Sure! Here’s a step-by-step solution: --- ## **Step 1: Calculate the Effective Cost (Present Value) for Each Lease Alternative Using a 6% Discount Rate** Let's break down both alternatives over the 5-year period: ### **Alternative 1: Net Lease with CPI Adjustments** - **Year 1:** $16/sq ft - **Years 2-5:** Increase by $.50/sq ft each year | Year | Rent per Sq Ft | |------|:--------------:| | 1 | $16.00 | | 2 | $16.50 | | 3 | $17.00 | | 4 | $17.50 | | 5 | $18.00 | Discount each year's payment at 6%: \[ PV = \sum \frac{\text{Rent}_t}{(1 + .06)^t} \] - **Year 1:** $16 / 1.06^1 = $15.09$ - **Year 2:** $16.5 / 1.06^2 = $14.69$ - **Year 3:** $17 / 1.06^3 = $14.27$ - **Year 4:** $17.5 / 1.06^4 = $13.83$ - **Year 5:** $18 / 1.06^5 = $13.47$ **Sum:** $15.09 + 14.69 + 14.27 + 13.83 + 13.47 = \$71.35$ **Explanation:** Each year’s rent is discounted back to present value at 6%. Adding these gives the total present value of the lease payments for Alternative 1. --- ## **Step 2: Calculate the Effective Cost for Alternative 2 (Gross Lease with CPI Adjustment)** - **Year 1:** $22/sq ft (includes all expenses) - **Years 2-5:** Increase by CPI (assumed 3% per year) | Year | Rent per Sq Ft (3% CPI) | |------|:----------------------:| | 1 | $22.00 | | 2 | $22.66 | | 3 | $23.34 | | 4 | $24.04 | | 5 | $24.76 | Discount each amount at 6%: - **Year 1:** $22 / 1.06^1 = $20.75$ - **Year 2:** $22.66 / 1.06^2 = $20.15$ - **Year 3:** $23.34 / 1.06^3 = $19.54$ - **Year 4:** $24.04 / 1.06^4 = $18.95$ - **Year 5:** $24.76 / 1.06^5 = $18.41$ **Sum:** $20.75 + 20.15 + 19.54 + 18.95 + 18.41 = \$97.80$ **Explanation:** Each year’s gross rent (with 3% CPI increase) is discounted at 6% and summed to get the present value for Alternative 2. --- ## **Final Answer** | Lease Alternative | Effective Cost (PV) | |----------------------------|---------------------| | Net lease with CPI adj. | $71.35 | | Gross lease with CPI adj. | $97.80 | **Conclusion:** The net lease with CPI adjustments ($71.35/sq ft present value) is less expensive than the gross lease with CPI adjustments ($97.80/sq ft present value) over the 5 years, using a 6% discount rate.