## The Levered Equity

As the residual building owner, what rate of return would you expect as proper compensation? You already know the building is worth $76,363.64 today. Thus, after the loan of $25,000, you need to pay in $51,363.64—presumably from your personal savings. Of course, you must compensate your lender: To contribute the $25,000 to the building purchase today, you must promise to pay the lender $29,375 next year. If the tornado strikes, the lender will confiscate your house, and all your invested personal savings will be lost. However, if the sun shines, the building will be worth $100,000 minus the promised $29,375, or $70,625. Your payoff table as the levered equity building owner is

Event rob

Value Discount Factor

Tornado Sunshine

It allows you to determine that the expected future levered building ownership payoff is 20% $0 + 80% ■ $70,625 = $56, 500. Therefore, the present value of levered building ownership is

Now compute the payoffs of the 60% post-mortgage (i.e., levered) ownership of the building. The method is exactly the same.

= Prob( Tornado ) ■ (PV if Tornado) + Prob( Sunshine ) ■ (PV if Sunshine) (5.32)

If the sun shines, your rate of return will be

if Sunshine:

If the tornado strikes, your rate of return will be

Again, knowing the state-contingent cash flows permits computing state-contingent rates of return and the expected rate of return.

The expected rate of return of levered equity ownership, that is the building with the bundled mortgage obligation, is

E(ft=0l1) = Trob(Tornado) ■ (rt=0,1 if Tornado) + Trob(Sunshine) ■ (rt=0 1 if Sunshine)

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