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Data Case #2: Fund raised from a new bond issue1 Currently, you are working as a financial analyst at IBM (International Business Machine Corporation). The firm plans to issue 30-year corporate bonds with a total face value of $50 million in the United States. Each bond has a face value of $1,000. The annual coupon rate is 3.5%. The firm plans to pay coupon once every year at the end of each year. Your boss asked you to estimate how much fund the firm could raise today. Answer the following three questions: Q1: How much your company would receive today by issuing the above 30-year bonds? Q2: What is the YTM (Yield to Maturity) of the bond? Q3: How much extra money your company could receive if your company manages to increase its credit rating by one notch? Basic concepts: 1) present value of a bond is the summation of all its discounted future cash flows. () = = 1 (1+1 )1 + 2 (1+2 )2 + + 1 (1+ 1 ) 1 + + (1+ ) (1) 2) find out the appropriate discount rate for each future cash flow. = , + (2) where Ri is the discount rate for year i , Rf,i is the risk-free rate, from the Government Treasury term structure of interest (yield curve) for year i and Si the credit spread which depends on the credit raging of your firm. For example, if an investor buys one bond, he/she will expect $35 at the end of each year for 35 the next 30 years. The present value of $35 at the end of 5th year will be (1+ )5 . Note that all those 5 discount rates (R1, R2, R3 and etc.) are expected to be different. Step 1: Draw a time line of 30 years and mark all future cash flows. Hint #1: to simplify your notation, you could work with just one bond ($1,000 face value) first. Step 2: Find Rf,i for i=1,2,3, .. 30. Go to http://finance.yahoo.com/bonds (hint #2: you have to interpolate your values, see the next page). Step 3: Find the relationship between spread (Si ) and the credit rating, i=1,2, ... 30. i) http://bondsonline.com/ ii) Click \"Today's Market\" on the left-hand side iii) Click \"US Corporate Debt spread data\"2 Step 4: Find the credit rating of your company and corresponding spread based on Step 3. i) In the Financial Markets Lab (OM111), choose a computer, assume it is FUNDS19. ii) Login with your Canisius' username and password iii) Go to https://www.capitaliq.com/home.aspx iv) Login: username: Griffin19, password: Golden19. v) Choose your firm 1 2 10/18/2013 by yuxing.yan at Canisius dot edu Note: spreads are expressed in basis point, see its definition at http://www.investopedia.com/terms/b/basispoint.asp vi) Click \"Credit Ratings\" under \"Fixed Income\" on the left. vii) You could use the credit rating under \"Currency LT\". Step 5: Apply the following formula to estimate the present value of each future cash flow. = (1+ ) (3) Step 6: Apply equation (1), i.e., take a summation. Note: Linear interpolation. First, let me use a simple example. Assume that the YTM for 5-year is 5%, the YTM for 10-year bond is 10%. What are the YTMs for 6, 7, 8, and 9-year bonds? A quick answer is 6% for 6-year bond, 7% for 7-year bond, 8% for 8-year bond and 9% for 9year bond. The basic idea is an equal incremental value. Assume that YTM for a 5-year bond is R5, YTM for a 10-year bond is R10. Since there are 5 intervals between year 5 and year 10. Thus, the incremental value between each year is = 105 5 For a 6-year bond, its value will be 5 + For a 7-year bond, its value will be 5 + 2 For a 8-year bond, its value will be 5 + 3 For a 9-year bond, its value will be 5 + 4 Here is more detailed explanation.3 If the two known points are given by the coordinates and , the linear interpolation is the straight line between these points. For a value x in the interval , the value y along the straight line is given from the equation 0 0 = 1 0 (4) 1 0 which can be derived geometrically from the figure on the right. It is a special case of polynomial interpolation with n = 1. Solving this equation for y, which is the unknown value at x, gives = 0 + ( 0 ) 1 0 1 0 = 0 + (0 )1 (0 )0 1 0 which is the formula for linear interpolation in the interval of (0 , 1 ). 3 http://en.wikipedia.org/wiki/Linear_interpolation