MIM700

Business FinanceBA303Michael DimondMichael DimondSchool of Business Administration

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

BondsMichael DimondSchool of Business Administration Bonds: Linking terminology to TVM functionsPV = PriceFV = Face Value (also called Par Value. Usually $1,000)n = Periods (usually semiannual)i = YieldPMT = 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.Michael DimondSchool of Business Administration 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.Heres 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% semiannualPMT = 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.Michael DimondSchool of Business Administration 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 semiannuali = 4% semiannualPMT = 50 semiannualSolve for PV = -1,152.4696Notice 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 $1,152.47Heres 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?Michael DimondSchool of Business Administration Bond pricing, yields, etc.Lets 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 semiannuali = Unknown. This is what we are solving for.PMT = 50 semiannualSolve 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%Michael DimondSchool of Business Administration Bond pricing, yields, etc.Heres 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 = -1,000FV = 1,000 n = 24 semiannualPMT = 50 semiannualSolve for i = 5.0000% semiannualYield = 2 x semiannual i = 2 x 5.0000% = 10%Michael DimondSchool of Business Administration More about bondsProvisions of bondsConvertability: A conversion feature allows bondholders to exchange the bond for a certain number of shares of stock.Callability: A call feature allows the bond issuer to repurchase the bonds before they mature (for a premium above the face value)Warrants: A sweetener which allows the bondholders to purchase a certain number of shares of stock at a specific price & time.Current Yield vs Yield to Maturity vs Yield to CallCurrent Yield: Annual Payment PriceYTM: 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)The approximation formula (PMT+((FV-PV)/n))/((FV+PV)/2) works only when bonds are selling close to par

Michael DimondSchool of Business Administration Interest ratesThe 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).Michael DimondSchool of Business Administration Capital: How a firm finances its assetsAll assets are backed by either equity or debt: A = L + SEEach type of capital has a different required rate of returnDebt has a yield demanded by investors (e.g. Bondholders)Common stock (equity) has a return demanded by investorsPreferred stock (equity) has a return demanded by investorsEach type of capital bears a different amount of riskDebt has the most structured arrangementCommon stock has the least structured arrangementBecause of risk, Kd < Kpfd < KeCapital Structure is the mixture of capital used in a companyMichael DimondSchool of Business Administration Perpetuity: The annuity which doesn't endWhat happens to PV as n increases?If all other TVM factors are unchanged, PV gets smaller as n increases100 (1+10%)1 = 90.9091100 (1+10%)5 = 62.0921100 (1+10%)20 = 14.8644100 (1+10%)40 = 2.2095100 (1+10%)60 = 0.3284100 (1+10%)100 = 0.0073What the value finally doesIf n gets large enough, the PV of a single CF becomes almost zero:100 (1+10%)1000 = 0.0000000000000000000000000000000000000004 This means any single additional cash flow does not significantly increase the sum of the present values, even though all of the remaining CFs have value.With a little math, the discounting of a perpetuity simplifies to:PVperp = CF/r

Michael DimondSchool of Business Administration Consider a $100 annual perpetuity ($100 per year forever).What if you require a 12% annual return?

Rather than trying to discount a infinite number of cash flows, we use the perpetuity formula.The value of a perpetuity: PVperp = CF/r100 0.12 = 833.3333 :. You would be willing to pay $833.33 right now to receive $100 per year forever.What would happen if your required rate of return was higher (15%)?What would happen if your required rate of return was higher (8%)?Valuing a perpetuity01234PV?i = 12% APR100100100100The timeline for a perpetuity has an arrow at the right end to indicate there is no end to the timelineMichael DimondSchool of Business Administration Consider a $100 annual perpetuity which grows 10% each year.What if you require a 12% annual return?

