Topic 2 Valuing Debt Securities. Bonds Valuation and

Topic 2 Valuing Debt Securities. Bonds Valuation and Interest Rates.

Topic 2 Mortgage securitization and financial crisis – discussion Bond features, factors that impact bond prices Types of bonds. Pure discount bonds. Coupon bonds Interest rates and bond valuation. Impact of the discount rate and timing of payments on bond valuation Term structure of interest rates Bond prices and yields. Current yield and yield to maturity. Relationships between coupon rate, required return, and bond price Bond valuation and bond yields

Objectives Understand what the process of mortgage securitization is and how it triggered the crisis Know main types of bonds and their characteristics Define bond features and how different factors could affect bond prices and yields Understand the term structure of interest rates and the determinants of bond yields Apply present value concept to valuation of bonds Use different models for bond yields estimation

Mortgage securitization and financial crisis NBC Video: Making Sense of the 2009 Financial Crisis

Financial crisis: lessons NBC Video: Report on the Financial Crisis of 2008 Says it Could Have Been Avoided

Bonds Bond – long-term contract under which a borrower agrees to make payments of interest and principal, on specific dates, to the bondholders.

Types of bonds Government bonds Municipal bonds Corporate bonds Domestic or foreign bonds

Value = + + + FCF1 FCF2 FCF∞ (1 + WACC)1 (1 + WACC)∞ (1 + WACC)2 Free cash flow (FCF) Market interest rates Firm’s business risk Market risk aversion Firm’s debt/equity mix Cost of debt Cost of equity Weighted average cost of capital (WACC) Net operating profit after taxes Required investments in operating capital − = Determinants of Intrinsic Value: The Cost of Debt ...

Key features of a bond Par value: Face amount, paid at maturity (assume $1,000). Coupon interest rate: Stated interest rate. Multiply by par value to get dollars of interest. Generally fixed. Maturity: Years until bond must be repaid. Declines. Issue date: Date when bond was issued. Default risk: Risk that issuer will not make interest or principal payments.

Types of bonds by the payment to investors Coupon bonds (fixed coupon and floating rate) Zero-coupon bonds Payment-in-kind bonds

Differences Between Debt and Equity Debt Not an ownership interest Creditors do not have voting rights Interest is considered a cost of doing business and is tax-deductible Creditors have legal recourse if interest or principal payments are missed Excess debt can lead to financial distress and bankruptcy Equity Ownership interest Common stockholders have a full range of voting rights according to the legislation Dividends are not considered a cost of doing business and are not tax deductible Dividends are not a liability of the firm until declared. Stockholders have no legal recourse if dividends are not declared An all-equity firm cannot go bankrupt

Sources of market data http://finance.yahoo.com/news/category-bonds http://www.bondsonline.com/Todays_Market/Composite_Bond_Yields_table.php

Bond valuation What factors do determine the value of the bond? •The discount rate (the yield that could be earned on alternative investments with similar risk and maturity) •Coupon rate •Timing of payments •Maturity of the bond

Cash flow includes equal regular interest payments and a par value at the maturity. Future cash flows should be discounted to the present (to the moment of valuation). What the cash flow from the bond is comprised of? How to measure a fundamental bond value?

V  bond value (should be the present value of its remaining cash flows) C  coupon payment provided at each period r  required rate of return per period used to discount the bond cash flows t  period of coupon payment N  number of periods to maturity M  par value Bond valuation

Example. Consider a bond that has 20 years remaining until maturity. Par value is $1000. Annual coupon rate is 14%, with annual payments period. Assume that the prevailing annualized yield on other bonds with similar characteristics is 14%. What is the bond’s fair value? Valuing bonds with fixed coupon payments

V  bond value (should be the present value of its remaining cash flows) C  coupon payment provided at each period r  required rate of return per period used to discount the bond cash flows t  period of coupon payment N  number of periods to maturity M  par value

In what case the value of the bond equals to the par value? When coupon rate equals to discount rate Valuing bonds with fixed coupon payments

Example. Par value is $1000. Annual coupon rate is 14%, with annual payments period. Assume that the prevailing annualized yield on other bonds with similar characteristics is 14%. What is the bond’s fair value? Assume we make a valuation of the same bond 5 years from now. Required rate of return did not change. Find the present value of all future payments, including par value, that will be paid to the investor 15 years from now.

