This risk-free loan pays off $20,000 for certain. The levered ownership pays either $0 or $80,000, and

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This risk-free loan pays off $20,000 for certain. The levered ownership pays either $0 or $80,000, and costs

$64,000/1.10 ≈ $58,182. Therefore, the rate of return is either −100% or +37.50%. You have already worked out full ownership in the text: It pays either $20,000 or $100,000, costs $76,364, and offers either −73.81% or +30.95%. By inspection, the levered equity project is riskier. In effect, building ownership has become riskier, because the owner has chosen to sell off the risk-free component and retain only the risky component.
Event Prob Building Value Mortgage Value Levered Ownership Tornado 20% $20,000 $20,000 $0 Sunshine 80% $100,000 $20,000 $80,000 Expected Value at Time 1 $84,000 $20,000 $64,000 Present Value at Time 0 $76,364 $18,182 $58,182 From Time 0 to Time 1, E(˜r) 10% 10% 10%

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