August 31st, 2003, 8:29 am
adamcox: If a goose lays golden eggs - how many golden eggs is the goose worth ? Assuming that the goose lays x eggs per month, we can simply PV all the eggs to arrive at the value of the goose.Using PV(egg) = x(t)*m*S/exp((r(t)-g(t))*t)Where m: Mass of egg in troy ounces.S: Spot price of gold per troy ounce.r(t): Interest Rate on cash with tenor tg(t): Interest Rate on Gold with tenor tt: Momemt of egg creation (distance in years)We can see that if eggs are produced in a linear manner (or any manner, as long as the rate of production does not display exponential or higher than exponential growth), we can arrive at a limit as t-->infinity, as we can treat the periodic flows of gold just like a perpetual bond. Assuming linear egg flows (with n eggs per year) and a flat term structure of R = r-g gives us:PV(Golden Goose) = Egg/(R/n)