DG Corp. has 10,000 bonds outstanding, with a face value of $1,000 each and a coupon rate of 4.75 percent. The bonds are selling at par, and interest is paid semiannually. What is the amount of the annual tax shield on debt if the tax rate is 23 percent?

Question

DG Corp. has 10,000 bonds outstanding, with a face value of $1,000 each and a coupon rate of 4.75 percent. The bonds are selling at par, and interest is paid semiannually. What is the amount of the annual tax shield on debt if the tax rate is 23 percent?

BlackTom AI · Accepted Answer

Each bond's annual coupon = $1,000 × 4.75% = $47.50, so total annual interest = $47.50 × 10,000 = $475,000; the tax shield = 23% × $475,000 = $109,250.

1. Relevant knowledge points and concepts
- Coupon rate (4.75%) is the annual interest percentage paid on the bond's face value.  
- Semiannual interest means payments are made twice a year, but the annual interest amount remains the same.  
- Interest paid on debt is tax-deductible, so the annual tax shield equals the annual interest expense multiplied by the corporate tax rate.

2. Step-by-step reasoning
- Compute the annual coupon per bond, then aggregate across all bonds, and finally apply the tax rate to find the tax shield.

3. Calculations with intermediate steps
- Annual coupon per bond = face value × coupon rate = $1,000 × 0.0475 = $47.50.  
- Semiannual coupon per payment = (4.75% / 2) × $1,000 = 0.02375 × $1,000 = $23.75 (two payments per year sum to $47.50).  
- Total annual interest for all bonds = $47.50 × 10,000 = $475,000.  
- Annual tax shield = tax rate × total annual interest = 0.23 × $475,000 = $109,250.

4. Why the correct answer is correct
- The tax shield arises from the deductibility of interest, so it must be the product of the actual interest expense ($475,000) and the tax rate (23%), giving $109,250. Semiannual payments do not change the annual total.

5. Why the other options are incorrect
- $475,000 is the total annual interest expense, not the tax shield (it omits the tax rate).  
- $155,250 and $363,825 do not equal 23% of the total interest and therefore do not represent the correct tax deduction amount; they result from incorrect multiplications or misapplied percentages.

6. Conclusion
- The annual tax shield on debt is $109,250, which matches the provided correct answer.

DG Corp. has 10,000 bonds outstanding, with a face value of $1,000 each and a coupon rate of 4.75 percent. The bonds are selling at par, and interest is paid semiannually. What is the amount of the annual tax shield on debt if the tax rate is 23 percent?单项选择题

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