QuestionJune 1, 2025

Rogue Racing Inc. has 1,000 par value bonds with a coupon rate of 8% per year making semiannual coupon payments. If there are twelve years remaining prior to maturity and these bonds are selling for 876.40 what is the yield to maturity for these bonds? 9.80% 8.00% 9.77% 8.33%

Rogue Racing Inc. has 1,000 par value bonds with a coupon rate of 8% per year making semiannual coupon payments. If there are twelve years remaining prior to maturity and these bonds are selling for 876.40 what is the yield to maturity for these bonds? 9.80% 8.00% 9.77% 8.33%
Rogue Racing Inc. has 1,000 par value bonds with a coupon rate of 8%  per year making semiannual coupon
payments. If there are twelve years remaining prior to maturity and these bonds are selling for 876.40 what is the
yield to maturity for these bonds?
9.80% 
8.00% 
9.77% 
8.33%

Solution
4.1(273 votes)

Answer

9.77\% Explanation 1. Identify the known values Par value = \ 1,000, Coupon rate = 8\%, Semiannual coupon payment = \frac{8\% \times 1,000}{2} = \ 40, Current price = \ 876.40, Years to maturity = 12. 2. Calculate total number of periods Total periods = 12 \times 2 = 24 (since payments are semiannual). 3. Use the yield to maturity formula for bonds The yield to maturity (YTM) can be found using the formula for bond pricing: \[ P = \sum_{t=1}^{n} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^n} \] Where ( P ) is the current price, ( C ) is the coupon payment, ( F ) is the face value, ( n ) is the total number of periods, and ( r ) is the yield per period. 4. Solve for yield using trial and error or financial calculator Using a financial calculator or software, input: - Present Value (PV) = -876.40 - Future Value (FV) = 1000 - Payment (PMT) = 40 - Number of Periods (N) = 24 Calculate for the interest rate per period, then annualize it by multiplying by 2.

Explanation

1. Identify the known values<br /> Par value $= \$ 1,000$, Coupon rate $= 8\%$, Semiannual coupon payment $= \frac{8\% \times 1,000}{2} = \$ 40$, Current price $= \$ 876.40$, Years to maturity $= 12$.<br /><br />2. Calculate total number of periods<br /> Total periods $= 12 \times 2 = 24$ (since payments are semiannual).<br /><br />3. Use the yield to maturity formula for bonds<br /> The yield to maturity (YTM) can be found using the formula for bond pricing:<br />\[ P = \sum_{t=1}^{n} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^n} \]<br />Where ( P ) is the current price, ( C ) is the coupon payment, ( F ) is the face value, ( n ) is the total number of periods, and ( r ) is the yield per period.<br /><br />4. Solve for yield using trial and error or financial calculator<br /> Using a financial calculator or software, input: <br />- Present Value (PV) = -876.40<br />- Future Value (FV) = 1000<br />- Payment (PMT) = 40<br />- Number of Periods (N) = 24<br /><br />Calculate for the interest rate per period, then annualize it by multiplying by 2.
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