If an investment of Rs. 1,000 generates cash inflows of Rs. 1,080 at the end of first year, the rate of return required to equate the present value of cash inflow with the cost of investment will be:

Question

Accepted Answer

The correct option is 2:

This question is a fundamental application of the Time Value of Money concept, specifically requiring us to calculate the Internal Rate of Return (IRR) for a single-period investment. The IRR is defined as the discount rate that makes the Present Value (PV) of the expected cash inflows equal to the initial cost of the investment. In this case, the investment cost is Rs. 1,000 and the future cash inflow is Rs. 1,080, received exactly one year later. We set the cost equal to the discounted future cash flow: $	ext{Cost} = \frac{	ext{Future Cash Flow}}{(1 + r)^1}$, where 'r' is the rate of return. Substituting the values gives: $1,000 = \frac{1,080}{(1 + r)}$. Solving for the discount factor $(1 + r)$ yields $1 + r = \frac{1,080}{1,000} = 1.08$. Therefore, the required rate of return, $r$, is $1.08 - 1 = 0.08$, or $8%$. This rate ensures that the initial capital is recovered, and an $8%$ return is earned on that capital, perfectly equating the present value of the inflow with the cost of investment.

The incorrect option is 1, 3, and 4:

The alternative rates provided, 7.12% (0.0712), 8.16% (0.0816), and 7.28% (0.0728), are incorrect because none of them equate the Present Value of the Rs. 1,080 cash inflow to the Rs. 1,000 cost of the investment. A core principle of financial management is that an investment is only acceptable if its present value, when discounted at the required rate, is equal to or greater than its cost. If we use a discount rate lower than $8%$ (such as $7.12%$ or $7.28%$), the resulting Present Value will be greater than Rs. 1,000, indicating a positive Net Present Value (NPV), but not the exact break-even rate the question asks for. Conversely, if we use a rate higher than $8%$ (like $8.16%$), the resulting Present Value will be less than Rs. 1,000, indicating a negative NPV, meaning the investment is earning less than that required rate. Only the $8%$ rate makes the NPV exactly zero.