As mentioned at the beginning of this section, one of the main objectives of business case value analysis is to estimate a product's relative worth to customers in the various value contexts in which it might be sold. A product's relative worth to a customer is the price at which the purchase inducement it offers a buyer is no more and no less than the purchase inducement offered by the customer's next best competing alternative.
A formula for estimating a product's relative worth in a specific value context can be derived from the value equation set forward by Anderson and Narus. The derivation requires just a few simple transformations of that equation, nothing more than the kind of thing we all learned in 9th grade algebra.
We start with the value equation:
| (Valuef - Pricef) | > | (Valuea - Pricea) |
| Firm's Offering | Alternate Offering | |
The first steps in this transformation involve replacing Pricef in the original formula with Relative Worthf and changing the > sign to an = sign. That makes the value equation formula look like this:
| Vf - rWf = Va - Pa |
Now we have a true equation, not an inequality. The equation says that the total value-in-use that Product F delivers less its Relative Worth amounts to the same net gain for the customer as the total value-in-use delivered by Product A less its price. That is the definition of relative worth: the price for Product F that produces a contribution to the customer's bottom line that is the same as that offered by the competing alternative. Put another way, when one of two offerings is priced at its relative worth, the two offerings' payoffs for the customer are the same.
To turn this equation into a formula for estimating Product F's relative worth, we need to rearrange the equation so that we have F's relative worth on one side and all the other elements on the other. We can move Vf over to the right hand side of the equation by subtracting Vf from both sides. Doing that gives us the equation:
| - rWf = Va - Pa - Vf |
Now we want to get rid of the minus sign in front of RWf. We can do that by multiplying all the terms on each side of the equation by -1. That gives us:
| rWf = - Va + Pa + Vf |
Grouping the V's gives us:
| rWf = Pa + (Vf - Va) |
Looking at this version of the equation, we see that Product F's relative worth is equal to the combination of two things: Product A's price and the difference between F's total value-in-use and A's total value-in-use.
We could stop here. However, for practical reasons, it will be useful for us to go one step further. That is to formally combine into a single term the two terms representing F's total value-in-use less A's total value-in-use. We can do that by replacing Vf - Va with a single term, which we will call differential value-in-use where Dvf-a = Vf- Va. The final version of the formula changes
| From | To | |
| rWf = Pa+(Vf - Va) | rWf = Pa+dVf-a | |
This is the formula for estimating a product's relative worth in any specific business value context.
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