Modigliani-Miller: Pick Your Capital Structure

The Setup

You're an entrepreneur funding a project that costs $800 today. Next year it pays $1,400 (50% chance, strong economy) or $900 (50% chance, weak economy). With r_U = 15%, its PV is $1,000.

Your goal: choose how to finance the $800 investment — how much debt vs. equity to issue — to maximize your profit today. The market will price your securities fairly (based on their cash flows and risk).

r_f = 5%

β = 1.0

MRP = 10%

r_U = 15%

Your Choice

Debt issued $400

The remaining amount will be raised by issuing equity — whatever the market is willing to pay for it.

Results

Responses: 0

Waiting for the reveal...

Cash Flows by State

$1,400

Strong Economy

$900

Weak Economy

Debt issued $0

Equity issued: $1,000

Equity Returns

Equity return = cash flow / price − 1

Return (strong) +40.0%

Return (weak) -10.0%

Expected return 15.0%

Return spread (risk from leverage)

50.0pp

Cost of Capital

D / E ratio 0.00

r_E (equity) 15.0%

r_D (debt) 5.0%

WACC 15.0%

Debtholders get paid first (a fixed amount in both states), so their claim is safe. Equityholders get whatever is left. As debt increases, the equity cash flows in the two states spread further apart in percent terms. The higher expected return acts as compensation for bearing that extra risk.

Equity Cost of Capital vs. Leverage

M-M II: r_E = r_U + (D/E)(r_U − r_D). More leverage → riskier equity → higher required return.

WACC vs. Leverage

Cheap debt is exactly offset by expensive equity. The weighted average stays at r_U = 15% regardless of capital structure.