I'm reading a book called "The #1 Guide to Startup Valuation: How to value your startup in 12 easy steps" (p. 22-23) by Joachim Blazer.
As one of the building blocks, namely "Return", the Carry Multiple is calculated.
There it says literally:
Assume that the investor buys shares with a payoff of 100.
And that he wants to make a net return multiple of 1.6.
And that he pays his investment manager (often in addition to fees) 20% of his profit in carried interest.
How much does he want to pay for this investment?
If you only look at the carry: 100 / ((1.6 – 20%) / (1.6 – 20% * 1.6)) = 100 / (1.4 / 1.3) = 100 / 1.1 = 91.
Or a carry multiple of: (1.6 – 20%) / (1.6 – 20% * 1.6) = 1.4 / 1.3 = 1.1.
What I don't understand is the logic behind the calculation of the carry multiple. Why is the equation for the multiple written like that, what is the explanation behind this equation? So to say, I search for a verbal explanation of the equation instead of the given mathematical explanation.
I appreciate any help!