Fm Unit 5 New

University of Technology, Jamaica Financial Management: Unit 5: Valuation of Bonds Types of Valuation: Book Value – the value of the asset as carried in the accounting records of the company. This is usually the original cost of the asset less any allowance for depreciation or permanent loss in value. Market Value – the price that is currently charged in the open market for an asset. Liquidation Value – the amount that can be realized for the asset when the company has to be broken up. This is usually a forced value and can be less than both the market value and the book value. Intrinsic Value – this is the fair value of an asset based on the amount of risk involved. This is the amount that an investor will want to pay for an investment and should be greater than or equal to the market value for the investment to be worthwhile. In General, the intrinsic value of an asset = the present value of the stream of expected cash flows discounted at an appropriate required rate of return. Bonds are normally long-term debt instruments issued by a company or government to raise funds. They may be either (i) zero coupon bonds which do not pay interest. (ii) Coupon bonds which do. The bond contract (indenture) lists all of the bond’s features eg rate of interest (the coupon rate), a par value (face value) and the maturity date, and also lists covenants (designed to protect the bondholders). The Issue date is the date when the bond was originally issued by the borrower. Bonds represent loans extended by investors to corporations and/or the government. They are issued by the borrower and purchased by the lender. Bonds typically pay fixed coupon payments at fixed intervals and pay the par value at maturity. Some bonds are callable, with provisions giving the issuer the right to redeem them before the maturity date. Early redemption is likely if market rates fall below the bond’s coupon rate. The issuer of callable bonds may then issue new bonds at the lower interest rate and use the proceeds to pay off the old callable bonds. This helps the issuer but hurts the investor who usually requires higher rates of return on callable bonds to compensate for the possible reduced return if bonds called. The bond’s fair value is the present value of the promised future coupon and principal payments. At issue, the coupon rate is set such that the fair value of the bonds is very close to, or equal to its par value. Later, as market conditions change, the fair value may deviate from the par value. To calculate the intrinsic value of a bond, simply discount the future cash flows which are (i) the coupon payment stream (an annuity), and (ii) the par/maturity value payment (a single sum) at the investor’s required rate of return. The present value of these two sets of cash flows are then added together to give the intrinsic value of the bond. Vb = $I (PVIFA i, n) + $M (PVIF i, n) Vb = the intrinsic value of the bond, $I = coupon payment, i = investor’s required rate of return, $M = maturity value (par value) Problem 1: a)

Find the fair value of a bond with a $1,000 par value, a remaining life of 10 years, and a coupon rate of 10% per year paid annually. Assume that at the present time, the required rate of return on the bond is 10% per year.

b) What would happen if expected inflation rose by 2%, causing k = 12%? When kd rises, above the coupon rate, the bond’s value falls below par, so it sells at a discount. If coupon rate < kd, then the bond will sell at a discount. c) What would happen if inflation fell, and kd declined to 7%? Price rises above par, and bond sells at a premium, if coupon rate > k d. Problem 2: Find the fair value of a bond with a $1,000 par value, a remaining life of 10 years, and a coupon rate of 10% per year paid semi-annually. Assume that at the present time, the required rate of return on the bond is 12% per year. Problem 3: Find the fair value of a bond with a $1,000 par value, a remaining life of 12 years, and a coupon rate of 9% per year paid semi-annually. Assume that at the present time, the required rate of return on the bond is 6% per year. Interest Rate Risk/Reinvestment Rate Risk/Default Risk: The likelihood that interest rates will rise is referred to as interest rate risk. When interest rates rise, investors are now getting lower returns on the bonds they hold than someone taking out a new investment today. Therefore, if the investor wanted to sell the bond with a lower interest rate than current rates, the market would offer less than par value for it. This bond would therefore have to be sold at a discount, because it is offering a lower rate than current rates. Bond values are therefore inversely related to interest rates. When interest rates rise, bond prices fall and are sold at a discount. When interest rates fall, bond prices rise and are sold at a premium. Longer term bonds are exposed to greater interest rate risks as the magnitude of the fall in the price will be much greater than for short term bonds of similar class. Reinvestment Rate Risk: refers to the risk of an investor having to reinvest at a lower rate of interest than that which he enjoyed previously. While a decrease in interest rates would lead to an increase in your bond's value, it

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also means that the cash flows received from existing bonds have to be reinvested at the new, lower market rates, leading to reduced income for the bondholders. Shorter term bonds are more exposed to reinvestment rate risks than longer term bonds. This is so because not only the interest earned will be reinvested at these lower rates but the principal will also be reinvested at these lower rates when the bonds mature. Only the interest on long term bonds will be exposed to reinvestment rate risks as the principal will normally not mature in the near future. Yield/Rate of Return The total yield or total rate of return on a bond at any point in time is equal to the sum of its current yield and its capital gains yield. The current yield is equal to the annual interest payment divided by the previous price and the capital gains yield is equal to the current price minus the previous price, all divided by the previous price i.e.

