1

Hint: Sinking Fund: If an annuity is left unpaid for n years then, the equivalent amount which may be paid at the end of nth year is the same as the amount of ordinary annuity certain.
$M = \dfrac{A}{r} \times \left[ {{{\left( {1 + r} \right)}^n} - 1} \right]$
where, A is the amount of each instalment, M is the (future) amount of annuity.
r is rate per period $\dfrac{r}{{100}}$ and n denotes period.
An annuity is a sequence of equal payments made at equal intervals of time, with compound interest on these payments.
The time between two successive payment dates of an annuity is called its payment period.
The payment of each single annuity is called an instalment.

Complete step-by-step answer:
Cost of new machine is Rs. 3 lacs
Scrap value of old machine is Rs.30000
Hence, money required for new machine after 7 years = Rs. 300000 – Rs. 30000 = Rs. 270000
If A is the annual deposit into sinking fund, then we have
Amount of annuity, M = Rs. 270000
Number of periods = 7 years
r = 5% = 0.05
$\begin{gathered}
  \therefore M = \dfrac{A}{r} \times \left[ {{{\left( {1 + r} \right)}^n} - 1} \right] \\
  270000 = \dfrac{A}{{0.05}} \times \left[ {{{\left( {1.05} \right)}^7} - 1} \right] \\
  A = \dfrac{{270000 \times 0.05}}{{{{\left( {1.05} \right)}^7} - 1}} \\
  \therefore A = Rs.33161.35 \\
\end{gathered} $

Note: Sinking fund is a fund created to discharge a known future liability. The fund is created by investing a certain sum annually at compound interest for a certain period.
Present value of the annuity is the current value of a sequence of equal periodic payments made over a certain period of time. If payments are not annual, values of r and n should be stated correctly.
This method is most suitable for a firm where capital is invested in the least hold properties.