MECH 431

# Future Value Analysis & Benefit Cost Ratio

Updated 2018-07-19

# Future Value Analysis & Benefit Cost Ratio

## Future Value Analysis

• One might want to look at the worth at some point in the future.
• Future worth analysis is identical to present worth analysis, except the the analysis is in the future.
• Analysis period for the alternatives must be the same (same as PWA). Extend analysis period to least common multiple (LCM) of all alternatives’ useful life time.

Recall the definitions:

Net Present Value (NPV): equivalent value of discounted project cashflow to present time (often time zero).

Net Future Value (NFV): equivalent value of compounded project cashflow to a desinated future point in ime. It is the accumulation of unrecoverd capital and required returns throughout the project.

• If NFV > 0, then the net cashflow at the end is profit, so one should accept the project.
• If NFV < 0, then the net cashflow at the end is loss, so one should reject the project.
• If NFV is 0, then marginally accept. (Perhaps one should consider additional factors that may influencce the projection).
• If all alternatives have NFV < 0, don’t forget the do nothing option.

Recall the economic criterion based on fixed input/output:

Situation Criterion
Fixed input Amount of capital is fixed Maximize future value of benefits
Fixed output Amount of benefit is fixed Minimize the future value of costs
Unconstrained Neither capital nor benefits are fixed Maximize NFV (maximize future value of benefits and minimize future value of costs)

Example: lecture slide example

A B C
Investment $2.5k$3.5k $5.0k Annual cost$900 $700$1000 with $100 increase each year Salvage value$200 $350$600
Life 5 5 5
Annual revenue $1.8k$1.9k \$2.1k with 15% growth rate
MARR 10% 10% 10%

We compute the NFV:

$\text{NFV}_A=(-2500)(F/P, 10\%,5)+(1800-900)(F/A, 10\%, 5)+200\\ \text{NFV}_B=(-3500)(F/P, 10\%, 5)+(1900-700)(F/A, 10\%, 5)+350\\ \text{NFV}_C=(-5000)(F/P, 10\%, 5)+(2100)(F/g, g=15\%, 10\%, 5)\\+(-1000)(P/A, 10\%, 5)+(-100)(F/G, 10\%, 5)+600$

Once computed, NFV for option C is highest. Therefore, this should be the option that should be taken.

## Benefit to Cost Ratio Analysis

In simple terms, it is the ratio of the benefit over costs:

$\text{Ratio}=\frac{\text{PW of benefit}}{\text{PW of costs}}=\frac{\text{FW of benefit}}{\text{FW of costs}}=\frac{\text{EUAB}}{\text{EUAC}}$

For a sensible decision, the benefit to cost ratio should be $\geq 1$.