Business Finance Michael Dimond

Bonds Bonds are long-term debt contracts used to raise capital Bonds are denominated in a set amount (most U.S. corporate bonds are $1,000) and can be bought and sold in a secondary market The bond indenture specifies the terms of the bond, including the rights and duties, the amounts and dates involved, standard debt provisions and restrictive covenants.

Bonds: Linking terminology to TVM functions PV = Price FV = Face Value (also called “Par Value.” Usually $1,000) n = Periods (usually semiannual) i = Yield PMT = Coupon Payment The Coupon Rate is only used to determine the coupon payment. For example, a 10% coupon rate on a $1,000 bond would give a $100 annual payment, which would be $50 semiannually.

Bond pricing, yields, etc. Bond terminology is what gives most students problems. Sometimes you need to make assumptions based on how the question is worded. Here’s a typical sort of a bond question: XYZ Company has a 10% bond with semiannual payments which matures in 12 years. The market rate for bonds of this risk is currently 8%. What is the price of this bond? The key to solving a question like this is to identify the relevant information and organize it: PV = Price = Unknown. This is what we are solving for. FV = Face Value = Not stated, so we assume $1,000. n = Periods = Semiannual for 12 years. 12 x 2 = 24, :. n = 24. i = Yield = Return demanded ÷ Periods per year = 8% ÷ 2 = 4% semiannual PMT = Coupon Payment = FV x Coupon Rate ÷ Periods per year = 1,000 x 10% ÷ 2 = 50, :. PMT = 50. The expression “10% bond” means a bond with a 10% coupon annual rate.

Bond pricing, yields, etc. Entering this information in a financial calculator lets us find an answer. PV = Price = Unknown. This is what we are solving for. FV = $1,000. n = 24 semiannual i = 4% semiannual PMT = 50 semiannual Solve for PV = -1,152.4696 Notice n, i and PMT are all semiannual values. These must all be in the same scale: Annual, semiannual, etc. The answer appears negative because it is a cash outflow. The price will be $1,152.47 Here’s another bond question: XYZ Company has a 10% semiannual bond which matures in 12 years and is selling for $1,050. What is the yield of this bond?

Bond pricing, yields, etc. Let’s try another. Entering this information in a financial calculator lets us find an answer, but it will be a semiannual answer. PV = -1,050 (remember, the price is a cash outflow, so it has a minus sign) FV = 1,000 n = 24 semiannual i = Unknown. This is what we are solving for. PMT = 50 semiannual Solve for i = 4.6499% Remember, n, i and PMT are all semiannual values. The result the calculator gives is the semiannual interest rate. To annualize it, multiply it by 2: Yield = 2 x semiannual i = 2 x 4.6499% = 9.2998%

Bond pricing, yields, etc. Here’s one more: XYZ Company has a 10% bond with semiannual payments which matures in 12 years and is selling for $1,000. What is the yield of this bond? In this case, the price and the face value are both 1,000. This means the bond is selling at par, which means the yield will equal the coupon rate (10%). To test this: PV = -1,000 FV = 1,000 n = 24 semiannual PMT = 50 semiannual Solve for i = 5.0000% semiannual Yield = 2 x semiannual i = 2 x 5.0000% = 10%

More about bonds What if I see a bond priced at something like “108”? Provisions of bonds Convertability: A conversion feature allows bondholders to exchange the bond for a certain number of shares of stock. Warrants: A “sweetener” which allows the bondholders to purchase a certain number of shares of stock at a specific price & time. Callability: A call feature allows the bond issuer to repurchase the bonds before they mature (for a premium above the face value) Current Yield vs Yield to Maturity vs Yield to Call Current Yield: Annual Payment ÷ Price YTM: Solve for i using the number of periods until the bond matures (remember to annualize if appropriate) YTC: Solve for i using the number of periods until the bond can be called (remember to annualize if appropriate)

Interest rates The coupon rate and the yield of a bond both reflect interest rates. The coupon rate reflects the interest which the market was demanding at the time the bond was planned. Risk determines the rate of return which investors will bear. What risks do bondholders face? The yield reflects the interest which the market requires right now. Again, this is based on the risk faced by holders of this bond. Can the riskiness of a company change between the time a bond is issued and the time it matures? The yield of a bond is the interest demanded by the market and is the “Cost of Debt” (Kd).

Capital: How a firm finances its assets All assets are backed by either equity or debt: A = L + SE Each type of capital has a different required rate of return Debt has a yield demanded by investors (e.g. Bondholders) Common stock (equity) has a return demanded by investors Preferred stock (equity) has a return demanded by investors Each type of capital bears a different amount of risk Debt has the most structured arrangement Common stock has the least structured arrangement Because of risk, Kd < Kpfd < Ke Capital Structure is the mixture of capital used in a company