Question

(4.1) A project produces profit of x dollars per year at the end of each year. Interest is r per year. The project life is infinite and there is no production cost. Write a simple expression for the present value V of the project.

(4.2) Assume the project in the previous question has a project life of 4 years. Write an expression for the present value V of the project, using the answer to the previous question to simplify the expression.

(4.3) Assume that there is an innovation that will yield a demand Q=50 - 0.25P. This demand will be the same always. The invention requires startup costs of $240,000. The marginal cost equals zero and the interest rate is 1%.

Should the government develop the innovation? (Sketch a figure to illustrate your answer.)

Answer 1

Question 1

Profit per year (A)m = $x

Interest rate (i) = r% per year

Time period (n) = ∞ (Infinite)

Calculate Present Value (V) of the project -

V = A(P/A, i, n)

V = x(P/A, r%, ∞)

Thus,

The expression for the present value (V) of the project is x(P/A, r%, ∞).

Question 2

Profit per year (A)m = $x

Interest rate (i) = r% per year

Time period (n) = 4

Calculate Present Value (V) of the project -

V = A(P/A, i, n)

V = x(P/A, r%, 4)

Thus,

The expression for the present value (V) of the project is x(P/A, r%, 4).