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 ```a. Serveal years ago, Castles in the Sand, Inc., issued bonds at face value at a yeild to maturity of 7 percent. Now, with 8 years left until the maturity of the bonds, the company has run into hard times and the yield to maturity on the bonds has increased to 15 percent. What has happended to the price of the bond? b. Suppose that investors believe that Castles can make good the promised coupon payments, but that the company will go bankrupt when the bond matures and the principal comes due. The expectation is that investors will receive only 80 percent of face value at maturity. if they buy the bond today, what yield to maturity do they expect to receive?``` Clarification of Question by brwnsgr-ga on 17 Jul 2006 01:37 PDT `FIN 438 PRACTICE PROBLEM` Request for Question Clarification by elmarto-ga on 17 Jul 2006 06:10 PDT ```Hello, The coupon rate on these bonds is not specified in your question. Does the original problem mention it? Thank you very much, elmarto``` Clarification of Question by brwnsgr-ga on 17 Jul 2006 13:39 PDT `This exactly the way the questions are written, there is not coupon rate stated.`
 ```Hello! The most important concept you need to know in order to answer these questions is that the value of a bond is equal to the present value of the cash flows provided by the bond (yearly coupon payments + capital payment at maturity date), using the yield to maturity (YTM) as the discount rate. Let's address the first question. I hadn't read correctly the question when I asked about the coupon rate. The problem states that the firm "issued bonds at face value at a yeild to maturity of 7 percent". If the bonds were issued at face value, then the coupon rate is identical to the YTM. So the coupon rate for these bonds was 7%. When the YTM rises, the market value of the bonds fall. Basically, when the YTM rises, we're using a higher discount rate for the present value calculation mentioned in the first paragraph. Therefore, this present value (the value of the bond) must fall. We can find exactly what will be the price of the bond after the YTM rises to 15%. Let's assume that the face value of the bond is \$100. The coupon payment is thus \$7. Therefore, the value of the bond, at 8 years to maturity, if the YTM becomes 15% will be (assuming the last coupon payment was paid yesterday): PV = 7/1.15 + 7/1.15^2 + 7/1.15^3 + ... + 107/1.15^8 = 64.10 Thus the value of the bond FALLS from face value (=\$100) to \$64.10 when the YTM rises from 7% to 15%. For the second question, we need to find the discount rate that makes the present value of the cash flows from this bond equal to its market value. Assuming that the stock is currently trading at \$64.10, as we found in the previous question, the equation we must solve now is: 64.10 = 7/(1+r) + 7/(1+r)^2 + 7/(1+r)^3 + ... + 87/(1+r)^8 Notice that the last payment is \$87: \$7 from the coupon and \$80 because the bond will pay 80% of the face value. This equation is very difficult to solve analytically, so I'll use an YTM calculator. You can find one online at: http://www.investopedia.com/calculator/AOYTM.aspx Enter the following values: Par Value = 80 (this is the face value; however, we'll be paid only 80% of it, so we must enter \$80) Market Value = 64.10 Annual Rate = 7/80 = 8.75% (this is the coupon rate as a percentage of the "par value" - since the coupon payment remains at 7, while we entered 80 as the par value, then we must tell the calculator that the annual rate is 8.75%, as 8.75% of \$80 is equal to \$7) Maturity in Years = 8 Payments = Annualy We get that the YTM on a bond with these features is 12.87%. Google search terms yield to maturity calculator ://www.google.com.ar/search?hl=es&q=yield+to+maturity+calculator&meta= I hope this helps! If you have any doubt regarding my answer, please don't hesitate to request clarification before rating it. Otherwise, I await your rating and final comments. Best wishes! elmarto```