Example. How the value of the bond will change 5 years from now if the required rate of return change to 16%? Return on the bond is lower than the market return, so its value should … decline

Example. How the value of the bond will change 5 years from now if the required rate of return change to 12%? Return on the bond is higher than the market return, so its value should … increase

If the bond has semiannual payments, the present value can be calculated as following: Valuation of bonds with semiannual payments C/2 – semiannual coupon payment r/2 – periodic discount rate used to discount the bond cash flows 2N – denominator exponent to reflect the doubling of periods

Consider a bond of 15 years before the maturity, 14% coupon rate paid semiannually, 12% required return, $1000 par value. Present value is calculated as following: Valuation of bonds with semiannual payments

What is the relationship between coupon rate, required return and bond value?

Interest Rate Risk Change in price due to changes in interest rates Interest rates up, bond value down! Long-term bonds have more interest rate risk than short-term bonds More-distant cash flows are more adversely affected by an increase in interest rates Lower coupon rate bonds have more interest rate risk than higher coupon rate bonds

The relationship between bond value and interest rates

Zero-coupon bonds Make no periodic interest payments (coupon rate = 0%) The entire yield to maturity comes from the difference between the purchase price and the par value Cannot sell for more than par value Sometimes called zeroes, or deep discount bonds Treasury Bills are examples of zeroes

Valuation of zero-coupon bonds V  value of a bond М  par value n  number of periods to maturity

Example. Zero-coupon bond with a par value of $1000, maturity of 5 years is traded for $630,12. Is it profitable to invest in this bond, if the investor considers the alternative investment with 12% annual return?

Yield to maturity Example. Suppose we are offered a 10-year, 11% annual coupon, $1000 face value bond at a price of $1200. What rate of interest would you earn on your investment if you bought the bond and held it to maturity? This rate is yield to maturity. It should be the same as a market interest rate.

Yield to maturity is the calculated return on investment that investors will get if they hold the bond to maturity. It takes into account the present value of all future cash flows, as well as any premium or discount to par that the investor pays. Yield to maturity Bonds yields at http://finance.yahoo.com

Bonds mature at a par value, which is almost always $1,000. A premium bond is any bond that is currently trading at a price above par. A discount bond is a bond trading at a price lower than par. Premium and discount Bonds yields at http://finance.yahoo.com

Example. Suppose we are offered a 10-year, 11% annual coupon, $1000 face value bond at a price of $1200. What rate of interest would you earn on your investment if you bought the bond and held it to maturity? Yield to maturity

V  current price of a bond C  coupon payments YTM  yield to maturity t  period of coupon payment N  number of periods of payment M  par value

Example. Suppose we are offered a 10-year, 11% annual coupon, $1000 face value bond at a price of $1200. What rate of interest would you earn on your investment if you bought the bond and held it to maturity? Yield to maturity Yield-2 YTM = 8,02%

Current yield Current yield is the rate of return an investor will get, without taking into account the value of the premium or discount of the purchase price. It is calculated by dividing the coupon by the price. The current yield is not a good indication of your return on investment. Yield to maturity and yield to call take into account the value of the discount or premium paid for the bond, and as such they offer a much better indication of the value of the bond.

Current yield Example. Suppose we are offered a 10-year, 11% annual coupon, $1000 face value bond at a price of $1200. What is the current yield? Yield-2 9,17%

Call provisions Some bonds can be called (redeemed) by the issuer on specified dates throughout the life of the bond. Issuer can refund (repurchase the issue) if interest rates decline. That helps the issuer to manage its debt, but hurts the investor. Therefore, coupon rates on callable bonds are higher. Most bonds assume a call premium. Usually they have a deferred call provision.

Yield to call Based on the current price of a bond, the yield to all calls should be calculated, and the investor should note the lowest yield to call and the yield to maturity.

