## Sunday, June 07, 2020

### PMP Prep: Range of Incentive Effectiveness (RIE) - How to Derive the Formulas?

We have understood the Range of Incentive Effectiveness (RIE) with the basics and the associated formulas in the earlier article

Now, let’s go a bit deeper and see how RIE is represented graphically in the cost-profit curve. This you need to know, before we derive the formulas for RIE. This will give you a better understanding.

The content of this article has been taken from: PMP Live Lessons – Guaranteed Pass

You can read the previous article on RIE here:
Range of Incentive Effectiveness in Procurement Management

Cost-Profit Curve in CPIF Contracts
The cost-profit curve is widely used by Contract Administrators or Procurement Managers. This is a two-dimensional (2D) graph and pictorially shows:
• RIE (min) point,
• RIE (max) point,
• Profit or Fee (max) point,
• Profit or Fee (min) point, and of course,
• Range of Incentive Effectiveness (RIE).

The cost-profit curve for a Cost Plust Incentive Fee (CPIF) contact is depicted in the below figure. Range of Incentive Effectiveness (RIE): Cost-Profit Curve

As shown above, in the X-axis we have cost, whereas profit is shown in the Y-axis. At RIE (minimum) cost point, the profit is maximum or it’s Fee (max). At RIE (maximum) cost point, the profit is minimum or it’s Fee (min). These are shown in red dotted lines.

Finally, RIE – the range in which the incentive is effective – is the range between RIE (min) and RIE (max).

The target cost is shown with blue dotted line and target cost/profit point is shown with a blue circle.The blue dotted lines are projected to X-axis giving you the target cost (TC) value and projected to Y-axis giving you the target profit (TF) value.

Below are few key points to note by looking at the above graph:
• At RIE (min), the profit is maximum or Fee (max).
RIE (min) in cost curve = Fee (max) in profit curve
• At RIE (max), the profit is minimum or Fee (min).
RIE (max) in cost curve = Fee (min) in profit curve
• Target Profit or Target Fee (TF) is less than the Fee (max), but more than Fee (min).
TF < Fee (max); TF > Fee (min)
• Target Cost (TC) is less than RIE (max), but more than the RIE (min).
TC < RIE (max); TC > RIE (min)

With these key points, let’s derive the formulas.

Deriving RIE Formulas
First, we will check upon the formula for RIE (min).

I. Formula for RIE (min) – Cost Underrun
RIE (min) will be during cost underrun. During cost underrun, the actual cost (AC) will be less than the target cost (TC). This is obvious. Hence:

Cost Underrun is the subtraction of actual cost from target cost, i.e.,
Cost Overrun = Target Cost (TC) - Actual Cost (AC)

Now, the actual fee (AF) will be an addition to the target (TF), along with the seller’s share of cost gain because of cost underrun. This is added, because the seller performed well from cost perspective and seller is entitled to gets it extra share.

But do note: the total fee given to the seller can NOT be more than the Fee (max).

Hence, from the seller’s perspective:
Actual Fee (AF) = Target Fee (TF) + (Cost Underrun) × SSR
= Target Fee (TF) + [Target Cost (TC) – Actual Cost (AC)] × SSR …. 

We already know at RIE (min) point from the earlier graph, the fee is at maximum or it is Fee (max). This is when you project the profit it into the Y-axis of the above graph. In an equation:

Actual Fee (AF) = Fee (max) …. 

Also, we know at this stage actual cost (AC) is in fact the RIE (min). This is when you project the cost it into the X-axis of the above graph. In an equation:

Actual Cost (AC) = RIE (min) …. 

Hence, considering equation  and equation  and putting these values in equation , we will have:

Fee (max) = Target Fee (TF) + [Target Cost (TC) – RIE (min)] × SSR
=> Fee (max) = TF + [TC- RIE (min)] × SSR
=> Fee (max) - TF = [TC- RIE (min)] × SSR
=> [ Fee (max) – TF ] / SSR = TC- RIE (min)
=> RIE (min) = TC – ( [ Fee (max) – TF ] / SSR )

This what I mentioned in earlier piece of RIE as the formula for cost underrun.

Next, we will derive the formula for RIE (max).

II. Formula for RIE (max) – Cost Overrun
RIE (max) will be during cost overrun. During cost overrun, the actual cost (AC) will be more than the target cost (TC). This is also obvious. Hence:

Cost Overrun is the subtraction of target cost from actual cost, i.e.,
Cost Overrun = Actual Cost (AC) - Target Cost (TC)

For the actual fee (AF), we have to subtract seller’s share ratio of cost overrun from the target fee (TF). This is subtracted, because the seller performed badly from cost perspective and seller will have to pay its share.

But do note: the total fee given to the seller can NOT be less than the Fee (min).

Hence, from the seller’s perspective:

Actual Fee (AF) = Target Fee (TF) – (Cost Overrun) × SSR
= Target Fee (TF) - [Actual Cost (AC) - Target Cost (TC)] × SSR …. 

We already know at RIE (max) point from the earlier graph, the fee is at minimum or it is Fee (min). This is when you project the profit it into the Y-axis of the above graph. In an equation:

Actual Fee (AF) = Fee (min) …. 

Also, we know at this stage actual cost (AC) is in fact the RIE (max). This is when you project the cost it into the X-axis of the above graph. In the equation:

Actual Cost (AC) = RIE (max) …. 

Hence, considering equation  and equation  and putting these values in equation , we will have:

Fee (min) = Target Fee (TF) - [Actual Cost (AC) - Target Cost (TC)] × SSR
=> Fee (min) = TF - [RIE (max) - TC] × SSR
=> [RIE (max) - TC] × SSR = TF – Fee (min)
=> RIE (max) - TC = [ TF - Fee (min) ] / SSR
=> RIE (max) = TC + [ (TF - Fee (min)] / SSR ]

This what I mentioned in earlier piece of RIE (max) as the formula for cost overrun.

III. Formula for RIE

Finally, the formula for RIE will be:

Conclusion
As noted in earlier part for RIE, questions on PTA have been coming in the PMP exam for quite some time. A related concept to know is Range of Incentive Effectiveness (RIE), which is used in CPIF contracts.

I don’t expect many questions on Range of Incentive Effectiveness (RIE) in the PMP exam. Like the concept of Point of Total Assumption (PTA), questions will be very few, if it comes. However, it is an excellent one to know and understand Procurement Management better.

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