Finance Revision Exercise 2 – Interest rates & Capital budgeting - solutions Finance – Revision Exercise 2 (i) – Interest rates, bonds, forward rates & shares 1. How would you write the following expression: the two year forward rate starting in three years time? With the interest rate notation, a. the start date is the first number, so in this case that will be 3 b. the second number is the duration of the forward rate which is added to the start date, in this case the length of the forward rate is 2 years and this is added to the start date to give 5 c. the answer is 3f5 2. If the one, two, three, four year spot rates are 5%, 6%, 7%, 8% respectively, what is the one year forward rate starting in two years time? (1 + 2f3) 3. = (1 + 0s3)3 (1 + 0s2)2 = (1.07)3 (1.06)2 = 1.09028 = 9.028% A bond is priced at £96.45 in the market. It’s coupon rate is 4%, the bond has four years to redemption. What is the yield to maturity? Lay out your cash flow like this and make a guess at the interest rate that solves the equation. year 0 1 2 3 96.45 + 4 ( 1 + r) + 4 (1 + r)^2 + 4 (1 + r)^3 4 + 104 = 0 (1 + r)^4 In this case the answer works out at 5% if you guess that first time. If you guess 4% and 6% you will get a positive and negative number, you get the YTM by interpolating from that point: YTM = src.doc r1 + ((N1/(N1+N2)) ( r2 – r1)) 1- Finance Revision Exercise 2 – Interest rates & Capital budgeting - solutions 4. If the one, two, three, and four year spot rates are 4%, 4.5%, 5% and 5.25%, what will be the price of a four year bond with a 7% coupon? Layout the cash flows as below and discount by the appropriate discount rate (the spot rate for that year). year Bond price = 1 2 3 4 7 1.04 + 7 1.045^2 + 7 1.05^3 + 107 1.0525^4 Bond price = £106.3835 5. There are three zero coupon government bonds, maturing in one, two and three years time. The prices are £93.50, £86.90, and £80.10 respectively. What are the spot rates that can be deriv