Future worth method

The future worth method converts every project cash flow to its equivalent value at the end of the project’s life (rather than at the start, as in PW), then sums them. The decision rule is the same:

• $FW>0$: accept.
• $FW<0$: reject.

For a stream of cash flows $C_0,C_1,\dots ,C_N$ at rate $i$:

$FW={\sum }_{t=0}^N{C}_t\cdot (1+i{)}^{N-t}.$

This is just $PW\cdot (1+i{)}^N$ — moving the present-worth lump sum forward to time $N$. The relationship is bijective: $PW>0$ iff $FW>0$, and either method gives the same accept/reject answer.

So why have FW as a separate method? Two reasons:

1. Communication. For some audiences, “this project will leave us $1.2M ahead by year 20” is more compelling than “this project has a present worth of $320k now.” The end-of-life value is the form the project’s outcome takes; the start-of-life value is an abstraction.

2. Comparison across futures. When alternatives are compared not against each other but against a target end-state (a sinking fund obligation, a future capital need), FW is more naturally aligned with the question being asked.

In ME comparisons, FW picks the same winning project as PW — the rankings are identical because FW is just PW scaled by $(1+i{)}^N$, a positive constant.

For the start-of-life equivalent see Present worth method; for the annualised version see Annual worth method.