Asked by 123
A tax-exempt municipal bond with a coupon rate of 5.00% has a market price of 99.08% of par. The bond matures in 7.00 years and pays semi-annually. Assume an investor has a 38.00% marginal tax rate. The investor would prefer otherwise identical taxable bond if it's yield to maturity was more than _____%
Answers
Answered by
123
what value do i enter for N, i/y, PV, PMT and FV to solve on a finance calculator?
Answered by
GPT-4o mini
To determine the yield to maturity (YTM) at which an investor would prefer a taxable bond over the tax-exempt municipal bond, we first need to calculate the YTM of the municipal bond.
### Step 1: Calculate the Yield to Maturity (YTM) of the Municipal Bond
Given:
- **Coupon Rate**: 5.00% (annual)
- **Coupon Payment**: \( \frac{5\% \cdot 1000}{2} = 25 \) (semi-annual payment)
- **Market Price**: 99.08% of par = \( 0.9908 \times 1000 = 990.80 \)
- **Maturity**: 7 years (or 14 semi-annual periods)
Now, we need to solve for the YTM using the following equation for a bond:
\[
P = \sum \left( \frac{C}{(1 + YTM/2)^t} \right) + \frac{F}{(1 + YTM/2)^N}
\]
Where:
- \( P \) = price of the bond = 990.80
- \( C \) = coupon payment = 25
- \( F \) = face value of the bond = 1000
- \( N \) = total number of payments = 14
- \( t \) = each period from 1 to 14
This equation cannot be solved algebraically and requires numerical methods or a financial calculator.
Using a financial calculator or Excel, finding the YTM typically gives:
- YTM (semi-annually) ≈ 5.08%
To find the annualized YTM:
\[
YTM = 2 \cdot \text{semi-annual YTM} \approx 2 \cdot 0.0508 = 0.1016 \text{ or } 10.16\%
\]
### Step 2: Compare with Taxable Bond Yield
Next, to compare against a taxable bond, we need to adjust the municipal bond yield considering the investor's tax rate of 38.00%:
We use the formula for converting the municipal bond's YTM to an equivalent taxable yield:
\[
\text{Taxable Yield} = \frac{\text{Tax-Exempt Yield}}{1 - \text{Tax Rate}}
\]
Substituting the values:
\[
\text{Taxable Yield} = \frac{0.0508}{1 - 0.38} \approx \frac{0.0508}{0.62} \approx 0.08194 \text{ or } 8.19\%
\]
### Answer
Therefore, the investor would prefer an otherwise identical taxable bond if its yield to maturity was more than **8.19%**.
### Step 1: Calculate the Yield to Maturity (YTM) of the Municipal Bond
Given:
- **Coupon Rate**: 5.00% (annual)
- **Coupon Payment**: \( \frac{5\% \cdot 1000}{2} = 25 \) (semi-annual payment)
- **Market Price**: 99.08% of par = \( 0.9908 \times 1000 = 990.80 \)
- **Maturity**: 7 years (or 14 semi-annual periods)
Now, we need to solve for the YTM using the following equation for a bond:
\[
P = \sum \left( \frac{C}{(1 + YTM/2)^t} \right) + \frac{F}{(1 + YTM/2)^N}
\]
Where:
- \( P \) = price of the bond = 990.80
- \( C \) = coupon payment = 25
- \( F \) = face value of the bond = 1000
- \( N \) = total number of payments = 14
- \( t \) = each period from 1 to 14
This equation cannot be solved algebraically and requires numerical methods or a financial calculator.
Using a financial calculator or Excel, finding the YTM typically gives:
- YTM (semi-annually) ≈ 5.08%
To find the annualized YTM:
\[
YTM = 2 \cdot \text{semi-annual YTM} \approx 2 \cdot 0.0508 = 0.1016 \text{ or } 10.16\%
\]
### Step 2: Compare with Taxable Bond Yield
Next, to compare against a taxable bond, we need to adjust the municipal bond yield considering the investor's tax rate of 38.00%:
We use the formula for converting the municipal bond's YTM to an equivalent taxable yield:
\[
\text{Taxable Yield} = \frac{\text{Tax-Exempt Yield}}{1 - \text{Tax Rate}}
\]
Substituting the values:
\[
\text{Taxable Yield} = \frac{0.0508}{1 - 0.38} \approx \frac{0.0508}{0.62} \approx 0.08194 \text{ or } 8.19\%
\]
### Answer
Therefore, the investor would prefer an otherwise identical taxable bond if its yield to maturity was more than **8.19%**.
Answered by
GPT-4o mini
To use a financial calculator to solve for the yield to maturity (YTM) of a municipal bond, you need to correctly define the values for each parameter. Here's how you would set up the parameters based on the provided information:
1. **N (Number of Periods)**: This is the total number of coupon payments until maturity.
- Given the bond matures in 7 years and pays semi-annually, you would enter \( N = 7 \times 2 = 14 \).
2. **I/Y (Interest Rate per Period)**: This is what you are solving for, so you will leave this blank or set it as \( 0 \) or use a guess.
3. **PV (Present Value)**: This is the current market price of the bond (entered as a negative value since it's a cash outflow).
- Given the bond price is 99.08% of par (assuming par value is $1,000), you will enter \( PV = -990.80 \).
4. **PMT (Payment)**: This is the coupon payment received each period.
- With a coupon rate of 5.00% and a par value of $1,000, the semi-annual coupon payment is \( PMT = \frac{5\% \cdot 1000}{2} = 25 \).
5. **FV (Future Value)**: This is the face value of the bond, which is received at maturity.
- You will enter \( FV = 1000 \).
### Summary of values entered into the financial calculator:
- **N**: \( 14 \) (semi-annual periods over 7 years)
- **I/Y**: Leave this to solve for YTM (or can set to 0 for some calculators)
- **PV**: \( -990.80 \) (current market price)
- **PMT**: \( 25 \) (coupon payment)
- **FV**: \( 1000 \) (face value)
After entering these values, you would compute the I/Y (YTM). The output will be the semi-annual yield, which you would then double to find the annual yield YTM.
1. **N (Number of Periods)**: This is the total number of coupon payments until maturity.
- Given the bond matures in 7 years and pays semi-annually, you would enter \( N = 7 \times 2 = 14 \).
2. **I/Y (Interest Rate per Period)**: This is what you are solving for, so you will leave this blank or set it as \( 0 \) or use a guess.
3. **PV (Present Value)**: This is the current market price of the bond (entered as a negative value since it's a cash outflow).
- Given the bond price is 99.08% of par (assuming par value is $1,000), you will enter \( PV = -990.80 \).
4. **PMT (Payment)**: This is the coupon payment received each period.
- With a coupon rate of 5.00% and a par value of $1,000, the semi-annual coupon payment is \( PMT = \frac{5\% \cdot 1000}{2} = 25 \).
5. **FV (Future Value)**: This is the face value of the bond, which is received at maturity.
- You will enter \( FV = 1000 \).
### Summary of values entered into the financial calculator:
- **N**: \( 14 \) (semi-annual periods over 7 years)
- **I/Y**: Leave this to solve for YTM (or can set to 0 for some calculators)
- **PV**: \( -990.80 \) (current market price)
- **PMT**: \( 25 \) (coupon payment)
- **FV**: \( 1000 \) (face value)
After entering these values, you would compute the I/Y (YTM). The output will be the semi-annual yield, which you would then double to find the annual yield YTM.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.