Economics Time Value Of Money Questions Long
Perpetuity due payment refers to a series of equal cash flows that occur at the end of each period indefinitely. In other words, it is a stream of payments that continues forever. The concept of perpetuity due payment is commonly used in finance and economics to calculate the present value or future value of an infinite cash flow stream.
To understand the application of perpetuity due payment in time value of money calculations, it is important to first grasp the concept of time value of money. Time value of money is the idea that a dollar received today is worth more than a dollar received in the future due to the potential to earn interest or invest the money. Therefore, to compare cash flows occurring at different points in time, we need to consider the time value of money.
When dealing with perpetuity due payment, the time value of money calculations involve determining the present value or future value of the infinite cash flow stream. The present value of a perpetuity due payment is the value of all the future cash flows discounted to their present value. The future value of a perpetuity due payment is the sum of all the future cash flows compounded to a specific future point in time.
To calculate the present value of a perpetuity due payment, we use the formula:
PV = C / r
Where PV is the present value, C is the cash flow received at the end of each period, and r is the discount rate or interest rate. The discount rate represents the opportunity cost of investing the money elsewhere.
For example, if you are expecting to receive $1,000 at the end of each year indefinitely, and the discount rate is 5%, the present value of this perpetuity due payment would be:
PV = $1,000 / 0.05 = $20,000
This means that the present value of the infinite stream of $1,000 payments is $20,000.
Similarly, to calculate the future value of a perpetuity due payment, we use the formula:
FV = C / (r - g)
Where FV is the future value, C is the cash flow received at the end of each period, r is the discount rate, and g is the growth rate of the cash flows. The growth rate represents the rate at which the cash flows are expected to increase over time.
For instance, if the cash flows are expected to grow at a rate of 3% per year, and the discount rate is 5%, the future value of the perpetuity due payment would be:
FV = $1,000 / (0.05 - 0.03) = $50,000
This means that the future value of the infinite stream of $1,000 payments, growing at a rate of 3% per year, is $50,000.
In summary, perpetuity due payment is a concept that involves a series of equal cash flows occurring indefinitely. It is commonly used in time value of money calculations to determine the present value or future value of the infinite cash flow stream. By discounting the future cash flows to their present value or compounding them to a specific future point in time, we can assess the value of perpetuity due payments in terms of their current or future worth.