Atlantis Corp operates in a MM world with perfect capital markets. Atlantis has $18,000 in debt and $32,000 in equity, a cost of debt of 4%, and a cost of equity of 16.5%. Atlantis is planning to issue new equity and use the proceeds to repay all its debt outstanding.

After it repays all it debt, the cost of capital for Atlantis (in percent, with one decimal) will be:

Question

Atlantis Corp operates in a MM world with perfect capital markets. Atlantis has $18,000 in debt and $32,000 in equity, a cost of debt of 4%, and a cost of equity of 16.5%. Atlantis is planning to issue new equity and use the proceeds to repay all its debt outstanding.

After it repays all it debt, the cost of capital for Atlantis (in percent, with one decimal) will be:

BlackTom AI · Accepted Answer

Atlantis operates in a world with perfect capital markets and no taxes, so the Modigliani-Manks framework applies cleanly. We start by computing the firm’s current weighted average cost of capital (WACC) using the given debt and equity values and their respective costs.

Step 1: Determine capital structure weights
- Total value V = D + E = 18,000 + 32,000 = 50,000
- Weight of debt: D/V = 18,000 / 50,000 = 0.36
- Weight of equity: E/V = 32,000 / 50,000 = 0.64

Step 2: Compute current WACC (no taxes)
- WACC = (D/V) * rD + (E/V) * rE
- WACC = 0.36 * 0.04 + 0.64 * 0.165
- WACC = 0.0144 + 0.1056 = 0.12 or 12.0%

Step 3: Apply MM proposition with no taxes (perpetual, perfect markets)
- In a world with no taxes, the WACC remains constant regardless of capital structure. The market value of the firm is unaffected by how it finances itself, and investors can replicate leverage on their own if desired.

Step 4: Consider the effect of repaying all debt
- After issuing new equity to repay all debt, the firm becomes all-equity financed. The new capital structure has D = 0 and E = V = 50,000.
- In this all-equity case, the firm’s cost of capital is simply the cost of equity, but in a MM world with no taxes, the firm’s overall cost of capital must equal the pre-repayment WACC of 12.0%, since the financing mix does not alter the aggregate discount rate used to value the firm’s cash flows.

Conclusion (as derived from the above): the cost of capital after the debt is repaid remains 12.0%, and the implied cost of equity in the all-equity structure would have to equal this same 12.0% to maintain consistency with MM no-tax assumptions.

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