How should you price a product in two different market segments when you are given the segment size, willingness to pay and segment development costs? How should you price two products in these two segments when the WTP for these two products are different? The first two sessions of class today were spent answering these two questions using the Salesoft, Cambridge and Keurig study cases.

Product variety and Pricing

Say, the WTP is lower in a second segment compared to the first segment. Naturally, price would have to be lowered when entering the new segment. What is the impact, called the dilution effect, of marketing the product in the second segment? Would it be worthwhile entering the new segment for the firm? The following analysis will determine the net impact to cash flows.

First, lets determine the cash flow from segment1 alone. We begin by calculating the unit contribution margin using the following step: Unit Contribution Margin (UCM) = [(selling price * realized price) – unit variable cost]. The net cash flow in a segment will be: Net Cash Flow  = UCM * segment size (Q) – Costs of segment development – Fixed Costs (FC)

Now, lets examine what happens when the product is offered at a lower price to segment2.

The stimulation effect of the new segment is: UCM2 *Q2 – cost-of-segment2-development -FC

Dilution effect of lowering price in segment-1 is: (UCM1 – UCM2) * Q1 (the loss of profit when the first segment notices lower price and purchases)

The net cash flow, CF2 is: (UCM2*Q2 – cost-of-segment2-development -FC)  –  (UCM1 – UCM2) * Q1

Two-Part Pricing

Here I demonstrate two-part pricing first by calculating a single optimal price using a simple price-demand relation, price elasticity and the Lerner rule. Next, I examine two different segments with different price elasticities and determine different prices for each segment. The data is taken from the Keurig case.

Single price:

Two-part pricing for 1-cup/day drinkers and 2-cups or more/day drinkers:

Now, lets model the Profit computation in terms of the cost of brewing system and the profits from selling the cups.

BREWER only profit = (P-brewer – Cost-brewer)*Q-brewer

BREWER & cups profit = (P-brewer – Cost-brewer + profit-cups)*Q-brewer

We can rewrite this as profit = (P-brewer – (Cost-brewer – profit-cups))*Q-brewer

Notice, how this view of the Profit shows us the DISCOUNT we just applied to the cost of manufacturing the brewer simply by factoring in the profits generated from selling the cups.

Now, we can use Lerner rule: P-optimal = n/(n+1) (Cost-brewer – profit-cups)

Here, Marginal Cost is (Cost-brewer – profit-cups).

Using the brewer price elasticity (from the case) of 3, we get P-optimal= $186.00 FROM (-3)/(-3+1) * (200 – 76) where 76 is the 5-year discounted (at 10%) cash flow of profits from cups. To see where 76 came from: For 2 cups priced at 50 cents a day, profit per year with royalty of 4 cents and 250 days = $20. OVer 5 years lifetime profit/brewer = $100, at 10% DCF, NPV = $76.

Lower the entry cost, make profits on ensuing purchases. This is a customer lock-in.