Russell Container Corporation has a $1,000 par value bond outstanding with 30 years to maturity. The bond carries an annual interest payment of $105 and is currently selling for $880 per bond. Russell Corporation is in a 25 percent tax bracket. The firm wishes to know what the after-tax cost of a new bond issue is likely to be. The yield to maturity on the new issue will be the same as the yield to maturity on the old issue because the risk and maturity date will be similar.
6. Compute the yield to maturity on the old issue and use this as the yield for the new issue.
Note: Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.
Yield on new issue %
b. Make the appropriate tax adjustment to determine the after-tax cost of debt.
Note: Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.
Answer (2)
Calculate the yield to maturity (YTM) using the formula: Y TM = 2 P a r Va l u e + C u rre n t P r i ce A nn u a l I n t eres t P a y m e n t + Y e a rs t o M a t u r i t y P a r Va l u e − C u rre n t P r i ce = 2 1000 + 880 105 + 30 1000 − 880 = 0.1160 .
The yield to maturity (YTM) expressed as a percentage is 11.60% .
Calculate the after-tax cost of debt using the formula: A f t er − t a x C os t o f De b t = Y TM × ( 1 − T a x R a t e ) = 0.1159574468 × ( 1 − 0.25 ) = 0.0870 .
The after-tax cost of debt expressed as a percentage is 8.70% .
Explanation
Calculate Yield to Maturity (YTM) First, we need to calculate the yield to maturity (YTM) on the old bond issue. The formula for YTM is: Y TM = 2 P a r Va l u e + C u rre n t P r i ce A nn u a l I n t eres t P a y m e n t + Y e a rs t o M a t u r i t y P a r Va l u e − C u rre n t P r i ce We are given: Annual Interest Payment = $105 Par Value = $1,000 Current Price = $880 Years to Maturity = 30
Substitute Values into YTM Formula Now, we substitute the given values into the YTM formula: Y TM = 2 1000 + 880 105 + 30 1000 − 880 Y TM = 2 1880 105 + 30 120 Y TM = 940 105 + 4 Y TM = 940 109 Y TM = 0.1159574468 Expressed as a percentage and rounded to two decimal places, the yield to maturity is 11.60%.
Calculate After-Tax Cost of Debt Next, we need to calculate the after-tax cost of debt. The formula for the after-tax cost of debt is: A f t er − t a x C os t o f De b t = Y TM × ( 1 − T a x R a t e ) We have already calculated the YTM as 0.1159574468, and we are given the tax rate as 25%, or 0.25.
Substitute Values into After-Tax Cost Formula Now, we substitute the values into the after-tax cost of debt formula: A f t er − t a x C os t o f De b t = 0.1159574468 × ( 1 − 0.25 ) A f t er − t a x C os t o f De b t = 0.1159574468 × 0.75 A f t er − t a x C os t o f De b t = 0.0869680851 Expressed as a percentage and rounded to two decimal places, the after-tax cost of debt is 8.70%.
Final Answer Therefore, the yield on the new issue is 11.60%, and the after-tax cost of debt is 8.70%.
Examples
Understanding the yield to maturity and after-tax cost of debt is crucial for companies when evaluating financing options. For instance, if Russell Container Corporation is considering issuing new bonds to fund an expansion project, they need to know the actual cost of this financing. The YTM helps them understand the return investors require, while the after-tax cost of debt shows the true cost to the company after considering tax benefits. This knowledge allows them to make informed decisions about whether the project's potential return justifies the cost of borrowing. Moreover, it helps in comparing debt financing with other options like equity financing or using retained earnings, ensuring the company chooses the most financially advantageous path.
The yield to maturity (YTM) calculated for Russell Container Corporation's bond is 11.60%. After accounting for taxes, the after-tax cost of debt is determined to be 8.70%. These values help assess the cost of financing through new bonds.
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