The capital value of an asset such as a machine is sometimes defined as the present value of all future net earnings. The actual lifetime of the asset may not be known, and since some assets may last indefinitely, the capital value of the asset may be written in the form

where r is the annual rate of interest compounded continuously.

Suppose that a large farm with a known reservoir of gas beneath the ground sells the gas rights to a company for a guaranteed payment at the rate of 10,000e0.04t dollars per year. Find the present value of this perpetual stream of income, assuming an interest rate of 12%, compounded continuously.

Transcribed Image Text:

[capital value] = 0 K(t)et dt,