When MV = Maturity Value of debt, $NP$ = Net Proceeds, $n$ = Number of years to maturity and $R$ = Annual interest, then the cost of Debt Capital $(K_d)$ (before tax) will be :

Question

Accepted Answer

The correct option is 3:
The formula provided in Option 3, $K\_{d}=\frac{R+(\frac{MV-NP}{n})}{(\frac{MV+NP}{2})}\times100$, represents the standard *approximate* method for calculating the Cost of Redeemable Debt Capital ($K\_d$) before tax. This method is a practical alternative to the more rigorous Internal Rate of Return (IRR) method. The logic is sound: the numerator, $R+(\frac{MV-NP}{n})$, correctly determines the average annual cost to the company, which comprises the annual interest payment ($R$) plus the average annual adjustment for the difference between the maturity value ($MV$) and the net proceeds ($NP$). This adjustment accounts for the gain (premium) or loss (discount) on the bond spread over its life ($n$). The denominator, $\frac{MV+NP}{2}$, accurately approximates the average investment or the average book value of the debt outstanding throughout its tenure, providing the correct base for calculating a percentage rate of return.

The incorrect option is 1:
The formula in Option 1, $K\_{d}=\frac{R-(\frac{MV+NP}{n})}{(\frac{MV-NP}{2})}\times100$, is incorrect as it fundamentally misrepresents the components of the cost of debt. The primary error lies in the denominator, $\frac{MV-NP}{2}$, which calculates half the value of the discount or premium, not the actual average book value of the debt instrument. The base for the cost of debt calculation must reflect the average principal amount used by the company. Furthermore, the numerator is conceptually flawed because it subtracts an average value term ($\frac{MV+NP}{n}$) from the annual interest ($R$), which does not correspond to the required calculation of interest plus the amortized discount/premium.

The incorrect option is 2:
Option 2 presents the formula $K\_{d}=\frac{R+(\frac{MV-NP}{n})}{(\frac{MV-NP}{2})}\times100$. While the numerator, $R+(\frac{MV-NP}{n})$, is correctly structured to include both the annual interest and the average annual adjustment for the difference in principal amount, the formula is rendered incorrect by its denominator. The expression $\frac{MV-NP}{2}$ represents half of the total discount or premium on the debt, which cannot serve as the average principal amount utilized by the firm. The denominator in the approximate cost of debt formula must be the average of the Net Proceeds and the Maturity Value, as this accurately reflects the average capital outstanding over the bond's life.

The incorrect option is 4:
The formula given in Option 4 is $K\_{d}=\frac{R-(\frac{MV-NP}{n})}{(\frac{MV-NP}{2})}\times100$. This option is incorrect because it contains errors in both the numerator and the denominator. Similar to Option 2, the denominator, $\frac{MV-NP}{2}$, is wrong because it uses half the discount or premium instead of the average capital outstanding. Crucially, the numerator incorrectly *subtracts* the annual amortized principal adjustment ($\frac{MV-NP}{n}$) from the annual interest ($R$). The approximate cost of debt must *add* this annual adjustment to the interest to find the total annual flow, as the amortized amount represents a cost to the firm regardless of whether the debt was issued at a discount or a premium.