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Business Finance

Business Finance. BA303 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

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Business Finance

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  1. Business Finance BA303Michael Dimond

  2. 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.

  3. 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.

  4. 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.

  5. 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?

  6. 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%

  7. 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%

  8. More about bonds • Provisions of bonds • Convertability: 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 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) • The “approximation formula” (PMT+((FV-PV)/n))/((FV+PV)/2)works only when bonds are selling close to par

  9. 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).

  10. 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

  11. Perpetuity: The annuity which doesn't end • What happens to PV as n increases? • If all other TVM factors are unchanged, PV gets smaller as n increases • 100 ÷ (1+10%)1 = 90.9091 • 100 ÷ (1+10%)5 = 62.0921 • 100 ÷ (1+10%)20 = 14.8644 • 100 ÷ (1+10%)40 = 2.2095 • 100 ÷ (1+10%)60 = 0.3284 • 100 ÷ (1+10%)100 = 0.0073 • What the value finally does • If 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

  12. Valuing a perpetuity • 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/r • 100 ÷ 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%)? The timeline for a perpetuity has an arrow at the right end to indicate there is no end to the timeline i = 12% APR 0 1 2 3 4 100 100 100 100 PV?

  13. Growing perpetuities • 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 = 5,000 • Expected growth has value • There is a rule: r > g • Notice this formula still works for a non-growing perpetuity. When growth = 0%, PVperp = CF/(r – 0) = CF/r i = 12% APR g = 10% 0 1 2 3 4 100 110 121 133.10 PV?

  14. Growing perpetuities • The 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-10 0.65 Dividend 6-Aug-10 0.65 Dividend 8-Nov-10 0.65 Dividend 8-Feb-11 0.65 Dividend 6-May-11 0.75 Dividend 8-Aug-11 0.75 Dividend 8-Nov-11 0.75 Dividend 8-Feb-12 0.75 Dividend 8-May-12 0.85 Dividend 8-Aug-12 0.85 Dividend • You could probably predict the next several dividends without much doubt.

  15. Stock: the Dividend Growth Model • Stock 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)

  16. Dividend Growth Model examples • You 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%) = 1.04 • 1.04 ÷ (0.12 – 0.04) = 1.04 ÷ 0.08 = 13.00:. You would be willing to pay $13.00 per share for XYZ Company • If 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 IBM

  17. More about common stock • Shares authorized vs issued vs outstanding • Classes of common stock (Class A vs Class B) • Voting rights & proxy ballots • Preemptive rights • Flotation • Foreign stock on the U.S. Market (ADRs)

  18. About Preferred Stock • Preferred 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 = 3.00 • 3.00 ÷ 0.09 = 33.3333:. The market price is $33.33 per share for XYZ Company Preferred Stock.

  19. More about preferred stock • Dividend does not grow • Par value • Flotation & uses

  20. Equity section of the Balance Sheet • Equity section line items usually include • Book 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 amounts • Retained earnings • Inferring events from the balance sheet & other data • The balance sheet shows a snapshot at the end of a period • Comparing two consecutive balance sheets can show changes • Retained 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?

  21. 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?

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