Question

Gertrude's Great Gloves issue bonds with a face value of $100, paying interest at j2 = 10%, redeemable in exactly 13 years. An investor purchases the bond for $115.10. Calculate the cost of debt (j2) for Gertrude's Great Gloves. You may give your answer as a percentage per annum to the nearest percent or use linear interpolation or a financial calculator to give a more accurate result.

Cost of debt = _____% pa

Answer 1

Cost of Redeemable Debt

Redeemable debt is a debt that is to be redeemed after a certain period. The formula used to calculate the cost of redeemable debt is as given below:

Cost of redeemable debt, Kd = I + 1/N (Rv - Np) x100 1/2 (Rv - Np)

where,

I = Interest

N = Number of years in which debt is to be redeemed

Rv = Redeemable value of Debt

Np = Net proceeds

Here, the variables in the formula can be substituted as:

I = 10% of 100 = 10 (The interest is paid at 10%. The face value of the bond is $100)

N = 13 years

Rv = 100

Np = 115.10

Cost of Debt, Kd = 10 + 1/13(100 - 115.10) x 100 1/2 (100 + 115.10)

(Remember to solve using BODMAS rule)

Upon simplifying the equation,

Kd = 10 + 1/13 x (-15.1) x100 1/2 x 215.10

Kd = 10 - 1.162 x 100 107.55

Kd = 8.838 x 100 107.55

Kd = 8.21757322175

8.218%

That is, the cost of debt is 8.218%