Business Ethics & Financial Management homework

BBA 3301, Financial Management 1

UNIT V STUDY GUIDE

Valuation of Securities

Learning Objectives Upon completion of this unit, students should be able to:

1. Calculate the value of a common stock using the constant-growth assumption.

2. Calculate the value of preferred stock. 3. Calculate the value of a corporate bond. 4. Calculate the value of a convertible bond. 5. Calculate the value of a zero coupon bond. 6. Apply the CAPM to calculate required return on common stock. 7. Calculate the intrinsic value of a stock option. 8. Describe the factors that impact option value.

Written Lecture As clearly seen in your daily lives, business relies on the issuance of financial assets to raise capital (money) to make investments, expand, or develop new products. Further, financial assets are a part of daily life in the areas of insurance, banking and retirement planning. This unit concentrates on the intrinsic valuation of financial assets. Financial assets can include a variety of investments. The two primary financial assets that will be addressed in this unit are fixed income (bonds) and equity (stock). Valuation involves the assessment of future cash flows discounted to present day. Similar to the methodology seen in Unit IV, discounting cash flows (DCF) is needed to value bonds and stocks. Rate of return used in discounting methodology is the interest rate that equates the present value of an investment’s expected future cash flows with its current price. Return is also known as yield or interest. Bonds represent a debt relationship in which an issuing company borrows and buyers lend. A bond issue represents borrowing from many lenders (investors) at one time under a single agreement. A bond’s term (or maturity) is the time from the present until the principal is returned. A bond’s face (or par) value represents the amount the firm intends to borrow (the principal) at the coupon rate of interest. The coupon rate is the fixed rate of interest paid by a bond. Most bonds pay coupon interest on a semiannual basis. Although bonds have fixed coupons, market interest rates constantly change. Changes in prevailing market interest rates (yield to maturity) result in changes in the market price of the bond. Bond prices and interest rates move in opposite directions:

 Selling at a premium – bond price increases above face value

 Selling at a discount – bond price falls below face value Longer term bond prices fluctuate more in response to changes in interest rates than shorter term bonds. This is known as interest rate risk.

Reading Assignment Chapter 7: The Valuation and Characteristics of Bonds Chapter 8: The Valuation and Characteristics of Stock

Supplemental Reading See information below.

Key Terms 1. Bonds 2. Call 3. Common stock 4. Convertible bond 5. Coupon 6. Face value (par value) 7. Financial asset 8. Option 9. Preferred stock

10. Put 11. Return 12. Term to maturity 13. Yield

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To value bonds it is important to note expected cash flows are predictable. Interest payments are fixed, occurring at regular intervals. Principal is returned along with the last interest payment at maturity. Below is an example of a corporate bond with 10 years to maturity, and a coupon rate of 10%:

The above figure can be found in your textbook on page 303.

Kinds of Bonds

 Secured bonds and mortgage bonds are backed by the value of specific assets – collateral.

 Debentures are unsecured bonds issued with higher interest rates.

 Subordinated debentures are lower in priority than senior debt.

 Junk bonds are issued by risky companies and pay high interest rates. Bonds are assigned quality ratings reflecting their probability of default. Higher ratings mean lower default probability. Bond rating agencies (such as Moody’s and S&P) evaluate bonds (and issuers), and assign a rating. A bond’s rating affects the size of the differential between the rate it must pay to borrow and the rate demanded by high quality issuers. It reflects the perceived risk of default of lower-quality issuers. Investment grade rating is important to institutional investors who are prohibited from trading below-investment-grade bonds Bond Valuation The price of a bond is the present value of a stream of interest payments plus the present value of the principal repayment.

If interest rates fall, a firm may wish to retire old, high interest bonds through a call provision. Thus corporations refinance old, high interest debt with new lower interest debt. Investors don’t like calls because they lose high interest. Call provisions usually have a call premium (to the investor) and a call protection where the bond won’t be called for a certain number of years. Corporate Bond Valuation Example: Assumptions: A $1,000 corporate bond with 15 years to maturity pays a coupon of 10% (semi-annual) and the market required rate of return is a) 8% b) 12%. What is the current selling price?

k,n

Interest payments are annuities--can use the present value of an annuity form

Principal repayment is a lump sum in ula:

PMT[PVFA

the futur

]

B PV(princiPV(interest payme pal repaymP +nt ) es nt)

k, n

e--can use the future value formula: FV[PVF ]

