Let's go through each part step by step.

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Given Data:

• Par Value ($F$) = $1,000
• Annual Coupon Rate = 13%
• Annual Coupon Payment ($C$) = $1,000 \times 0.13 = 130$
• Years to Maturity ($N$) = 15
• Market Price ($P$) = $1,130
• Required Yield to Maturity ($r$) = 10%

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(a) Compute the bond's yield to maturity (YTM).

The Yield to Maturity (YTM) is the discount rate ($r$) that equates the present value of future cash flows (coupon payments and face value) to the current market price:

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

Substituting the values:

$1,130 = \sum_{t=1}^{15} \frac{130}{(1+YTM)^t} + \frac{1000}{(1+YTM)^{15}}$

Since solving for $YTM$ requires an iterative numerical approach, I will calculate it using a numerical solver.

Let's compute the YTM. numpy as np from scipy.optimize import fsolve

Given data

F = 1000 # Face value C = 130 # Annual coupon payment N = 15 # Years to maturity P = 1130 # Market price

Function to solve for YTM

def bond_ytm(y): return sum([C / (1 + y) ** t for t in range(1, N + 1)]) + (F / (1 + y) ** N) - P

Solve for YTM using numerical solver

ytm_solution = fsolve(bond_ytm, 0.1)[0] # Initial guess is 10%

Convert to percentage

ytm_percentage = ytm_solution * 100 ytm_percentageThe Yield to Maturity (YTM) is approximately 11.17%.

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(b) Determine the value of the bond given your required rate of return (10%).

The value of the bond is found using the Present Value (PV) formula:

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

where $r = 10\% = 0.10$. Let's calculate it. Given required rate of return r_required = 0.10

Calculate present value of coupons and face value

PV_coupons = sum([C / (1 + r_required) ** t for t in range(1, N + 1)]) PV_face = F / (1 + r_required) ** N

Total bond value

bond_value = PV_coupons + PV_face bond_valueThe value of the bond, given your required rate of return (10%), is approximately $1,228.18.

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(c) Should you purchase the bond?

• The value of the bond ($1,228.18$) is higher than its market price ($1,130$).
• This means the bond is undervalued relative to your required rate of return.
• Since the bond's fair value is higher than the price you would pay, you should purchase the bond.

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Summary of Results:

Calculation	Result
YTM	11.17%
Value of Bond	$1,228.18
Should you buy?	Yes (Since value > price)

Would you like more details or explanations?

Here are 5 related questions to expand your understanding:

1. What happens to the bond price if interest rates increase?
2. How does YTM compare to the current yield of a bond?
3. What is the difference between premium and discount bonds?
4. How would the bond's value change if it paid semiannual interest?
5. What are the risks of investing in bonds?

Tip:

When YTM is higher than the coupon rate, the bond sells at a discount. When YTM is lower than the coupon rate, the bond sells at a premium.