Mathematics for FinancePYQ June 22Question 1544 of 512
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ABC Ltd. Wants to lease out an asset costing 3,60,000\displaystyle 3,60,000 for a five year period. It has a fixed rental of 1,05,000\displaystyle 1,05,000, per annum payable annually starting from the end of first year. Suppose rate of interest is 14%\displaystyle 14\% per annum compounded annually on which money can be invested by the company. Is this agreement favourable to the company.

Options

AYes
BNo
CIt depends
DNone of these
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Correct Answer

✅ Option a — Yes

All Options:

  • AYes
  • BNo
  • CIt depends
  • DNone of these

Detailed Solution & Explanation

To determine whether the lease agreement is favorable, we calculate the Present Value (PV\displaystyle PV) of the lease rentals and compare it with the asset cost: PV=R×[1−(1+i)−ni]PV = R \times \left[ \frac{1 - (1+i)^{-n}}{i} \right] Given: * Annual lease rental (R\displaystyle R) = 1,05,000\displaystyle 1,05,000 * Time (n\displaystyle n) = 5\displaystyle 5 years * Interest rate (i\displaystyle i) = 14%\displaystyle 14\% p.a. = 0.14\displaystyle 0.14 Substituting the values: PV=1,05,000×[1−(1.14)−50.14]PV = 1,05,000 \times \left[ \frac{1 - (1.14)^{-5}}{0.14} \right] Using (1.14)−5≈0.51937\displaystyle (1.14)^{-5} \approx 0.51937: PV=1,05,000×3.43308≈3,60,473.50PV = 1,05,000 \times 3.43308 \approx 3,60,473.50 Since the Present Value of the lease rentals (3,60,473.50\displaystyle 3,60,473.50) is greater than the cost of the asset (3,60,000\displaystyle 3,60,000), the leasing agreement is favorable to the lessor. Hence, **Option A** is the correct answer.

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