Final answer:
To calculate the present value of Asset X which offers perpetual cash flows of $100,000 every 3 months with a 12% compounded quarterly interest rate, we use the perpetuity present value formula, which results in a value of $3,333,333.33 for immediate cash flows.
Step-by-step explanation:
The question asks how much to pay today for Asset X which generates perpetual cash flows of $100,000 every 3 months with a 12% annual interest rate, compounded quarterly, and with the first payment occurring immediately. This type of problem is a present value calculation and can be solved using the formula for the present value of a perpetuity. Since the interest rate is compounded quarterly, we should adjust the annual rate to a quarterly rate.
First, we need to find the quarterly interest rate by dividing the annual rate by 4. This gives us 12% / 4 = 3% per quarter. To find the present value of Asset X, we use the present value of a perpetuity formula:
Present Value = Cash Flow / Quarterly Interest Rate
Substituting the values, we get:
Present Value = $100,000 / 0.03 = $3,333,333.33
As Asset X provides cash flows immediately, we do not need to adjust for any delays in payment, so $3,333,333.33 is the amount one should be willing to pay for Asset X.
The provided information explains the concept of present discounted value (PDV), which is used to calculate how much a future payment is worth in today's dollars considering the opportunity cost of not investing at the current market interest rate. It's important to remember that when the market interest rates rise, the PDV of existing fixed-income securities, like bonds, will decrease because new issuances offer higher returns, impacting the opportunity cost to investors holding the older securities.