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. Same decision rule:

• $FW>0$: 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 $FW>0$, so either method gives the same accept/reject answer.

So why keep FW as a separate method? Two reasons.

1. Communication. For some audiences, “this project will leave us $1.2M ahead by year 20” lands better than “this project has a present worth of $320k now.” The end-of-life value is the form the project’s outcome actually 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 lines up more naturally with the question being asked.

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

For the annualised version see Annual worth method.