Respuesta :
Answer:
Step-by-step explanation:
To compute the new price of the bond, we'll first determine the components of the required return (yield to maturity) and then use the bond pricing formula. Here are the steps:
1. Calculate the real rate of return, which is the base rate without inflation or risk premiums:
\[ \text{Real rate of return} = 4\% = 0.04 \]
2. Calculate the new inflation premium, which is given as 2%:
\[ \text{New inflation premium} = 2\% = 0.02 \]
3. Calculate the new risk premium, which remains at 5%:
\[ \text{Risk premium} = 5\% = 0.05 \]
4. Calculate the new required return (yield to maturity):
\[ \text{Required return} = \text{Real rate of return} + \text{New inflation premium} + \text{Risk premium} \]
\[ \text{Required return} = 0.04 + 0.02 + 0.05 = 0.11 = 11\% \]
Next, we'll use the bond pricing formula to calculate the new price of the bond. The bond pricing formula is given by:
\[ \text{Bond Price} = \frac{\text{Annual Coupon Payment}}{\text{Required Return}} \times \left(1 - \frac{1}{(1 + \text{Required Return})^\text{Number of Years}}\right) + \frac{\text{Face Value}}{(1 + \text{Required Return})^\text{Number of Years}} \]
Given:
- Face Value (FV) = $1,000 (the price per bond at issuance)
- Annual Coupon Payment (CP) = $140 (14% of $1,000)
- Required Return (RR) = 11%
- Number of Years (N) = 15 years remaining until maturity
Plugging in the values into the bond pricing formula:
\[ \text{Bond Price} = \frac{140}{0.11} \times \left(1 - \frac{1}{(1 + 0.11)^{15}}\right) + \frac{1000}{(1 + 0.11)^{15}} \]
Calculating the values:
\[ \text{Bond Price} = 1272.73 \times \left(1 - \frac{1}{1.11^{15}}\right) + \frac{1000}{1.11^{15}} \]
\[ \text{Bond Price} = 1272.73 \times \left(1 - \frac{1}{3.542835}\right) + \frac{1000}{3.542835} \]
\[ \text{Bond Price} = 1272.73 \times (1 - 0.2823) + 282.3 \]
\[ \text{Bond Price} = 1272.73 \times 0.7177 + 282.3 \]
\[ \text{Bond Price} = 913.64 + 282.3 \]
\[ \text{Bond Price} = \$1195.94 \]
Therefore, the new price of the bond is approximately $1195.94.
