Your cousin is entering medical school next fall and asks you for financial help. He needs $65,000 each year for the first two years. After that, he is in residency for two years and will be able to pay you back $10,000 each year. Then he graduates and becomes a fully qualified doctor, and will be able to pay you $40,000 each year. He promises to pay you $40,000 for 5 years after he graduates.
Assuming a discount rate of 5%, determine the net present value associated with this loan.
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: E
The PV of all cash inflows and outflows is [math]\mathrm{PV}=\frac{-65}{1.05}+\frac{-65}{1.05^2}+\frac{10}{1.05^3}+\frac{10}{1.05^4}+\frac{40}{1.05^5}+\ldots+\frac{40}{1.05^9}=\$ 38,478,57[/math].
I am taking a financial gain by helping him out.
References
Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.