Question 7 1 pts To help finance a major expansion, Castro Chemical Company sold

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Question 7 1 pts To help finance a major expansion, Castro Chemical Company sold a noncallable bond several years ago that now has 20 years to maturity. This bond has a 9.25% annual coupon, paid semiannually, sells at a price of $875, and has a par value of $1,000. If the firm's tax rate is 40%, what is the component cost of debt for use in the WACC calculation? O a) 5.95% O b) 5.63 O c) 6.48% O d) 6.15% e) 5.31% Question 8 1 pts Keys Printing plans to issue a $1,000 par value, 20-year noncallable bond with a 7.00% annual coupon, paid semiannually. The company's marginal tax rate is 40.00%, but Congress is considering a change in the corporate tax rate to 32.50%. By how much would the component cost of debt used to calculate the WACC change if the new tax rate was adopted? O a)0.44% b) 0.54% ( c) 0.43% O d) 0.57% ( e) 0.53% O

Explanation / Answer

7. We have following formula for calculation of bond’s yield to maturity

Bond price P = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n

Where

Price of the bond P = Selling price = $875

C = coupon payment = 9.25%/2 of $1000 = $46.25 semiannual coupon

n = number of payments = 20 years *2 = 40

i = interest rate, or yield to maturity =?

M = value at maturity, or par value = $ 1000

Therefore,

$ 875 = $ 46.25 * [1 – 1 / (1+i) ^40] /i + 1000 / (1+i) ^40

By trial and error method we got the value of i = 5.40%

Or annual rate I = 5.40% *2 = 10.80%

But component cost of debt used in WACC calculation is after tax cost of debt which is equal to Yield to maturity *(1-T)

Where T is tax rate = 40%

Therefore after tax cost of debt = 10.80*(1-40%) = 6.48%

Therefore correct answer is option c. 6.48%

8. We have following formula for calculation of bond’s yield to maturity

Bond price P0 = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n

Where

Price of the bond P0 = Selling price = $1000

C = coupon payment = 7%/2 of $1000 = $35 semiannual coupon

n = number of payments = 20 years *2 = 40

i = interest rate, or yield to maturity =?

M = value at maturity, or par value = $ 1000

Therefore,

$ 1000 = $ 35 * [1 – 1 / (1+i) ^40] /i + 1000 / (1+i) ^40

By trial and error method we got the value of i = 3.5%

Or annual rate I = 3.5% *2 = 7% (if the bond is selling at par then yield to maturity will be equal to coupon rate)

But component cost of debt used in WACC calculation is after tax cost of debt which is equal to Yield to maturity *(1-T)

If tax rate T = 40%

After tax cost of debt = 7 %*( 1-40%) = 4.20%

And after change if tax rate T = 32.5%

After tax cost of debt = 7 %*( 1-32.5%) = 4.73%

Therefore the change in WACC component = 4.73% - 4.20% = 0.53%

Therefore correct answer is option e. 0.53%

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