It is clear to me why the benefits accruing from an investment should be discounted. What I wish to understand is what the correct way discount the investment itself is.
Assuming zero inflation, consider that at a personal discount rate of $\rho$, the net present value of an investment $K$ can be computed as $$ \frac{R}{\rho - \mu} - K\ , $$ where $R$ is the expected revenue flow with trend $\mu$. If this quantity is positive, the investment is a good one. But suppose I pose the question of how much I stand to gain by delaying the investment to some later time $t$, say. The return term above is modified to $R_0 e^{\mu t}/(\rho - \mu)$, and if I leave $K$ as is, this new NPV will be strictly greater than the old value: a speculative bubble. I hence have two questions.
- Should $K$ be discounted when computing the NPV of the investment at some future time? If so, what would the rationale be? I can understand the time value of money applied to the return, but why should a future investment (i.e. a future cost) be discounted?
- If the answer to (i) is in the affirmative, would it make sense to use a different discount rate for $K$ than $\rho$? It seems to me that costs should be discounted differently (more gently) than returns.