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<h2 class="hd hd-2 unit-title">Zero-Coupon Bonds</h2>
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Zero-Coupon Bonds
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<ol>
<li>A 5-year zero-coupon bond with a face value of $100 is trading for $91.27. What is the 5-year spot interest rate (\(r_{0,5}\))?
<p><p style="display:inline">\(r_{0,5} = \)</p><div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_52446a9e45d34fdb90c178f25a5c03cb_2_1" class=" capa_inputtype inline textline">
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<li>Calculate the term structure of interest rates given the following zero-coupon bond prices:
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<table><thead><tr class="header"><th align="left">Maturity</th><th align="center">1 year</th><th align="center">2 years</th><th align="center">5 years</th><th align="center">10 years</th><th align="center">30 years</th></tr></thead><tbody><tr><td align="left">Price</td><td align="center">$99.81</td><td align="center">$98.98</td><td align="center">$91.27</td><td align="center">$73.83</td><td align="center">$29.38</td></tr></tbody></table>
<p><p style="display:inline">\(r_{0,1} = \)</p><div class="inline" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_52446a9e45d34fdb90c178f25a5c03cb_3_1" class=" capa_inputtype inline textline">
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<p><p style="display:inline">\(r_{0,2} = \)</p><div class="inline" tabindex="-1" aria-label="Question 3" role="group"><div id="inputtype_52446a9e45d34fdb90c178f25a5c03cb_4_1" class=" capa_inputtype inline textline">
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<p><p style="display:inline">\(r_{0,5} = \)</p><div class="inline" tabindex="-1" aria-label="Question 4" role="group"><div id="inputtype_52446a9e45d34fdb90c178f25a5c03cb_5_1" class=" capa_inputtype inline textline">
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<p><p style="display:inline">\(r_{0,10} = \)</p><div class="inline" tabindex="-1" aria-label="Question 5" role="group"><div id="inputtype_52446a9e45d34fdb90c178f25a5c03cb_6_1" class=" capa_inputtype inline textline">
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<p><p style="display:inline">\(r_{0,30} = \)</p><div class="inline" tabindex="-1" aria-label="Question 6" role="group"><div id="inputtype_52446a9e45d34fdb90c178f25a5c03cb_7_1" class=" capa_inputtype inline textline">
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<h3 class="hd hd-2">Zero-Coupon Bonds </h3>
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<h2 class="hd hd-2 unit-title">Coupon Bonds</h2>
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Coupon Bonds
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Suppose that the 1-, 2-, and 3-year zero-coupon bonds have the following prices, and corresponding spot rates:
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<table><thead><tr class="header"><th align="left">Maturity</th><th align="center">1 year</th><th align="center">2 years</th><th align="center">3 years</th></tr></thead><tbody><tr><td align="left">Price</td><td align="center">$952</td><td align="center">$898</td><td align="center">$842</td></tr><tr><td align="left">Spot rate</td><td align="center">5.04%</td><td align="center">5.53%</td><td align="center">5.90%</td></tr></tbody></table>
<ol><li>What is the price of a 3-year risk-free bond with a face value of $1000, and an annual coupon rate of 5%?
<p><p style="display:inline">Price = $</p><div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_2542f362cb6e44e2a7ac1bdcbaefcec7_2_1" class=" capa_inputtype inline textline">
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</li><li>What is its yield-to-maturity (\(y\))?
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<h2 class="hd hd-2 unit-title">Yield Spread, Risk Premium, and Default Premium</h2>
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Yield Spread, Risk Premium, and Default Premium
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<div><p>Consider the following zero-coupon bonds with $1000 face values:</p><ul><li>10-year Treasury zero-coupon bond selling for $463.19</li><li>10-year zero-coupon bond issued by AZ Biotech selling for $321.97</li></ul>
If the expected payoff of AZ Biotech's bond is $762.22, what is the yield spread, default premium, and risk premium of the bond?
<p><p style="display:inline">Yield Spread = </p><div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_1ca76f7adc4948319bf49d2211b49f8d_2_1" class=" capa_inputtype inline textline">
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<p><p style="display:inline">Default Premium = </p><div class="inline" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_1ca76f7adc4948319bf49d2211b49f8d_3_1" class=" capa_inputtype inline textline">
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<p><p style="display:inline">Risk Premium = </p><div class="inline" tabindex="-1" aria-label="Question 3" role="group"><div id="inputtype_1ca76f7adc4948319bf49d2211b49f8d_4_1" class=" capa_inputtype inline textline">
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<h2 class="hd hd-2 unit-title">Present Value of Growth Opportunities</h2>
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Present Value of Growth Opportunities
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<p>iDoc, an internet health service company, is expected to generate $1 in earnings per share next year and in the years to follow, from its existing assets. It plans to announce a new program to expand its business. This new program will increase its plow back ratio (the fraction of earnings retained by the company) from 0% to 50% next year. The return on equity for the new investments will be 12%. The expansion is expected to continue forever at the same rate. The cost of capital is 10%.
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<li>What is its future growth rate (\(g\)) under the new program?
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<li>What is the change in iDoc&#8217;s stock price in response the announcement?
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