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Texas Instruments BAII Plus Key Strokes*: a) 1,000 = FV, 30 = N, 4 = I/Y, 50=PMT, CPT PV = $1,172.92

b) 1,000 = FV, 30 = N, 6 = I/Y, 50=PMT, CPT PV = $862.35

*Note N, I/Y and PMT are adjusted for a semi-annual basis! Zero Coupon Bond Valuation Example: Assumptions: A U.S. Government bond with a face amount of $10,000 with 12 years to maturity is yielding 4%. What is the current selling price? Algebraic Solution: $10,000/(1.04)12 = $6,245.97 Texas Instruments BAII Plus Key Strokes: 10,000 = FV, 12 = N, 4 = I/Y, 0=PMT, CPT PV = $6,245.97 A sinking fund provision requires an issuer to call in and retire a fixed percentage of the issue each year called. Convertible bonds are unsecured bonds exchangeable for a fixed number of shares of stock at the bondholder's discretion. Convertible bonds are usually issued at lower coupon rates. The following factors impact their valuation:

 Conversion ratio - the number of shares of stock received for each bond

 Conversion price - the implied stock price if bond is converted into a certain number of shares

Advantages of Convertible Bonds To issuing companies

 Convertible features are “sweeteners” enabling a risky firm to pay a lower interest rate

 Viewed as a way to sell equity at a price above market

 Usually have few or no restrictions To Buyers

 Offer the chance to participate in stock price appreciation

 Offer a way to limit risk associated with a stock investment A convertible’s price can depend on either its value as a traditional bond or the market value of the stock into which it can be converted. A convertible is always worth at least the larger of its value as a bond or as stock. Upon conversion convertible bonds cause dilution in EPS. EPS drops due to the increase in the number of shares of stock. Thus, outstanding convertibles represent a potential to dilution of EPS. Convertible Bond Example Harry Jenson purchased one of Algo Corp.’s 9%, 25-year convertible bonds at its $1,000 par value a year ago when the company’s common stock was selling for $20. Similar bonds without a conversion feature returned 12% at the time. The bond is convertible into stock at a price of $25. The stock is now selling for $29. Algo pays no dividends. (Notice that this bond’s coupon rate was set below the market rate for nonconvertible issues.)

 Harry exercised the conversion feature today and immediately sold the stock he received. Calculate the total return on his investment.

 What would Harry’s return have been if he had invested $1,000 in Algo’s stock instead of the bond?

BBA 3301, Financial Management 4

BBA 3301, Financial Management 5

The above figure can be found in your textbook on page 319-321.

Common Stock Income in a stock investment comes from dividends and the gain or loss on the difference between the purchase and sale price. A stock’s intrinsic value is based on assumptions about future cash flows made from fundamental analysis of the firm and its industry. A stock’s value today is the sum of the present values of the dividends received while the investor holds it and the price for which it is eventually sold. This is often based on predicted growth rates since forecasting exact future prices and dividends is difficult. Known as the Gordon Growth Model, the Dividend Valuation Model and also a variation of the Discounted Cash Flow approach, the following model is the core to intrinsically valuing common stock: Pe = D0 x (1 +g) / (Ke – g) or Pe = D1 / (Ke – g) Where: D0 = Most recent (past) annual dividend on one share of common stock. Note, dividends on common stock are usually paid on a quarterly basis so we must sum the last four quarters or annualize the most recent quarter. By multiplying D0 by (1 +g) we calculate D1. g = sustainable growth. (if g is not given is then it is calculated as ROE x Retention Ratio of Earnings*) ROE = Return on Equity or Net Income/Owner’s Equity Retention Ratio = EPS-DPS/EPS (EPS = Earnings per share; DPS =Dividends per share) Ke = Required return on equity capital It should be noted that for the above model to be valid, the corporation must pay

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a dividend and g < Ke. Otherwise, the results are nonsensical and the model lacks practical value. There are two primary methods to assess the cost of common equity capital. Using the Dividend Valuation Model, we can isolate Ke as: Ke = (D1/ Pe) + g If there is a need for new stock, flotation costs may occur resulting in the following equation: Ke = [D1/( Pe-F)] + g; Where F = flotation or selling costs. We can also use the Capital Asset Pricing Model (CAPM) to calculate Ke: Ke = Rf + B (Km- Rf) Where: Rf = Risk-free rate of return (annual). The proxy for this is usually the return on a U.S. Treasury. Km = Average annual market return (usually from an index for longer periods of time) B = Beta coefficient that is a measure of systematic risk. As Beta increases so does risk. The valuation of preferred stock is identical to the technique used for common stock. The only difference relates to the growth assumption in the model. In contrast to common stock dividends, preferred stock dividends are constant and do not grow. Thus, the equation to value a share of preferred stock is: Pp = Dp/Kp Where: Dp = Annual dividend paid on one share of preferred stock (note the dividend is constant) Kp = The required return (discount rate expressed in percentage terms) on the preferred stock given its risk characteristics. Note, this is also considered the cost of preferred equity. Through basic algebraic adjustments, we can isolate Kp in the following equation: Kp = Dp/Pp If there are flotation costs the equation is: Kp = Dp/(Pp – F) Where F = flotation/selling costs. Example of Gordon Growth Model (DDM): ABC Corp is expected to grow at a constant rate of 5% a year into the indefinite future. It recently paid a dividend of $1.00 a share. The rate of return on stocks similar to Atlas is about 10%. What should a share of Atlas Motors sell for today? = D0 (1+g)/(k-g) =$1.00 (1.05)/(.10-.05) = $21.00 A zero growth stock is a perpetuity. Preferred Stock is an example of a perpetuity and a hybrid security with characteristics of common stock and bonds. Preferred stock pays a constant dividend forever. An example of the valuation of

