1. INTRODUCTION TO FINANCE INSTRUCTOR:MICHAEL E. ASAMOAH 1

2. Lecture 4 VALUATION OF LONG-TERM SECURITIES Ref.:CHAPTER 4 OF FUNDAMENTAL OF FINANCIAL MANAGEMENT BY VAN HORNE AND WACHOWICZ 2

3. Learning Objectives By the end of the lecture students should be able to: Distinguish among the various terms used to express value, including liquidation value, going- concern value, book value, market value, and intrinsic value. Value bonds, preference shares, and ordinary shares. Calculate the rates of return (or yields) of different types of long-term securities. List and explain a number of observations regarding the behaviour of bond prices. 3

4. Valuation Concepts 1. What is Value? 2. What are the various terms used in valuation – liquidation, book value, market value and intrinsic value 4

5. Valuation Concepts The amount that can be realised if an asset or group of assets is sold separately from its operating organisation. Liquidation Value The amount that can be realised from the sale of an enterprise as a continuing operating business. Going- concern Value 5

6. Valuation Concepts cont. The accounting value of an asset (Cost minus Accumulated Depreciation). The accounting value of an enterprise (Total Assets minus Total Liabilities and Preference Shares). Book Value The market price of an asset. Market Value The price at which a security should be traded if it is properly priced based on all factors that affect valuation. In short, the intrinsic value of a security is it’s economic value. If markets are reasonably efficient and informed, the current market price of a security should fluctuate closely around its intrinsic value. Intrinsic Value 6

7. Valuation Bonds 1. What is a Bond? 2. Bond terms and features 3. Types of bonds 7

8. Bond - Introduction A bond is a long term security that is issued in connection with a borrowing arrangement. The borrower issues (i.e., sells) a bond to the lender for some amount of cash; the bond is in essence the “IOU” of the borrower. The arrangement obligates the issuer to make specified payments to the bondholder on specified dates. These payments are mostly semi-annual in nature. By definition, a bond is a security that obligates the issuer to make specified payments to the holder over a period of time. 8

9. Bonds: Terms And Features FACE VALUE: The stated value of the bond. The redeemable amount of the bond upon maturity. Same as par or maturity value. COUPON RATE: The stated rate of interest on a bond. The annual interest expressed as a percentage of the bond’s face value. COUPON The interest payments made to the bondholder. WARNING!! The coupon rate IS NOT the discount rate used in the Present Value calculations 9

10. Bonds: Terms And Features MATURITY The life of the bond The amount of time before the face value of the bond becomes due. BOND PRICE The price at which a bond is issued. A bond may be sold At discount or At par value or At premium BOND INDENTURE, This is the contract between the issuer and the bond holder. ZERO-COUPON BOND A bond paying no coupons 10

11. Types of Bonds These include: Treasury Notes and Treasury Bonds Corporate Bonds International Bonds Callable Bonds and Puttable Bonds Convertible Bonds Floating Rate Bonds 11

12. Valuation Bonds 1. Bond Pricing 2. Valuation of perpetual bonds 3. Valuation of bonds with finite maturity 4. Valuation of a zero coupon bond 5. Bond yields 12

13. Bond Pricing A bond’s coupon and principal repayments occurs months or years into the future. Therefore, the price the investor would be willing to pay for a claim to these payments depends on the value of cedi to be received in the future compared to cedi in hand today. However, this “present value” (or time value) calculation depends on the market interest rates. Therefore, the price of a bond is the Present Value of all cash flows generated by the bond (i.e. coupons and face value) discounted at the required rate of return. 13

14. Bond Pricing Bond value = P. V of coupons + P. V of par value at maturity. If the required rate of return (discount rate) is r, the maturity date is n, then the value of a bond can be written as The first term of the formula is the present value of an annuity ( equal coupon payments). The second term is the present value of a single amount (final maturity value) NB: Hope you remember the P.V of annuity formula. 14

15. Valuation of Perpetual Bonds Bond held forever. Holder is entitle to only interests forever without ultimate receipt of face value. What is it? Calculated as the present value of a perpetuity (i.e. receipt of interest forever). Intrinsic Value, Calculation of Intrinsic Value 15

16. Valuation of Bonds with Finite Maturity The holder is entitled to two cash flows – interests and the maturity value. The intrinsic value is the PV of all future interests and the face value. Non- zero Coupon Bonds 16

17. Valuation of Bonds with Finite Maturity cont. No periodic interest payments. Usually sold at a huge discount. The value is the PV of the maturity value. Zero Coupon Bonds 17

18. Valuation of Bonds with Finite Maturity cont Semiannual Compounding of Interest Price = This is the case where interest payments are paid twice a year. It is thus necessary to modify the bond equation to account for compounding twice a year. 18

