Textbook Problem

Present Value The board of directors of a corporation is calculating the price to pay for a business that is forecast to yield a continuous flow of profit of $500,000 per year. The money will earn a nominal rate of 5% per year compounded continuously. The present value of the business for $t_0$ years is

Present value $={\displaystyle {\int }_0^{t_0}500,000e^{-0.05t}}dt.$

(a) Find the present value of the business for 20 years.

(b) Find the present value of the business in perpetuity (forever).