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a preferred stock involving a dividend of $2.00 and a required return of 20%. =D/k =$2.00/.20 = $10.00 The two-stage growth model values a stock that is expected to grow at an unusual rate for a limited time. This involves using the Gordon model to value the constant portion and find the present value of the non-constant growth periods. Options give the holder the temporary right to buy or sell an asset at a fixed price. Effectively, options owners can speculate on price changes without holding the asset. There are two primary types of options:

 Call option is an option to buy. It gives an owner (the holder) the right to buy stock at a fixed price (the exercise or strike price) for a specified time period. Once expired, it can’t be exercised

 Put option is an option to sell stock at a specified price by a specified date. The put buyer profits if underlying stock declines.

 Intrinsic value involves the option being “in-the-money.” For example in a call option, it is in the money when the option’s strike price is below the current stock price. A call option is out-of-the-money if the strike price is above the current stock price

Option Example The following information refers to a three-month call option on the stock of Oxbow, Inc.

 Price of the underlying stock: $30

 Strike price of the three-month call: $25

 Market price of the option: $8

a. What is the intrinsic value of the option?

The intrinsic value represents how much the option is in-the-money. Since the stock price is $30 and the call option’s strike price is $25, the option is in-the-money by $5, which is the intrinsic value.

b. What is the option’s time premium at this price?

The time premium represents the difference between the market price of the option and the intrinsic value, or $8 - $5 = $3.

c. If an investor writes and sells a covered call option, acquiring the

covering stock now, how much has he invested?

The premium ($8) that the writer receives for the option will offset some of the purchase price of the stock ($30), therefore the investor has invested $30 - $8 = $22.

d. What is the most the buyer of the call can lose?

The buyer can lose, at most, 100% of his investment which is the purchase price of the option of $8.

e. What is the most the writer of a naked call option on this stock can lose?

In theory since the stock price can rise to any price the writer can lose an infinite amount. However, a prudent writer would limit his losses by purchasing the stock once it started to rise in value.

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Just before the option’s expiration, Oxbow is selling for $32. f. What is the profit or loss from buying the call?

The buyer would exercise the option paying $25 for the stock and simultaneously selling the stock for $32, resulting in a gain of $7. However, this gain would be offset by the $8 premium paid for the option, resulting in an overall loss of $1.

g. What is the profit or loss from writing the call naked?

A naked writer would have to buy the stock for $32 and sell it to the option owner for $25, resulting in a loss of $7. However, this loss would be offset by the premium received on the writing of the option of $8, resulting in an overall gain of $1.

h. What is the profit or loss from writing the call covered if the covering

stock was acquired at the time the call was written?

The call writer bought the stock for $30 and sold it for $25, resulting in a loss of $5, but the loss is offset by the $8 premium received for writing the option. The overall gain is $3.

Based on the Fischer Black and Myron Scholes Option Pricing Model, options are based on the following factors:

 Price of underlying stock

 Strike price of option

 Time remaining until expiration of option

 Volatility of underlying stock’s market price

 Risk-free interest rate

Supplemental Reading From the CSU Library:

Raice, S., Das, A. & Letzing, J. (2012, 03 May). Facebook sets $28-$35 IPO range. Wall Street Journal (Online). Retrieved from Wall Street Journal database.

Marte, J. (2012, 01 May). The SmartMoney Report: Muni buyers gain peace of mind, but will likely lose some yield. Wall Street Journal (Online). Retrieved from Wall Street Journal database.

Zweig, J. (2011, 05 February). The Intelligent Investor: Preferred stock: Are those juicy yields worth the extra risk? Wall Street Journal (Online). Retrieved from Wall Street Journal database.

Hodson, J. (2011, 23 April). Best Buy chairman buys. Wall Street Journal (Online). Retrieved from Wall Street Journal database.