19. Bond Valuation - Illustration How much should each of the following bonds sell for? 1. A 10% GHS100 bond with 5 years to maturity and a discount rate of 12% 2. A 10% GHS100 bond with 10 years to maturity and a discount rate of 8% 3. A 8% GHS1000 bond with 30 years to maturity and a discount rate of 10% 4. What is the price of a 5.0 % annual coupon bond, with a GHS 1,000 face value, which matures in 3 years? Assume a required return of 2.15%. 5. What is the value if the coupon payments in Que (4) is paid semi-annually

20. Intrinsic Value, Face Value and Behavior of Bond Price Bond Value Vs Face Value ImplicationBehavior of Rational Investors Where face value is greater than intrinsic value. The bond is overvalued.A rational investor would be prepared to buy the bond at a discount (i.e. pay a price that is less than the face value). Where the face value is equal to the intrinsic value. The bond is properly valued to reflect its true value. The bond would sell at par value (i.e. pay a price equal to the face value) Where face value is less than the intrinsic value. The bond is undervalued.A rational investor would be prepared to buy the bond at a premium (i.e. pay a price that is greater than the face value). 20

21. Valuation of Shares 1. Stocks and stock markets 2. Differences between Preference and Ordinary Shares 3. Reasons for valuation 21

22. Stocks And Stock Market o Primary Market - Market for the sale of new securities by corporations. Eg. Initial Public Offering o Secondary Market - Market in which previously issued securities are traded among investors.  Common Stock - Ownership shares in a publicly held corporation.  Ordinary share/stock – equity without priority for dividends or insolvency.  Shareholders (owners of equity in a company) have rights to elect directors to run company...sometimes by proxy.  Dividend - Periodic cash distribution from the firm to the shareholders. 22

23. Stock and the stock market Preference shares: Securities often bearing annual rate of dividend... Holders of preference shares are entitled to receive dividends first before if any for ordinary dividends holders.. Have no voting rights....unless dividends are in arrears.....in which case the dividends are cumulative. Participating preference shares....share in profits over and above their dividend rates... Convertible preference shares....ordinary shares... Redeemable preference shares: gives company right to buy back the shares... 23

24. Why value shares? Share of a company may be valued for the following reasons: To determine an appropriate price for the entity’s stock in the case of a merger/acquisition To help decisions regarding buying or selling shares of a private company. To place an appropriate value on a stock to be listed on the stock exchange (IPO) To value shares in a private company for tax /legal purposes To value a subsidiary/division for disposal. To use the company as a collateral for a facility. In order to compensate owners in gov’t takeovers 24

25. Stock Valuation Methods Stock valuation could be done by using one of the following approaches 1. Income approach 2. Asset bases: The value of assets is the value of assets – liabilities. 3. Earnings bases : Valuation could be done through P/E ratio, Earnings yield, Super profit methods 4. Dividend approach: Valuation could be done using Constant dividend model or the Dividend growth model 5. Cash flow approach: This in inflow – outflow. Net cash flow is then discounted to get NPV. 25

26. Valuation of Shares 1. Valuation of preference shares: Both redeemable and irredeemable. 2. Valuation of ordinary shares: 26

27. Valuation of Preference Shares Usually promises a fixed dividend. It may have a maturity date or not. Preference Shares Pays the fixed dividend forever. Value = D p /k d Irredeemable Pref. Shares Pays the fixed dividend and the call value upon retirement of the share. Redeemable Pref. Dividends 27

28. Preferred Stock Example  UT Stock has an 8%, GHS1000 par value issue outstanding. The appropriate discount rate is 10%. preferred stock  What is the value of the preferred stock?  If the management of UT Bank has an option to call back the share after 5yrs at a price of GHS 1200, what value will you place on a share at the end of the fifth year? 28

29. Sol Question 1 Div P GHS 80.00 Div P = GHS 1000 ( 8% ) = GHS 80.00. k P 10% k P = 10%. VDiv P k P GHS 80.0010% GHS800 V = Div P / k P = GHS 80.00 / 10% = GHS800 Question 2 NB: Use the formula for finding the value of a finite bond bearing in mind, the values for t and n considering duration left Or use the value of an ordinary annuity. 29

30. Valuation of Ordinary Shares common stockWhat cash flows will a shareholder receive when owning shares of common stock? Future dividends Future sale of the common stock shares The value is taken to be the discounted value of all expected cash dividends. Basis of Valuation Value would be the discounted value of dividends received forever. Where share is to be held forever Value would be the discounted value of all expected cash dividends, and the expected sales price at the end of the specified time period. Where share is to be held for a specified time period 30

