Question

Question 4 Suppose today is January 1, 2009. On January 1, 1999, MAM Industries issued a 30-year bond with a 9% coupon and a $915 $1,000 face value, payable on January 1, 2029. The bond now sells for (4.1) Use this bond to determine the firm's after-tax cost of debt (Assume a 34% tax rate). (4.2) Suppose MAM Industries also issued a 30-year bond five years ago-it has value and a 10% coupon. (4.2a) If the bond currently sell for $1,000, what is the after-tax costs of debt capital, as indicated by the market value of this outstanding bond? (4.2b) Suppose five years from now the MAM bond described in 4.2a has a market price of $1,100. What is the after-tax cost of debt capital at that time?

Answer 1

Q. 4.1) Cost of debt of bond is yield to maturity (YTM) :

YTM = (C + ((P - M) / n)) / ((P + M) /2)

Here,

C (Coupon Interest) = Coupon rate * Par value = $1000 * 9% = $90

P (Par value) = $1000

M (Market price) = $915

n (years to maturity) = 20 years

Tax rate = 34% or 0.34

Now, put the values into formula,

YTM = ($90 + (($1000 - $915) / 20)) / (($1000 + $915)/2)

YTM = ($90 + $4.25) / $957.50

YTM = 0.0984 or 9.84%

After tax cost of debt = YTM * (1 - tax rate)

After tax cost of debt = 0.0984 * (1 - 0.34)

After tax cost of debt = 0.0649 or 6.49%

Note : Here, bonds remaining years to maturity of 20 years upto 01/01/2019 from now ie. 01/01/2009 is to be taken for YTM calculation.

Q. 4.2.a) Bond remaining years (n) to maturity = 25 years from now.

C (Coupon) = Par value * Rate = $1000 * 10% = $100

P (Par value) = $1000

M (Market price) = $1000

Tax rate = 34% or 0.34

Now,

YTM = ($100 + (($1000 - 1000)/25)) /( ($1000 + 1000) /2)

YTM = ($100 + 0) / $1000

YTM = 0.10 or 10%

After tax cost of debt = 0.10 * (1 - 0.34)

After tax cost of debt = 0.066 or 6.60%

Q 4.2.b) Years to maturity = 25

Coupon = $1000 * 10% = $100

P (Par value) = $1000

M (Market price) =$1100

Tax rate = 34% or 0.34

Now,

YTM = ($100 + ($1000 - $1100) / 25) / (($1000 + $1100)/2)

YTM = ($100 - $4) / $1050

YTM = 0.0914 or 9.14%

After tax cost of debt = 0.0914 * (1 - 0.34)

After tax cost of debt = 0.0603 or 6.03%