Yield to maturity (YTM) / Internal rate of return (IRR) captures the total yield of the investment. That is, it is the true rate of return if the investment is held to maturity and each interest payment is reinvested at the YTM. The Yield to Maturity represents the Internal Rate of Return of the Bond. 1.

The Rodriques formula: used to estimate the yield to maturity (YTM)

If the bond pays interest more than once per year, “I”= the annual payment divided by the number of compounding periods per year, and n = equal to the number of periods per year times the number of years. Problem 4: a) Find the Yield to Maturity (YTM) of a bond with a $1,000 par value, a remaining life of 10 years, and a coupon rate of 9% per year paid annually. The bond is currently selling for $887. b)

What would the Yield to Maturity (YTM) be if the price were $1,134.20.

Problem 5: Find the Yield to Maturity (YTM) of a bond with a $1,000 par value, a remaining life of 12 years, and a coupon rate of 9% per year paid semi-annually. The bond is currently selling for $1076.23. Bond Basics Par Value or Maturity Value A bond is issued with a stated value, known as the par, or face, value. This is the value at which the bond will be bought back by the issuer upon its maturity. Most bonds are issued with a $1,000 par value. While a bond's current value (market value) can and usually does fluctuate during its lifetime, this par value remains fixed. Coupon Rate At issue, most bonds also offer a fixed interest rate, or coupon rate. This is the annual rate of interest, calculated as a percentage of the par value that the holder of the bond will earn. For example, if a $1,000 par value bond has a 5% coupon rate, each year the holder of that bond will earn 5% of $1,000, or $50. Yield to Maturity This is the total return an investor receives from a bond, based on the annual interest rate and any profit or loss realized on the sale of the bond. YTM is the yield calculation used to compare the value of bonds with different issue and maturity dates, coupon rates, and par values. Present Value (PV)- Intrinsic Value of the bond Another important bond concept is present value--the assumption that, due to inflation, a specified sum of money received today will be worth more than the same amount received at some point in the future. Because bonds are based on the foundation of "payments over time," investors should be aware of this relationship between the values of money received today and the same amount received later.

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The present value of a bond would be equal to the present value of all future cash flows, which is PV of total coupon payments to be received over the remaining life of the bond plus the present value of the maturity value. Current Yield : bond's annual interest payment divided by its current price. It gives an indication of the cash income a bond will generate in a given period. It is not an accurate measure of the bond's total expected returns since it doesn't take include capital gains or losses that could be realized if it were held to maturity (or to call). For example, a zero-coupon bond will always have a current yield of zero since it does not pay coupon, but its total returns are greater than zero since it generates returns through capital gains. Reinvestment Risk Bond investors are faced with reinvestment risk--the threat that if interest rates fall, the interest payments and principal that investors receive will have to be reinvested at lower rates. This is important because the yield-tomaturity calculation we discussed earlier assumes that all payments received are reinvested at the exact same rate as the original bond's coupon rate. However, this is rarely the case. As a result, brokers and portfolio managers try to account for reinvestment risk by calculating a bond's duration--the number of years required to recover the true cost of a bond, considering the present value of all coupon and principal payments received in the future. Duration can be used to compare bonds with different issue and maturity dates, coupon rates, and yields to maturity. The duration of a bond is expressed as a number of years from its purchase date. Duration determines the economic life of a bond, and is a clear indication of its interest-rate risk (i.e., how much it will move in response to changing interest rates.) You can then buy, sell, or hold bonds according to how you think they will perform. Interest Rate Risk Another risk that bond investors face is interest-rate risk--the risk that rising interest rates will make their fixedinterest-rate bonds less valuable. Bond Market Interest Rates Bonds are very sensitive to changes in interest rates. When a bond is issued, it pays a fixed rate of interest, called a coupon rate, until it matures. If you sell the bond on the secondary market before it matures, however, the value of the bond will be affected by current market interest rates. Investors have names for markets of rising and falling bond prices. When interest rates rise and bond prices fall (by around 20% or more) or are expected to fall over an extended period, investors call it a bear market. In a bear market, bond traders tend to sell off their bonds to avoid falling values. In a bullish bond market, investors buy bonds to take advantage of an expected fall in interest rates and a rise in bond prices. They aim to buy low and sell high when bond prices increase. It is important to note that stocks and bonds may move in opposite directions. It is possible that when the stock market is bearish, the bond market may be bullish and vice versa. Bond prices also have a relationship to their yields. Bond Ratings Bonds are rated as to their quality by rating agencies. The main ratings agencies are Moodies, Standard & Poors, and Fitch. Different rating symbols might be used by different agencies, but they cover the same quality range. Ratings range from “Prime” or “Investment Grade” with ratings from AAA at the top end of this range to BBB at the lower end. Bonds that are not investment grade are also rated, ranging from various degrees of “speculative” at BB down to “In Default” at D at the low end.

