# Cost Of Debt

Cost of debt is the interest rate that the company pays on its debt content of the
capital structure. It can be measured as before tax cost of debt or after tax cost
of debt. Tax plays an important role as the debenture interest expense is allowed
as an expense for tax purposes. Debt may be issued at par, at premium or at a discount.
It may be irredeemable or redeemable.

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__Cost of Irredeemable debt:__
Irredeemable debentures are those debentures issuing by which the company has no
obligations to pay back the value of the debenture on some fixed date or time and
has the full authority to choose any time to pay back the debt until the company
is a going entity and does not default in it’s interest payments. So we take into
account only the sale value (SV) while evaluating the cost of irredeemable debentures.

**Before tax cost of Irredeemable debt :-**

Interest/Sale Proceeds or Sale value of debentures

I / SV

Where:

I = Annual fixed interest and

SV = Sale value of debentures

Or

I / SV

Where:

I = Annual fixed interest and

SV = Sale value of debentures

**After tax cost of Irredeemable debt :-**

Kd = (1-T) * Before tax cost of debt

Kd = (1-T) * I/SV

Where:

T = Tax rate

Kd = After tax cost of debt

I = Annual interest payment

SV = Sale value of debentures

Kd = (1-T) * I/SV

Where:

T = Tax rate

Kd = After tax cost of debt

I = Annual interest payment

SV = Sale value of debentures

The SV of debentures would be adjusted for issuance at discount or premium. This would be net of commission and floatation costs if any.

**Example:**

**Debt issued at par :-**

Let us consider an example where a concern sells a new issue of 6% irredeemable debentures to raise $100,000 and realizes the full face value of $100. The company falls in 40% tax bracket. Debts are issued at par.

Before tax cost of debt = Interest / Sale value or Interest /Principal being issued at par = $6,000 / $100,000 * 100 = 6%

Cost of debt after tax = (1 - T) * Before tax cost of debt

**->**(1 - 0.40) * 6%

**->**0.036 or 3.6%

**Debt issued at premium or discount :-**

Let us consider the same example with only difference is that the debentures are issued at 10% premium.

So the Sale value or net proceeds would be = $100,000 + 10% = $110,000

Kd = I (1 - T) / SV

Where:

Kd = cost of debt after tax

SV = Sale value of debentures

T = Tax rate

I = Annual interest payment

Cost of debt = $6,000 / $110,000 * (1 - 0.40) = 3.27%

If the above debentures were issued at 10% discount, then the cost of debt would be $6,000 / $90,000 * (1 - 0.40) = 4%.

__Cost of Redeemable debt:__
For redeemable debentures, the maturity date is fixed initially. The meaning redeemable
denotes that the debentures would be redeemed by the company at a fixed date or
after a specified period of notice. So, we take the average of Sale Value and Redeemable
value while calculating the cost of redeemable debentures.

**Before tax cost of Redeemable debt :-**

Kd (before tax) = (I + [ RV - SV ] / n)
divided by ( RV + SV ) / 2

Where:

I = Annual fixed interest

RV = Redeemable Value of debenture net of commission and floatation costs, if any. This SV would also be adjusted if issued at a discount or at a premium.

N = Term of debt till maturity

Where:

I = Annual fixed interest

RV = Redeemable Value of debenture net of commission and floatation costs, if any. This SV would also be adjusted if issued at a discount or at a premium.

N = Term of debt till maturity

**After tax cost of Redeemable debt :-**

Kd (after tax) = Kd
(before tax) * ( 1 - T )

Where:

T = tax rate

Thus,

Kd (after tax) = ((I + [ RV - SV ] / n) / (( RV + SV ) / 2)) * ( 1 - T )

Where:

T = tax rate

Thus,

Kd (after tax) = ((I + [ RV - SV ] / n) / (( RV + SV ) / 2)) * ( 1 - T )

**Example:**

Say a firm issues debentures worth $100,000 and realizes $98,000 after allowing
2% commission to brokers. They carry an interest rate of 10% and are due for maturity
at the end of 10th year. The company has 40% tax bracket. Redeemable value = $100,000;
Sale value = $98,000.

Cost of debt (after tax) = (1 - 0.40) * (($10,000 + [$100,000 - 98,000] / 10) / (($100,000 + 98,000) / 2))

Cost of debt (after tax) = 6.18%

Cost of debt (after tax) = (1 - 0.40) * (($10,000 + [$100,000 - 98,000] / 10) / (($100,000 + 98,000) / 2))

Cost of debt (after tax) = 6.18%