A total income generated by a continuous financial flow f (t) varying as a function of time t over a period of k years is given by
TI = \int _0^k f(t) dt
In addition, a compound interest rate is continually compounded by r% a year, so the present value of the financial flow over the same period of time is given by
PV = int _0^k f(t)e^(-rt) dt
A company is thinking about buying a patent that will provide it with a continuous financial flow (in thousands of dollars per year) of f (t) = 20t. The continuous interest rate is 5% per year.
a) What is the total income generated by the patent over a period of 10 years
b) The company will purchase the patent if the present value of the financial flow over a period of 10 years is higher than the acquisition cost. What is the maximum amount the company is willing to spend to acquire the patent?
For a) I just assume that I plug f(t)=20t in the first formula so total income = int _0^{10} 20t dt = 1,000,000 $ but does it doen't include the 5% interest... What I'm I missing ?
For b) I use the second formula so : int _0^{10} 20te^{-0.05t} dt = 721,632,08 $ max that the company is willing to pay.
I'm I missing something ?
TI = \int _0^k f(t) dt
In addition, a compound interest rate is continually compounded by r% a year, so the present value of the financial flow over the same period of time is given by
PV = int _0^k f(t)e^(-rt) dt
A company is thinking about buying a patent that will provide it with a continuous financial flow (in thousands of dollars per year) of f (t) = 20t. The continuous interest rate is 5% per year.
a) What is the total income generated by the patent over a period of 10 years
b) The company will purchase the patent if the present value of the financial flow over a period of 10 years is higher than the acquisition cost. What is the maximum amount the company is willing to spend to acquire the patent?
For a) I just assume that I plug f(t)=20t in the first formula so total income = int _0^{10} 20t dt = 1,000,000 $ but does it doen't include the 5% interest... What I'm I missing ?
For b) I use the second formula so : int _0^{10} 20te^{-0.05t} dt = 721,632,08 $ max that the company is willing to pay.
I'm I missing something ?