Calculating the Present Value of a Perpetuity

A perpetuity is a type of investment that pays a fixed amount of money to the investor indefinitely. In this case, the stock pays an annually an amount of rupees 10 from 6th year onwards. To calculate the present value of the perpetuity, we need to use the following formula:

PV = C / r

Where PV is the present value, C is the annual payment, and r is the discount rate.

Step-by-Step Calculation

1. Identify the annual payment: In this case, the annual payment is rupees 10.

2. Determine the discount rate: The discount rate is the rate of return required by the investor. In this case, the rate is 20%.

3. Calculate the present value: Using the formula above, we can calculate the present value as follows:

PV = 10 / 0.20
PV = 50

Therefore, the present value of the perpetuity is rupees 50.

Explanation

The present value is the value of the perpetuity in today's dollars. By calculating the present value, we can determine how much the investment is worth today, given the future cash flows. The discount rate is used to account for the time value of money, which is the idea that money is worth more today than it is in the future due to inflation and other factors. In this case, the discount rate is 20%, which means that the investor requires a return of 20% to invest in this stock. The perpetuity pays rupees 10 per year from the 6th year onwards, which means that the investor would receive rupees 10 each year indefinitely. By dividing the annual payment by the discount rate, we can determine the present value of the perpetuity. In this case, the present value is rupees 50.