Cost Benefit Analysis is a technique used to determine if the financial benefit s of a project outweigh the associated cost of undertaking the project in the first place. For a short term project where the benefit may be an immediate one-time cash windfall this may be as simple as subtracting the total of all the project cost from the total of all of the project benefits. If the total is positive, then the project may be worth completing.
Project Duration = 2 months
Project Costs = $50,000
Immediate Project Benefits = $75,000
$75,000 - $50,000 = $25,000
However, project costs and benefits rarely result in such a simple example. Project costs and benefits often occur over time. For this reason, Cost Benefit Analysis should consider all project cost and benefits in terms of the present value (PV) of money.
To determine the present value of a future cost or benefit we discount the value of the dollars to account for time. To calculate the Present Value we use the formula PV = FV /[(1 + i)^t].
PV = Present Value
FV = Future Value
i = Discount Rate
t = time
In our example, if the $50,000 cost was incurred immediately and the $75,000 benefit was realized 3 years in the future, using a 5% discount rate would result in the following:
PV = $75,000 / [(1 + .05)^3] = $64,787.82
$64,787.82 - $50,000 = $14,787.82
The net benefit of this project is now clearly less than originally thought.
Taking this a step further, consider the example where we have multiple cashflows (costs and benefits) over time.
@ T0, Cost = -$25,000
@ T1, Cost = -$25,000, Benefit = $15,000
@T2, Benefit = $30,000
@T3, Benefit = $30,000
By subtracting the present value of future costs from the present value of future benefits, we can arrive at the Net Present Value (NPV) of the costs and benefits for each year of the project. The sum of all NPV calculations will give us the NPV of the entire project.
NPV = FVben – FVcost / [(1 + i)^t]
NPV0 = $0 - $25,000 / [(1 + .05)^0] = -$25,000
NPV1 = $15,000 - $25,000 / [(1 + .05)^1] = -$9,523.81
NPV2 = $30,000 - $0 / [(1 + .05)^2] = $27,210.88
NPV3 = $30,000 - $0 / [(1 + .05)^3] = $25,915.13
For a total of $18,602.20 in benefit.