How after-tax cost of debt works

WACC weights the cost of equity and the cost of debt by the market share of each claim. Interest counts as a cost of doing business wherever the tax code says it does, so a company that pays interest usually pays less tax. That is why the debt term is $r_d(1-t)$ and the equity term is not. Dividends and buybacks come out of profit that has already been taxed.

$$r_d(1-t) = 5\% \times (1 - 0.25) = 3.75\%$$

On the calculator's first sheet, equity is $6,000,000 at 9 percent and debt is $4,000,000 at 5 percent, taxed at 25 percent. After-tax debt cost is 3.75 percent. WACC is $0.60 \times 9\% + 0.40 \times 3.75\% = 6.9\%$. That 3.75 percent is what this page owns.

The WACC calculator returns the after-tax cost of debt alongside the blend. The WACC explorer holds $r_e$, $r_d$, and tax still and lets you drag the debt share: more deductible debt pulls WACC toward 3.75 percent, not toward 5 percent. Book value is not a stand-in for market equity when you form the weights.

Add the two market values: $6,000,000 plus $4,000,000 is $6{,}000{,}000 + 4{,}000{,}000 = 10{,}000{,}000$ of capital. Equity weight is 60 percent. Debt weight is 40 percent. Take the tax relief off the 5 percent: $5\% \times 0.75 = 3.75\%$. Weight each cost: 5.4 points from equity, 1.5 points from after-tax debt. The blend is 6.9 percent.

Because the weights add to 1, WACC lands between the 9 percent cost of equity and the 3.75 percent after-tax cost of debt. 6.9 percent sits 40 percent of the way down that range, which is exactly the debt weight. Equity is the residual claim. Debt is the fixed one. Only the fixed claim is deductible.

Keep the same $6,000,000 of equity and $4,000,000 of debt, the same 9 percent and 5 percent. Set the tax rate to 0, either because the rules do not allow a deduction or because there is no taxable profit to shelter. After-tax debt cost equals the 5 percent the lender charges. WACC becomes $0.60 \times 9\% + 0.40 \times 5\% = 7.4\%$.

The shield was worth 0.5 percentage points on this sheet: 6.9 percent against 7.4 percent. That gap is the debt weight times the cost of debt times the tax rate, $0.40 \times 5\% \times 0.25 = 0.5\%$. A loss-making firm that cannot use the deduction this year is closer to the zero-tax case. The formula still multiplies by $(1-t)$. $t = 0$ is the honest input.

The relief lowers the company's cost without lowering the lender's return. The tax authority pays the difference. It makes debt cheaper to the borrower, not free.

Keep rates the same and flip the mix to $4,000,000 of equity and $6,000,000 of debt. After-tax debt cost is still 3.75 percent, because neither the coupon nor the tax rate moved. WACC falls to $0.40 \times 9\% + 0.60 \times 3.75\% = 5.85\%$.

Holding both input costs still is what makes that fall look free. Every extra unit borrowed puts a fixed claim ahead of the shareholders, so the cost of equity rises with the leverage ratio. Lenders watching cover thin out want more as well. Reprice the 40/60 mix at 11 percent on the equity and 6 percent on the debt, which is 4.5 percent after the same deduction, and WACC reads 7.1 percent, above the 6.9 percent it started from.

WACC against cost of equity puts 6.9 percent next to the 9 percent equity rate so the mix is visible. This page does not re-derive the weighted average. It keeps $r_d(1-t)$ in view.

Use the current yield the firm would pay to issue new debt, not the coupon on a bond issued years ago. A 4 percent coupon on a book that now yields 5 percent is not the marginal cost. The current yield against YTM page is the bond-side version of that point. After-tax cost of debt then applies $(1-t)$ to that market rate.

The $t$ is the marginal rate on the profit the interest actually shelters, over the life of the cash flows being discounted, not the effective rate from last year's accounts. In the United States, interest on business borrowing is generally deductible against taxable income, subject to a cap tied to earnings. Other countries set different rules. The rate in the formula is the one that actually applies to this firm.

How unlevered beta works is the other side of the same tax term: Hamada uses $(1-t)$ when stripping financial leverage out of an equity beta.

It is not a full WACC, not a coupon on an old bond, and not a claim that more debt is cheaper. The three sheets are 3.75 percent after-tax debt cost inside a 6.9 percent WACC, the same mix with tax at zero (5 percent, WACC 7.4 percent), and the same 3.75 percent inside a 5.85 percent WACC on a 60 percent debt mix. This is educational material, not financial advice.