Logic of using Parent's PE when valuing RemainCo and SpinCo of a spinoff?

Question

Reading an older book by Maurece Schiller, there is a section about ways to value companies planning / undergoing a spinoff. In it, he uses the parent's PE multiple to value the earnings of both the SpinCo and RemainCo. This is a bit confusing to me, since I would think that it would make more sense to use multiples from businesses whose fundamentals are more closely comparable to the separated businesses (the way I usually see relative valuation done) and the use of the old parent multiple seems a bit arbitrary. From the book...

For example, if the parent company stock is priced at $60, based on 12 times earnings of $5 a share, exclude the subsidiary’s contribution of [assumed in this example to be] $1 a share, and then calculate the price of the stock. This would be 12 times $4, or $48 a share. The next step is to estimate the value of the subsidiary’s stock based on 12 times earnings. If we assume the subsidiary earnings of $2.50 a share [the total undistributed earnings of the subsidiary in this example], then the estimated value would be $30 a share. Adding the values of the parent and the subsidiary shares of $48 and $30 respectively, we have an indicated worth of the parent stock of $78 a share as a divestiture situation.

Can someone explain the logic of using the parent's multiple rather than some other comparable business here (assuming such comps exist)?

Answer 1

Recently asked someone with formal finance education about a similar valuation decision they made when analyzing a spinoff situation, and they said something to the effect of...

I made the decision not to [use multiples from comps as opposed to the parent's valuation ratios] in order to illustrate how the market, at the time, was implicitly valuing two separate businesses in one basket. By being lumped together in one entity, my thought was they might still act like they trade on the same multiple when they shouldn't. [As for considering the available comps for these businesses] These facts are taken into consideration in determining the future/intrinsic value, where SpinCo is comp'd against some SpinCo-equivalent comp's multiple...

So basically, using the parent's multiple for a relative valuation of the Remain- and Spin-Co encodes an assumption that the market will still view (at the initial time of the spinoff, anyway) the new businesses under the same multiple valuation as the parent (though I still have not found anything explaining Schiller's specific reasoning for doing the same or how this logic would work in the case of a spinoff with a different business than the main business of the parent).