37. Mojo mining has a bond outstanding that sells for $2,210 and matures in 22 years. The bond pays semiannual coupons and has a coupon rate of 7.46%. The par value is $2000. If the company's tax rate is 25%, what is the aftertax cost of debt?
37. Mojo mining has a bond outstanding that sells for $2,210 and matures in 22 years. The bond pays semiannual coupons and has a coupon rate of 7.46%. The par value is $2000. If the company's tax rate is 25%, what is the aftertax cost of debt?
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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![**Bond Cost of Debt Calculation Example**
**Problem Statement:**
Mojo Mining has a bond outstanding that sells for $2,210 and matures in 22 years. The bond pays semiannual coupons and has a coupon rate of 7.46%. The par value is $2,000. If the company's tax rate is 25%, what is the after-tax cost of debt?
**Given Data:**
- Current Bond Selling Price: $2,210
- Maturity Period: 22 years
- Coupon Payment Frequency: Semiannual
- Coupon Rate: 7.46% (annual)
- Par Value: $2,000
- Company's Tax Rate: 25%
**Steps to Calculate After-Tax Cost of Debt:**
1. **Calculate the semiannual coupon payment:**
- Annual coupon payment = Coupon rate × Par value
- Semiannual coupon payment = (Annual coupon payment) / 2
- Semiannual coupon payment = (0.0746 × $2,000) / 2 = $149.20
2. **Determine the total number of semiannual periods:**
- Total semiannual periods = Maturity period (in years) × 2
- Total semiannual periods = 22 × 2 = 44
3. **Calculate the yield to maturity (YTM) on a semiannual basis:**
- This requires solving for the yield in the following bond price formula:
\[
P = \sum_{t=1}^{n} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^n}
\]
- \( P \) = present value (current bond price) = $2,210
- \( C \) = semiannual coupon payment = $149.20
- \( F \) = face (par) value of the bond = $2,000
- \( n \) = total semiannual periods = 44
- \( r \) = semiannual yield to maturity (to be calculated)
Solving for \( r \) (semiannual YTM) requires using iterative methods or financial calculators.
4. **Convert the semiannual YTM to an annual YTM:**
- Annual YTM = Semiannual YTM × 2
5. **Determine the after-tax cost of debt:**
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F62ca1c58-ac8a-4380-bd93-744ecdfbeb4a%2F056868b1-217a-4ad6-8d6f-1d5adbf9cefe%2Fnylgxk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Bond Cost of Debt Calculation Example**
**Problem Statement:**
Mojo Mining has a bond outstanding that sells for $2,210 and matures in 22 years. The bond pays semiannual coupons and has a coupon rate of 7.46%. The par value is $2,000. If the company's tax rate is 25%, what is the after-tax cost of debt?
**Given Data:**
- Current Bond Selling Price: $2,210
- Maturity Period: 22 years
- Coupon Payment Frequency: Semiannual
- Coupon Rate: 7.46% (annual)
- Par Value: $2,000
- Company's Tax Rate: 25%
**Steps to Calculate After-Tax Cost of Debt:**
1. **Calculate the semiannual coupon payment:**
- Annual coupon payment = Coupon rate × Par value
- Semiannual coupon payment = (Annual coupon payment) / 2
- Semiannual coupon payment = (0.0746 × $2,000) / 2 = $149.20
2. **Determine the total number of semiannual periods:**
- Total semiannual periods = Maturity period (in years) × 2
- Total semiannual periods = 22 × 2 = 44
3. **Calculate the yield to maturity (YTM) on a semiannual basis:**
- This requires solving for the yield in the following bond price formula:
\[
P = \sum_{t=1}^{n} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^n}
\]
- \( P \) = present value (current bond price) = $2,210
- \( C \) = semiannual coupon payment = $149.20
- \( F \) = face (par) value of the bond = $2,000
- \( n \) = total semiannual periods = 44
- \( r \) = semiannual yield to maturity (to be calculated)
Solving for \( r \) (semiannual YTM) requires using iterative methods or financial calculators.
4. **Convert the semiannual YTM to an annual YTM:**
- Annual YTM = Semiannual YTM × 2
5. **Determine the after-tax cost of debt:**
-
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