Revision as of 00:28, 5 December 2023 by Admin (Created page with "The term structure of spot interest rates is given in the table below: {| class="table" |- |'''Maturity (years)''' ||1 ||2 ||3|| 4|| 5|| 6 |- |'''Interest rate (%)''' ||3.5 ||3.0 ||4.0 ||4.0 ||4.0 ||4.0 |} You have just signed a lease on an office building with a rental payment of $1 million per year forever. The first payment is due one year from now. What is the present value of the lease? <ul class="mw-excansopts"> <li>22M</li> <li>23M</li> <li>24M</li> <li>25M</l...")
Dec 05'23
Exercise
The term structure of spot interest rates is given in the table below:
| Maturity (years) | 1 | 2 | 3 | 4 | 5 | 6 |
| Interest rate (%) | 3.5 | 3.0 | 4.0 | 4.0 | 4.0 | 4.0 |
You have just signed a lease on an office building with a rental payment of $1 million per year forever. The first payment is due one year from now.
What is the present value of the lease?
- 22M
- 23M
- 24M
- 25M
- 26M
References
Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.
Dec 05'23
Solution: D
[[math]]
\begin{aligned} & P V_1=\frac{1}{1+3.5 \%}=0.9662, P V_2=\frac{1}{(1+3 \%)^2}=0.9426 \\ & \text { From } P V_3 \text { on, sum PV }=1 /(1+4 \%)^3+1 /(1+4 \%)^4+\ldots \\ & =\frac{1}{(1+4 \%)^2}\left(\frac{1}{1.04}+\frac{1}{1.042}+\frac{1}{1.043} \ldots\right) \\ & =\frac{1}{(1+4 \%)^2} \times \frac{1}{0.04}=23.1139
\end{aligned}
[[/math]]
Therefore the total = 25.02268
References
Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.