To find the present value at t=0*t*=0, we need to discount the value calculated above back 2 years.

You're correct! Since the payments start at $ t = 3 $, and the present value of the perpetuity was calculated for $ t = 3 $, you only need to discount it back **2 years** to find the present value at $ t = 0 $.

Let’s correct that calculation:

### **Corrected Calculation:**

1. **Calculate the Present Value of the Perpetuity at $ t = 3 $:**

   \[
   PV_{\text{at } t=3} = \frac{1,000,000}{0.0373} \approx 26,820,645.21 \text{ dollars}
   \]

2. **Discount this Value Back to $ t = 0 $:**
   - To find the present value at $ t = 0 $, we now discount back 2 years:

   \[
   PV_{\text{at } t=0} = PV_{\text{at } t=3} \times \frac{1}{(1 + r)^2}
   \]

   \[
   PV_{\text{at } t=0} = 26,820,645.21 \times \frac{1}{(1.0373)^2} \approx 24,942,919.41 \text{ dollars}
   \]

### **Conclusion:**
The present value of your perpetual lease payments, assuming the interest rate remains at 3.73%, is approximately **$24,942,919.41** at time $ t = 0 $.

---

Would you like to explore how a change in interest rates might affect this value, or any other aspect of the problem?

### Relative Questions:
1. How does the present value change if you discount for 1 year instead of 2?
2. What impact would a delay in starting the payments (e.g., starting at t=5) have on the present value?
3. How would the present value calculation differ if payments were to increase by 2% annually?
4. What would be the present value if the interest rate drops to 2.5%?
5. How does the perpetuity formula apply to different financial scenarios like pensions or annuities?

### Tip:
Always double-check the time period over which you discount future cash flows to ensure accurate present value calculations.

Learn how to calculate the present value of perpetuity payments by discounting them back 2 years. This problem involves applying the present value formula and discounting technique to determine the current value of future cash flows. Suitable for advanced college-level students and financial professionals.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation