To determine the yield to maturity (YTM) and decide whether purchasing the bond is a good investment, let's break down the problem.

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Given:

• Face value of the bond $F = 1000$ dollars
• Coupon rate $C = 8\%$ per annum
• Annual coupon payment $P = 1000 \times 0.08 = 80$ dollars
• Current bond price $PV = 955$ dollars
• Years to maturity $n = 13$ years

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(a) Yield to Maturity (YTM)

The YTM can be found by solving the following equation:

$PV = \sum_{t=1}^{n} \frac{C}{(1 + YTM)^t} + \frac{F}{(1 + YTM)^n}$

Where:

• $PV$ is the current price of the bond ($955)
• $C$ is the annual coupon payment ($80)
• $F$ is the face value of the bond ($1000)
• $n$ is the number of years to maturity (13 years)
• $YTM$ is what we are solving for.

Since this is a complex non-linear equation, I will solve it numerically. Let's proceed. scipy.optimize import newton

Given bond information

face_value = 1000 # Face value of the bond coupon_payment = 80 # Annual coupon payment current_price = 955 # Price paid for the bond years_to_maturity = 13

Bond price formula function

def bond_price(ytm): # Calculate the present value of coupons and face value coupon_pv = sum(coupon_payment / (1 + ytm) ** t for t in range(1, years_to_maturity + 1)) face_value_pv = face_value / (1 + ytm) ** years_to_maturity return coupon_pv + face_value_pv - current_price

Solve for the YTM using the Newton method

ytm_solution = newton(bond_price, 0.1) # Initial guess of 10%

Convert to percentage

ytm_percentage = ytm_solution * 100 ytm_percentage### (a) Yield to Maturity (YTM)
The yield to maturity on the bond is approximately 8.59%.

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(b) Should You Purchase the Bond?

A comparable-risk bond offers a yield of 10%, while the bond in question has a YTM of 8.59%. Since the yield is lower than that of the comparable bond, you should not purchase the bond unless there are other factors making it more attractive (such as tax advantages or lower risk).

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Would you like a more detailed explanation of the YTM calculation or clarification on any part of this problem?

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Related Questions

1. What factors can influence bond prices apart from interest rates?
2. How does the bond's time to maturity affect its sensitivity to interest rate changes?
3. What is the relationship between bond prices and yield to maturity?
4. How would semiannual coupon payments affect the YTM calculation?
5. What other risks should be considered when evaluating bonds?

Tip:

The bond's YTM is essentially the internal rate of return (IRR) that equates the bond's cash flows to its current price. Solving it often requires iterative methods or financial calculators.