Question

Suppose the gain to an innovating firm is $200,000 a year and the patent the firm obtains has a life of 20 years. The interest rate is 10%. What is the Present Value of innovation to the innovating firms? In the patent race, what might each firm be willing to spend on research and development (R&D)?

Answer 1

The objective is to find the present worth of an equal payment made at the end of every interest period for n interest periods at an interest rate of i compounded at the end of every interest period.

P = A[((1 + i)ⁿ – 1)/i(1 + i)ⁿ]

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

(P/A, i, n) = Equal payment series present worth factor

A = Annual equivalent payment = $200,000

n = Number of interest periods = 20 years

i = Interest rate = 10% or 0.1

P = Present worth

P = 200,000[((1 + 0.10)²⁰ – 1)/0.10(1 + 0.10)²⁰]

P = 200,000(P/A, 10%, 20)

P = 200,000[((1.1)²⁰ – 1)/0.1(1.1)²⁰]

P = 200,000 × 8.514

P = $1,702,712.74

So, in the patent race each firm will be willing to spend $1,702,712.74 on research and development.