Yield to call Example. Suppose we are offered a 10-year, 11% annual coupon, $1000 face value bond at a price of $1200. What rate of interest would you earn on your investment if you bought the bond and held it to maturity? The bonds may be called in 5 years at 109% of face value (call price $1090). What is the yield to call? The previous example:

Yield to call Example. Suppose we are offered a 10-year, 11% annual coupon, $1000 face value bond at a price of $1200. What rate of interest would you earn on your investment if you bought the bond and held it to maturity? The bonds may be called in 5 years at 109% of face value (call price $1090). What is the yield to call? Yield-2 7,59%

Graphical Relationship Between Price and YTM

Bond Prices: Relationship Between Coupon and Yield If YTM = coupon rate, then par value = bond price

If YTM > coupon rate, then par value > bond price Price below par = “discount” bond If YTM < coupon rate, then par value < bond price Price above par = “premium” bond Bond screener at http://finance.yahoo.com

YTM: rate of return? Will the investor receive the YTM if interest rates will change over time until maturity? Yes, the rate of return on the bond investment equals to the YTM Will the rate of return on the investment in the bond be equal to the YTM in case of reinvestment of coupon payments? No. There are two different strategies – investment in the bond and reinvestment .

In case of semiannual payments: what will be the effective annual rate? Challenging question The effective annual rate will be higher than in case of annual payments at the same coupon rate.

What will be the EAR in the example? Consider a bond of 15 years before the maturity, 14% coupon rate paid semiannually, 12% required return, $1000 par value. Is this a rate of return on the investment in the bond?

Assume, you buy a bond between interest payment dates, how much should you pay? How the valuation model for the bond will change? Challenging question No change in the valuation. The buyer should pay the price plus accrued interest.

Example. Consider a bond of 15 years before the maturity, 14% annual coupon rate paid semiannually, 12% required return, $1000 par value. Assume you buy a bond 3 months before it’s semiannual payment. How much should you pay? Basic price (see previous examples) plus accrued interest that equals to

Term Structure of Interest Rates Term structure is the relationship between time to maturity and yields, all else equal Yield curve – graphical representation of the term structure and describes YTM (yield to maturity) for different maturities of debt instruments. It reflects risk and expectations regarding future interest rates.

Upward-Sloping Yield Curve Normal – upward-sloping; long-term yields are higher than short-term yields

Downward-Sloping Yield Curve Inverted – downward-sloping; long-term yields are lower than short-term yields

http://www.bloomberg.com/markets/rates/index.html stockcharts.com/charts/yieldcurve.html Long-term rates should raise because of expectations of higher interest rates reflecting inflation and risk. Inverted yield curve could be a signal of recession.

http://finance.yahoo.com/bonds/composite_bond_rates Bond yields

U.S. Treasury bonds interest rates on different dates Yield Curve for March 1980 Yield Curve for February 2000 Yield Curve for March 2009

What moves the yield curve (bond prices)? Expectations regarding the benchmark interest rate (risk-free rate) - Federal Funds Rate, Refinancing rate The benchmark rate responds to changes in inflation and real GDP growth Bond yields

Changes in bond values over time and total return Current yield = coupon rate/current price Capital gains yield = YTM = current yield + capital gains yield Change in price Beginning price Tool kits-bonds. Chapter. Section 5.4

What happens to a bond price over time? To set up this problem, we will enter the different interest rates, and use the array of cash flows (see tool kits). The following example operates under the precept that the bond is issued at par ($1,000) in year 0. From this point, the example sets three conditions for interest rates to follow: interest rates stay constant at 10%, interest rates fall to 5%, or interest rates rise to 15%. Then the price of the bond over the fifteen years of its life is determined for each of the scenarios. Tool kits-bonds. Chapter. Section 5.4 Changes in bond values over time and total return

Changes in bond values over time

Example Suppose the bond was issued 20 years ago and now has 10 years to maturity. What would happen to its value over time if the required rate of return remained at 10%, or at 13%, or at 7%? See next slide.

M 1,372 1,211 1,000 837 775 30 25 20 15 10 5 0 r = 7%. r = 13%. r = 10%. Bond value ($) vs. years remaining to maturity

At maturity, the value of any bond must equal its par value. The value of a premium bond would decrease to $1,000. The value of a discount bond would increase to $1,000. A par bond stays at $1,000 if r remains constant.

What Drives Yields?Expectations about the Future The pure expectations theory provides a relationship between short-term interest and long term yields. The expectations theory says that long term yields are averages of expected one period (e.g., one year) yields.

