VIPSolutions*Give me explanation and calculation step by step clealry with final answer* The Maximus Corporation is considering a new investment, which would be financed from debt. Maximus could sell new $ 1 , 0 0 0 par value bonds at a new price of $ 9 2 0 . The bonds would mature in 1 3 years, and the coupon interest rate is 1 0 % . Compute the after - tax cost of capital to Maximus for bonds, assuming a 3 4 % tax rate. Show work
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*Give me explanation and calculation step by step clealry with final answer* The Maximus Corporation is considering a new investment, which would be financed from debt. Maximus could sell new $ 1 , 0 0 0 par value bonds at a new price of $ 9 2 0 . The bonds would mature in 1 3 years, and the coupon interest rate is 1 0 % . Compute the after - tax cost of capital to Maximus for bonds, assuming a 3 4 % tax rate. Show work
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Asked by: Yelligadala Praneesh
Created at: 2025-05-27 04:09:25
Asked by: Yelligadala Praneesh
Created at: 2025-05-27 04:09:25
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Let's break down the problem and solve it step by step:
### **Given:**
- **Par value of bond (\(FV\))** = $1,000
- **Current price (\(P_0\))** = $920
- **Coupon rate** = 10% of par value
- **Coupon payment (\(C\))** = 10% of $1,000 = $100 per year
- **Time to maturity (\(N\))** = 13 years
- **Tax rate (\(T\))** = 34%
We need to **compute the after-tax cost of debt**.
---
## **Step 1: Calculate the Before-tax Cost of Debt (\(K_d\))**
The cost of debt is the yield to maturity (YTM) on the bond. The YTM is the rate (\(K_d\)) that equates the present value of all future cash flows (coupon payments + principal repayment) to the current price of the bond.
The formula is:
\[
P_0 = \sum_{t=1}^{N} \frac{C}{(1+K_d)^t} + \frac{FV}{(1+K_d)^N}
\]
Where:
- \(P_0\) = Current price of the bond
- \(C\) = Coupon payment per year
- \(FV\) = Face value of the bond
- \(N\) = Number of years to maturity
- \(K_d\) = Before-tax cost of debt (YTM)
For calculation, we'll use an **approximation formula** for YTM:
\[
K_d \approx \frac{C + \frac{FV - P_0}{N}}{ \frac{FV + P_0}{2} }
\]
Plug in the numbers:
- \(C = \$100\)
- \(FV = \$1,000\)
- \(P_0 = \$920\)
- \(N = 13\)
\[
K_d \approx \frac{100 + \frac{1,000 - 920}{13}}{ \frac{1,000 + 920}{2} }
\]
\[
K_d \approx \frac{100 + \frac{80}{13}}{960}
\]
\[
K_d \approx \frac{100 + 6.15}{960}
\]
\[
K_d \approx \frac{106.15}{960}
\]
\[
K_d \approx 0.1106 \text{ or } 11.06\%
\]
---
## **Step 2: Calculate After-tax Cost of Debt**
Interest payments on bonds are tax-deductible, so the after-tax cost is:
\[
K_{d,after-tax} = K_d \times (1 - T)
\]
Where:
- \(T = 34\% = 0.34\)
\[
K_{d,after-tax} = 0.1106 \times (1 - 0.34)
\]
\[
K_{d,after-tax} = 0.1106 \times 0.66
\]
\[
K_{d,after-tax} = 0.072996
\]
\[
K_{d,after-tax} \approx 7.30\%
\]
---
## **Step 3: **Final Answer**
**The after-tax cost of capital to Maximus for the bonds is \(\boxed{7.30\%}\).**
---
### **Summary Table**
| Step | Calculation | Result |
|------------------------------|--------------------------------------------------|-----------|
| Coupon Payment (\(C\)) | \(10\% \times \$1,000\) | \$100 |
| Approximated YTM (\(K_d\)) | \(\frac{100 + \frac{80}{13}}{960}\) | 11.06% |
| After-tax Cost (\(K_{d,after-tax}\)) | \(11.06\% \times (1 - 0.34)\) | 7.30% |
---
**Final Answer:**
\[
\boxed{7.30\%}
\]
is the after-tax cost of capital for the bonds for Maximus Corporation.
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