Calculate Cost of Capital from Bond Debt Formula

Reviewed and verified for financial accuracy by David Chen, CFA.

Use this calculator to determine the estimated pre-tax Cost of Debt (Yield to Maturity) for a bond, a critical component in calculating a firm’s Weighted Average Cost of Capital (WACC).

Cost of Capital from Bond Debt (YTM)

Annual Coupon Payment ($C$):

Face Value (Par Value, $FV$):

Current Market Price ($P$):

Years to Maturity ($n$):

Calculated Pre-Tax Cost of Debt ($r_d$):

Cost of Capital from Bond Debt Formula:

$$r_d \approx \frac{C + \frac{(FV – P)}{n}}{\frac{(FV + P)}{2}}$$

Where:

$r_d$: Approximate Cost of Debt (Yield to Maturity)
$C$: Annual Coupon Payment
$FV$: Face Value (Par Value)
$P$: Current Market Price
$n$: Years to Maturity

Formula Source: For a deeper understanding of bond pricing and the approximation method, consult reliable financial sources. Investopedia – Yield to Maturity and CFA Institute Guidance are excellent references.

Variables:

Annual Coupon Payment ($C$): The dollar amount of interest paid to the bondholder each year. It is calculated by multiplying the bond’s Coupon Rate by its Face Value.
Face Value ($FV$): The principal amount the issuer pays back to the bondholder at maturity. This is typically $\$1,000$.
Current Market Price ($P$): The price at which the bond is currently trading in the market. This is the amount an investor pays to acquire the debt.
Years to Maturity ($n$): The number of years remaining until the bond issuer is obligated to repay the Face Value.

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What is the Cost of Capital from Bond Debt?

The Cost of Debt is the effective interest rate a company pays on its borrowings, primarily through bonds and loans. For publicly traded bonds, this cost is best represented by the **Yield to Maturity (YTM)**, which is the total return anticipated on a bond if it is held until its maturity date.

The YTM calculation is crucial because it represents the minimum rate of return a company must earn on its assets to satisfy its bondholders. In financial modeling, the pre-tax Cost of Debt ($r_d$) is multiplied by $(1 – \text{Tax Rate})$ to arrive at the after-tax cost, which is then used in the WACC formula.

When a bond trades at a discount ($P < FV$), the investor earns a capital gain at maturity, pushing the YTM higher than the coupon rate. When a bond trades at a premium ($P > FV$), the YTM will be lower than the coupon rate due to the expected capital loss at maturity.

How to Calculate Cost of Capital from Bond Debt (Example):

Consider a bond with a \$1,000 Face Value, a 5% Coupon Rate, 5 years to maturity, and a current market price of \$950.

Determine Annual Coupon Payment ($C$): $0.05 \times \$1,000 = \$50$.
Calculate Annual Amortization of Premium/Discount: $(\$1,000 – \$950) / 5 \text{ years} = \$10 \text{ per year}$. (Since it’s a discount, this is added to the coupon).
Calculate Average Annual Return (Numerator): $\$50 \text{ (Coupon)} + \$10 \text{ (Amortization)} = \$60$.
Calculate Average Investment Value (Denominator): $(\$1,000 \text{ (FV)} + \$950 \text{ (P)}) / 2 = \$975$.
Calculate Approximate YTM: $\$60 / \$975 \approx 0.0615$ or $6.15\%$.

Frequently Asked Questions (FAQ):

What is the difference between Cost of Debt and WACC? The Cost of Debt is the cost associated with a single source of financing (bonds and loans). The WACC (Weighted Average Cost of Capital) is the average cost of all financing sources, including debt, preferred stock, and common equity, weighted by their proportion in the capital structure.

Is the Cost of Debt usually calculated pre-tax or after-tax? The pre-tax Cost of Debt is the YTM calculated here. However, for calculating WACC, the after-tax Cost of Debt is used because interest payments are tax-deductible expenses for the corporation.

Why does the calculator use an approximation formula? Calculating the exact Yield to Maturity requires finding the discount rate that equates the bond’s present value to its market price, which involves iterative methods. The approximation formula provides a very close estimate that is suitable for general calculator use.

When is the Cost of Debt equal to the Coupon Rate? The Cost of Debt (YTM) is exactly equal to the bond’s Coupon Rate only when the Current Market Price ($P$) is equal to the Face Value ($FV$). This means the bond is trading at par.