The Pure Expectations Theory Yield on an n period bond at time t is equal to the average of the expected one period interest rates between t and t+n The above statement is called the expectations theory of term structure of interest rates

The Pure Expectations Theory The expectations theory implies: Case 1: If investors expect the future one period interest rates to rise then the current yield curve upward sloping Case 2: If investors expect no change in the future one period interest then the current yield is flat Case 3: If investors expect the future one period interest rates to fall then the current yield curve downward sloping

The Central Bank and the TermStructure The Fed manages the one period interest rate (fed funds rate) Expectations theory today’s yield curve reflects the markets expectations of future Fed actions regarding the Fed Funds rate There is an important link between the yield curve and Federal Reserve’s monetary policy If the economy is likely to go into a recession then investors expect the Federal Funds interest rate to fall, hence current yield curve is downward sloping

If you receive news that real GDP growth will decline (i.e., a recession) then the yields will fall (bond prices rise) in anticipation of a Fed funds interest rate cut If you receive news about higher future inflation then current yields will rise (bond prices fall) in anticipation of higher future Fed funds rate

r = r* + IP + DRP + LP + MRP. Here: r = Required rate of return on a debt security. r* = Real risk-free rate. IP = Inflation premium. DRP = Default risk premium. LP = Liquidity premium. MRP = Maturity risk premium.

What is the nominal risk-free rate? Here: rrf = Nominal risk-free rate r* = Real risk-free rate IP = Inflation premium

Bond Spreads, the DRP, and the LP A “bond spread” is often calculated as the difference between a corporate bond’s yield and a Treasury security’s yield of the same maturity. Therefore: Spread = DRP + LP. Bond’s of large, strong companies often have very small LPs. Bond’s of small companies often have LPs as high as 2%. http://finance.yahoo.com/bonds/composite_bond_rates

Bond spreads

Bond Ratings % defaulting within: S&P and Fitch Moody’s 1 yr. 5 yrs. Investment grade bonds: AAA Aaa 0.0 0.0 AA Aa 0.0 0.1 A A 0.1 0.6 BBB Baa 0.3 2.9 Junk bonds: BB Ba 1.4 8.2 B B 1.8 9.2 CCC Caa 22.3 36.9 Source: Fitch Ratings

Bond Ratings and Bond Spreads Long-term Bonds Yield (%) Spread (%) 10-Year T-bond 2.68 AAA 5.50 2.82 AA 5.62 2.94 A 5.79 3.11 BBB 7.53 4.85 BB 11.62 8.94 B 13.70 11.02 CCC 26.30 23.62

What factors affect default risk and bond ratings? Financial ratios Debt ratio Coverage ratios, such as interest coverage ratio or EBITDA coverage ratio Profitability ratios Current ratios

When the bond market is called to be efficient? Bond prices fully reflect all the information that is publicly available How would bond prices adjust given the fact that company experienced very weak sales the last quarter?

Return and risk on international bonds An additional factor that affects the return to investors from another country is exchange rate risk Foreign interest rates movements Exchange rate fluctuations

Using Spreadsheets PRICE(Settlement,Maturity,Rate,Yld,Redemption,Frequency,Basis) YIELD(Settlement,Maturity,Rate,Pr,Redemption, Frequency,Basis) Settlement and maturity need to be actual dates The redemption and Pr need to be given as % of par value Click on the Excel icon for an example

Exercise (home) and required reading Use the file: in-class and home exercise 2.1 Reading: 1.Determinants of market interest rates: BE, Chapter 5, sections 5.7-5.15. 2.High Corporate Profits May Reduce Risk in High-Yield Bonds: http://www.nytimes.com/2011/10/09/business/mutfund/high-corporate-profits-could-reduce-risk-in-junk-bonds.html?partner=yahoofinance

Work the Web Bond yield information is available online One good site is Bonds Online Click on the Web surfer to go to the site Follow the “bond search,” “search/quote center,” “corporate/agency bonds,” and “composite bond yields” links Observe the yields for various bond types, and the shape of the yield curve

http://finance.yahoo.com Search for: investing/bonds/bonds screener Find quotes and yields for US corporate and government bonds Work the Web