You have just inherited an office building. You expect the annual rental income (net of maintenance and other cost) for the building to be $100,000 for the next year and to increase at 5% per year indefinitely. A expanding internet company offers to rent the building at a fixed annual rent for 5 years. After year 5, you could re-negotiate or rent the building to another tenant.

What is the minimum acceptable fixed rental payments for this five-year agreement? Use a discount rate of 12%.

• 105,000
• 107,100
• 109,300
• 113,300
• 115,800

References

Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.

Solution: C

Assuming the rent payments are paid at the beginning of the year, the PV of the floating rent for the next 5 years is

[[math]] \$ 100,000+\frac{\$ 100,000 * 1.05^1}{1.12^1}+\cdots+\frac{\$ 100,000 * 1.05^4}{1.12^4}=\$ 441,285.71 [[/math]]

This must be equal to

[[math]] \$ 441,285.71=F+\frac{F}{1.12}+\frac{F}{1.12^2}+\frac{F}{1.12^3}+\frac{F}{1.12^4} [[/math]]

Solve for [math]F[/math], to get [math]F=\$ 109,300.67[/math]

References

Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.