Respuesta :
The pre-tax cost of debt is yield to maturity of the debt.
The yield to maturity of debt is calculated as -
Yield to maturity = ]Coupon payment + ( Face value - Current price) / Number of years)] / [ ( Face value + Current price) / 2]
Here,
Coupon payment = $ 29.50 (semi-annual, thus 5.9% / 2 * 1000)
Face value = $ 1,000
Price = $ 1,000 * 108% = $ 1,080
Number of years = 12 ( semi-annual, thus 6 years * 2)
Pre-tax cost of debt = [ 29.50 + (1,000 - 1080/12)] / [ (1000+1080)/2 ]
Pre-tax cost of debt = 2.196 %
Annual pre-tax cost of debt = = 2.20 % * 2 = 4.40%
After tax cost of debt = ( 1 - tax rate ) * Annual pre-tax cost of debt
After tax cost of debt = ( 1 - 35%) * 4.40 %
After tax cost of debt = 2.86 %
The yield to maturity of Shanken corp. is 4.39%, it is calculated because interest is tax-deductible, which effectively creates “tax protection” that is interest rates reduce the taxable income of a company.
What is Yield to maturity?
Yield to maturity (YTM) rate of return on a bond is assumed by the investor holding the asset until its date of growth. It is the sum of all its remaining coupon payments.
The interest rate on maturity increases or decreases depending on its market value and how many remaining payments are to be made.
With the given information yield to maturity can be calculated as follows:
[tex]\rm\,Yield\,to\,maturity = [Coupon\,payment + \dfrac{( \dfrac{Face\,value - Current\,price)}{Number\,of\,years)}}{ \dfrac{( Face\,value + Current\,price)}2}]\\\\Where, Coupon payment = \$ 29.50 [\dfrac{5.9}{2}\times \,100]\\\\[/tex][tex]\rm\,Face\,value = \$ 1,000\\\\Current\,price= \$ 1,080\, [ 1,000 \times\,\dfrac{108}{100}]\\\\Number\, of \,years\, = 12 \,( semi-annual, \,thus\,6\,years\times 2)\\\\Pre-\,tax\,cost\,of\,debt = [29.50 + \dfrac{ \dfrac{(1,000 - 1,080)}{12}}{ \dfrac{( 1,000 + 1,080)}2}]\\\\\\= 2.196\%\\ \\Annual\,pre- tax\,cost\, of\,debt\, = 2.196 \times 2 = 4.392\%[/tex]
Hence, the annual pre-tax cost of debt is equal to 4.39%
To learn more about yield to maturity, refer to the link:
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