Answer:
If the discount rate used to estimate the value of a perpetuity is cut in half, the present value estimate will increase.
Step-by-step explanation:
The present value of a perpetuity is calculated by dividing the cash flow by the discount rate. The discount rate represents the rate of return required by an investor to compensate for the time value of money and the risk associated with the investment.
When the discount rate is cut in half, it means that the required rate of return has decreased. This reduction in the discount rate leads to an increase in the present value estimate.
For example, let's say the cash flow of a perpetuity is $1,000 and the discount rate is 10%. The present value would be calculated as follows:
Present Value = Cash Flow / Discount Rate
Present Value = $1,000 / 0.10
Present Value = $10,000
Now, if the discount rate is cut in half to 5%, the new present value would be:
Present Value = $1,000 / 0.05
Present Value = $20,000
As you can see, by reducing the discount rate, the present value estimate doubled from $10,000 to $20,000. This demonstrates that a lower discount rate leads to a higher present value estimate for a perpetuity.