A machine costing Rs. 3,00,000 will have its scrap value of Rs. 50,000. The company at present plans to put Rs. 36,650 per annum at the end of each year in a sinking fund at the rate 5% per annum for the replacement of the machine after its useful life. Suppose the new machine will cost Rs. 4,00,000 at that time, then the useful life (approx.) of the machine is:
[Given: \((1.4775)^{1/8} \approx 1.05\)]
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 8 yrs
At replacement time the old machine is sold for its scrap value, so the sinking fund must provide the rest of the new machine’s cost:
\(400000 - 50000 = 350000\)
The deposits of R = 36650 at the end of each year form an annuity whose amount after n years is
\( \displaystyle A = R\,\frac{(1 + i)^n - 1}{i} \)
So
\( \displaystyle 36650 \times \frac{(1.05)^n - 1}{0.05} = 350000 \)
\( \displaystyle (1.05)^n - 1 = \frac{350000 \times 0.05}{36650} = \frac{17500}{36650} = 0.4775 \)
\((1.05)^n = 1.4775\)
The given value \((1.4775)^{1/8} \approx 1.05\) means \((1.05)^8 \approx 1.4775\), so \(n = 8\). The useful life is about 8 years.
Tip: The fund is meant for the replacement, so use the cost of the new machine less the scrap value; the old machine’s cost (Rs. 3,00,000) does not enter the calculation.