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TUTORIAL QUESTIONS 1.

The Pennington Corporation issued a new series of bonds on January 1, 1979. The bonds were sold at par ($1,000), have a 12 percent coupon, and mature in 30 years, on December 31, 2008. Coupon payments are made semiannually (on June 30 and December 31). [ST-2] a.What was the YTM of Pennington’s bonds on January 1, 1979? b.

What was the price of the bond on January 1, 1984, 5 years later, assuming that the level of interest rates had fallen to 10 percent?

c.On July 1, 2002, Pennington’s bonds sold for $916.42. What was the YTM at that date? (d) 2.

3.

The Garraty Company has two bond issues outstanding. Both bonds pay $100 annual interest plus $1,000 at maturity. Bond L has a maturity of 15 years, and Bond S a maturity of 1 year. [7-5] a.

What will be the value of each of these bonds when the going rate of interest is (1) 5%, (2) 8%, and (3) 12%? Assume that there is only one more interest payment to be made on Bond S.

b.

Why does the longer-term (15-year) bond fluctuate more when interest rates change than does the shorter-term bond (1-year)?

The Heymann Company’s bonds have 4 years remaining to maturity. Interest is paid annually; the bonds have a $1,000 par value; and the coupon interest rate is 9%. [7-6] a.What is the yield to maturity at a current market price of (1) $829 or (2) $1,104? b.

Would you pay $829 for one of these bonds if you thought that the appropriate rate of interest was 12% - that is, if kd = 12%? Explain your answer.

5.

A 10-year, 12% semiannual coupon bond with a par value of $1,000 sells for $1,100. (Assume that the bond has just been issued.) What is the bond’s yield to maturity? [7-8a.]

6.

What is interest rate risk? Which bond has more interest rate risk, an annual payment 1-year bond or a 10-year bond? Why? [7-23g.]

7.

What is reinvestment rate risk? Which has more reinvestment rate risk, a 1-year bond or a 10-year bond? [7-23h.]

8.

Why would a firm wish to call a bond before its maturity date?

9. Callaghan Motor’s bonds have 10 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon rate is 8%.The bonds have a yield to maturity of 9%. What is the current market price of these bonds [8.1] 10. Wilson Wonder’s bonds have 12 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon rate is 10%. The bonds sell at a price of $850. What is their yield to maturity? [8.2] 11. Your company has raised financing by issuing 25-year bonds on January 1, 2009. They mature on December 31, 2033 and have a par value of $1,000 and a coupon rate of 8%. Coupon payments are made semi-annually. (i) (ii) (iii)

What would the value of the bonds be on June 30, 2027, if interest rates had risen to 12%? What would be their value on December 31, 2023, if interest rates had fallen to 6%? If the bonds had a value of $925.00 on December 31, 2028, what would be their yield to maturity on that date?

Answer (i)

VB = I (PVIFAi,n) + M (PVIF i,n) = 40(PVIFA6,13) + 1,000 (PVIF6,13) 40(8.8527) + 1,000(.4688) = 354.11 + 468.80 = $822.91

(ii)

VB = 40(PVIFAi,n) + 1,000(PVIFi,n) = 40(PVIFA3,20) + 1,000(PVIF3,20) = 40(14.8775) + 1,000(.5537) = 595.10 + 553.70 = $1,148.80

(iii)

YTM= I + M- Po n M + Po 2 2

= 40 + 1,000 – 925 = 40 +7.50 = .0494 x 2 = 9.88% 10 962.5 1,000 + 925 2 2 4