The current term structure of interest rates is flat at 3.73%, and is expected to shift down. You have locked into a long-term lease on a real estate in Cambridge to pay $1 million a year forever, starting 3 years t=3 from now t=0

To analyze the financial implications of the scenario you provided, let's break down the key components:

1. **Flat Term Structure of Interest Rates:** The current term structure is flat at 3.73%. This means that the interest rate for borrowing or lending money is the same across all maturities (short-term, medium-term, and long-term).

2. **Expected Shift Down:** If the term structure is expected to shift down, the future interest rates are likely to be lower than 3.73%.

3. **Long-term Lease Payment:** You have committed to paying $1 million annually, starting 3 years from now (t = 3) and continuing forever.

### Present Value of the Lease Payments

The present value (PV) of these perpetual lease payments can be calculated using the formula for the present value of a perpetuity that starts at a future date:

\[
PV = \frac{C}{r} \times \frac{1}{(1 + r)^t}
\]

Where:
- $ C $ is the annual payment ($1,000,000).
- $ r $ is the interest rate (3.73% or 0.0373).
- $ t $ is the time before the payments start (3 years).

### Calculation:

1. **Calculate the present value of the perpetuity:**

\[
\text{PV of Perpetuity} = \frac{1,000,000}{0.0373} = 26,816,023.57
\]

2. **Discount this value back to the present (t = 0):**

\[
\text{Present Value} = 26,816,023.57 \times \frac{1}{(1 + 0.0373)^3} 
\]

\[
\text{Present Value} = 26,816,023.57 \times 0.90091 = 24,162,897.87
\]

### Interpretation:

The present value of your lease payments, given the current flat term structure at 3.73%, is approximately $24,162,897.87. This amount represents how much those future payments are worth in today's dollars. If the term structure shifts downward as expected, the present value of these payments would increase, meaning the lease would become more costly in present value terms.

Would you like further details on this calculation or have any other questions?

### Follow-Up Questions:

1. How would the present value change if the interest rate drops to 3%?
2. What would be the impact on the present value if the lease payments were to start at t = 5 instead of t = 3?
3. How does the concept of duration relate to the present value of these cash flows?
4. What happens to the present value if payments increase by 2% per year after the first payment?
5. How would you calculate the present value if the payments were made semi-annually instead of annually?

### Tip:

Always consider the time value of money when evaluating long-term financial commitments. Small changes in interest rates can significantly impact the present value of future cash flows.

Explore the financial implications of lease payments and interest rate changes. Calculate the present value of perpetual lease payments starting in 3 years at an interest rate of 3.73%. Learn how slight changes in interest rates can affect future cash flows.

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