10th Edition

Ron Larson + 1 other

ISBN: 9781285057095

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 = ∫ 0 t 0 500 , 000 e − 0.05 t d t .

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

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

To determine

To calculate: For the function P=∫0to500000e−0.05tdt; the present value of the business for 20 years

Profit per year is $500,000.

Rate is 5% per year compounded continuously.

The present value function is:

P=∫0to500000e−0.05tdt

Formula used:

The integration formula:

∫ef(x)dx=ef(x)(1f′(x))

Calculation:

Solve the integral

P=∫0to500000e−0.05tdt as below:

P=∫0to500000e−0.05tdt=500000∫0toe−0

To determine

To calculate: The present value of the business in perpetuity for the function P=∫0to500000e−0.05tdt.

Check out a sample textbook solution.

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Calculus Calculus 10th Edition