<p>For the questions below, assume that the asset in question is a bond<br />wit

Question

<p>For the questions below, assume that the asset in question is a bond<br />with a two year maturity which will pay $100 at the end of the first year and $100 at the<br />end of the second year. Calculate your answers to the nearest cent.</p>
<p><br />1) Assume that the current interest rate is 5.25% and that it is expected to rise to<br />5.5% next year. Additionally assume that agents do not care about risk. What is<br />the price today of this two-year bond?</p>
<p><br />2) Calculate the yield to maturity and graph the yield curve. Is the slope positive or<br />negative? Explain why.</p>
<p><br />3) Calculate the price of the bond if the Fed raises the current interest rate to 5.5%<br />and the rate is expected to remain there for the coming year. Does the increase in<br />the interest rate increase of decrease the price of the bond?</p>
<p><br />4) Return to the assumptions in 1) about interest rates over time, but now assume<br />that agents do care about risk. In fact they want a risk premium of 1%.<br />Recalculate the price of the bond and explain how risk affects it.</p>
<p><br />5) Calculate the yield to maturity under the new assumption about risk and graph the<br />yield curve. How does the slope compare to the slope of your original yield<br />curve?</p>

Explanation / Answer

1) Calculating the price of the bond :

P0 = C1 / (1+ i)^1 + C2 / (1+i)^2 + M / (1+i)^2
= 100 / (1+0.0525) + 100 / (1+0.055)^2 + $1000 / (1+0.055)^2
= $95 + $89.84 + $898.47
= $1083.31

2) Calculating the YTM

Step1: Go to excel and click "insert" to insert the function.
Step2: Select the Rate function as we are fidning the yield in this case.
step3: Enter the values as Nper = 2; PMT = -100; PV = 1083; FV = -1000
Step4: Click "OK" to get the desired value.

The value comes to "0.055 or 5.5%"
The yield curve is positive.

3)Calculating the price of the bond :

Step1: Go to excel and click "insert" to insert the function.
Step2: Select the Rate "PV" function as we are fidning the bond price in this case.
step3: Enter the values as Rate = 5.5%; Nper = 2; PMT = -100; FV = -1000
Step4: Click "OK" to get the desired value.

The value comes to "$1,083.08"

Therefore, the price of the bond is $1,083.08

4) Bond yield plus the risk premium determines the price od the bond

Bond yield + Risk premium = 5.5% + 1%

                                        = 6.5%

Calculating the price of the bond at 6.5%

Step1: Go to excel and click "insert" to insert the function.
Step2: Select the Rate "PV" function as we are fidning the bond price in this case.
step3: Enter the values as Rate = 6.5%; Nper = 2; PMT = -100; FV = -1000
Step4: Click "OK" to get the desired value.

The value comes to "$1,063.72"

5) Calculating the YTM

Step1: Go to excel and click "insert" to insert the function.
Step2: Select the Rate function as we are fidning the yield in this case.
step3: Enter the values as Nper = 2; PMT = -100; PV = 1063.72 FV = -1000
Step4: Click "OK" to get the desired value.

The value comes to "0.065 or 6.5%"

Therefore, the YTM is 6.5%

The slope will be an upward slope compared to the original yield curve.

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