As long as the percent growth rate is constant, this formula will give the present value: PVperp = CF/(r g)PVperp = 100 (0.12 0.10) = 100 0.02 = 5,000Expected growth has valueThere is a rule: r > gNotice this formula still works for a non-growing perpetuity. When growth = 0%, PVperp = CF/(r 0) = CF/r

Growing perpetuities01234PV?i = 12% APRg = 10%110100121133.10Michael DimondSchool of Business Administration Growing perpetuitiesThe general formula for valuing any perpetuity:PVperp = CF/(r-g)What a share of stock does:A stock which pays a dividend is a perpetuity. There is no anticipated end to the timeline, and there is an expected cash flow which behaves in a predictable fashion.For example, IBM stock has paid a dividend regularly since 1962. Looking at the quarterly amounts, the pattern is easy to see:6-May-100.65 Dividend6-Aug-100.65 Dividend8-Nov-100.65 Dividend8-Feb-110.65 Dividend6-May-110.75 Dividend8-Aug-110.75 Dividend8-Nov-110.75 Dividend8-Feb-120.75 Dividend8-May-120.85 Dividend8-Aug-120.85 DividendYou could probably predict the next several dividends without much doubt.Michael DimondSchool of Business Administration Stock: the Dividend Growth ModelStock acts like a perpetuity, so we can adapt the value of a perpetuity to value a share of stock:P0 = D1/(r-g)Notice the price (P0) is at time zero (right now) and the expected dividend (D1) is the cash flow which determines the current price.In many cases, the most recent dividend is given instead of the expected dividend. If this happens, you need to determine the expected dividend:D1 = D0 x (1+g)Michael DimondSchool of Business Administration Dividend Growth Model examplesYou require a 12% return on investment. If XYZ Company stock just paid a $1.00 dividend and dividends are expected to grow 4% per year forever, how much would you pay for a share of this stock?D0 = 1.00 :. D1 = 1.00 x (1 + 4%) = 1.041.04 (0.12 0.04) = 1.04 0.08 = 13.00:. You would be willing to pay $13.00 per share for XYZ CompanyIf IBM stock has an expected annual dividend of $3.79 (four quarters of dividends), a growth rate of 14.9% and you require 16.8% return, what price would you pay for IBM stock?3.79 (0.168 0.149) = 3.79 0.0190 = 199.4737:. You would be willing to pay $199.47 per share for IBMMichael DimondSchool of Business Administration More about common stockShares authorized vs issued vs outstandingClasses of common stock (Class A vs Class B)Voting rights & proxy ballotsPreemptive rightsFlotationForeign stock on the U.S. Market (ADRs)Michael DimondSchool of Business Administration About Preferred StockPreferred stock is an ownership stake (equity) which comes with a contracted payout.The dividend is frequently a percentage of the par value of the stock.For example, 5% preferred stock with a $10.00 par value would have an annual dividend of $0.50.Because it is a percent of the par value, the dividend does not grow.The dividend is a perpetuity, so we use the perpetuity formula to value preferred stock.XYZ Company has preferred stock with a $3.00 dividend and investors require a 9% return for this preferred equity. What is the market price?D0 = 3.00 :. D1 = 3.003.00 0.09 = 33.3333:. The market price is $33.33 per share for XYZ Company Preferred Stock.

Michael DimondSchool of Business Administration More about preferred stockDividend does not growPar valueFlotation & usesMichael DimondSchool of Business Administration Equity section of the Balance SheetEquity section line items usually includeBook value of common stock, sometimes divided into par value and additional amounts paid to the company (APIC)Book value of preferred stock, also showing par value and additional amountsRetained earningsInferring events from the balance sheet & other dataThe balance sheet shows a snapshot at the end of a periodComparing two consecutive balance sheets can show changesRetained earnings will increase based on profits (net income) and be reduced by payouts (such as dividends). Can you rearrange this data to solve for missing parts?Stock issuance will affect both the stock at par value and the additional paid-in capital. Can you determine the number of shares or the share price from data like this?Michael DimondSchool of Business Administration If this company paid $180,000 in dividends during 2012

What was their 2012 Net Income?

How many shares did the company issue & sell during 2012?

What was the average price-per-share of the new stock sold in 2012?

Michael DimondSchool of Business Administration