Present value under uncertain asset life: an evaluation of relative error

Abstract

We evaluate the relative errors attributable to using the expected economic life of an asset to calculate present value instead of the correct approach of calculating the expected present value when the cessation point of the asset is uncertain. We compare the continuous-time case of exponential cash flows and exponentially distributed asset life with its discrete-time analogue of geometric cash flows and geometrically distributed asset life. We find that if the discount rate and growth rate are equal, the error is always zero. If the growth rate exceeds the discount rate, the error can easily be severe and reach 100%. If the discount rate exceeds the growth rate, the error cannot exceed 30%, but such large errors may occur for any expected asset life. In the discrete case, this error limit depends on expected asset life and is somewhat lower for shorter lives. For realistic cases, even a small percentage point difference between the discount rate and the growth rate can lead to considerable errors.