31. Valuation of Ordinary Shares cont. Value is discounted value of constant dividend treated as a perpetuity V = Dps/K e Where Dividend is Constant (No Growth) In case of constant growth, the Gordon Growth Model (i.e. dividend discount model) Where growth is not constant, dividend should be estimated using the various growth rates and then discount each dividend based on the timing of the dividend and applicable required rate of return. Where There is Growth in Dividend 31

32. Dividend Discount Model Model used to compute intrinsic value of an ordinary share assuming an expected growth pattern. Share is assumed to be held forever. What is it? Expected growth in dividend is assumed to be constant. Value of Share, V = D 0 (1 + g) or r – g This model is reasonable for companies in the mature stage. The earnings and dividends of such companies are quite stable. Constant Growth 32

33. Example Example 1 UT Bank has just paid annual dividend of GHS 3.50. If dividend grows at 10%. Given a discount rate is 15%. common stock What is the value of the common stock? Assume the dividend of UT has a zero growth rate. What is the value of the common stock? Example 2 What is the value of a stock that expects to pay a GHS3.00 dividend next year, if dividend increases at a rate of 8% per year, indefinitely? Assume a 12% expected return. 33

34. Non-constant Growth Where dividends grow at variable rate from the year to year, the value, the Value of a share is the present value of all projected dividends and the present value of the price at the given date or date of sale. In that case, the following steps should be followed: Step 1: Project Dividends for all relevant years starting from year 1 Step 2: Discount those dividends as in step 1 at the investor’s discount rate 34

35. Non-constant Growth Step 3: Project the price at the Nth year using  Pn = Dn (1+g) r - g Step 4: Find the present value of the price at the Nth year Step 5: Add all the present values of Dividends as in step 2 Step 6: Find the sum of step 5 and step 4. This will give the value of a share whose dividends grow at variable rates. 35

36. Example – Non Constant Growth UT Bank just paid a dividend of GHS 3.50 per share. If UT Bank expects its dividend to grow at a rate of 16% for the first 3 years and 8% thereafter, What is the value of the common stock of UT Bank. The appropriate discount rate is 15%. 36

37. Solution – UT Bank  Determine the annual dividends. D 0 = GHS 3.50 (this has been paid already) D 1 GHS 4.06 D 1 = D 0 (1 + g 1 ) 1 = GHS 3.50 (1.16) 1 =GHS 4.06 D 2 GHS 4.71 D 2 = D 0 (1 + g 1 ) 2 = GHS 3.50 (1.16) 2 =GHS 4.71 D 3 GHS 5.46 D 3 = D 0 (1 + g 1 ) 3 = GHS 3.50 (1.16) 3 =GHS 5.46 D 4 GHS 5.897 D 4 = D 3 (1 + g 2 ) 1 = GHS 5.46(1.08) 1 =GHS 5.897  We determine the PV of cash flows. D 1 D 1 GHS 4.06 GHS 3.532 PV(D 1 ) = D 1 (PVIF 15%, 1 ) = GHS 4.06 (0.870) = GHS 3.532 D 2 D 2 GHS 4.71 GHS 3.561 PV(D 2 ) = D 2 (PVIF 15%, 2 ) = GHS 4.71 (0.756) = GHS 3.561 D 3 D 3 GHS 5.46 PV(D 3 ) = D 3 (PVIF 15%, 3 ) = GHS 5.46 (0.658) = GHS 3.593  Determine the annual dividends. D 0 = GHS 3.50 (this has been paid already) D 1 GHS 4.06 D 1 = D 0 (1 + g 1 ) 1 = GHS 3.50 (1.16) 1 =GHS 4.06 D 2 GHS 4.71 D 2 = D 0 (1 + g 1 ) 2 = GHS 3.50 (1.16) 2 =GHS 4.71 D 3 GHS 5.46 D 3 = D 0 (1 + g 1 ) 3 = GHS 3.50 (1.16) 3 =GHS 5.46 D 4 GHS 5.897 D 4 = D 3 (1 + g 2 ) 1 = GHS 5.46(1.08) 1 =GHS 5.897  We determine the PV of cash flows. D 1 D 1 GHS 4.06 GHS 3.532 PV(D 1 ) = D 1 (PVIF 15%, 1 ) = GHS 4.06 (0.870) = GHS 3.532 D 2 D 2 GHS 4.71 GHS 3.561 PV(D 2 ) = D 2 (PVIF 15%, 2 ) = GHS 4.71 (0.756) = GHS 3.561 D 3 D 3 GHS 5.46 PV(D 3 ) = D 3 (PVIF 15%, 3 ) = GHS 5.46 (0.658) = GHS 3.593 37

38. Solution – UT Bank  Find the price at the Nth year (The Constant Growth Period) P 3 GHS 5.897 P 3 = GHS 5.897 / (0.15 - 0.08) = $84.2 [CG Model]  Find the Present Value of the Price at the Nth year P 3 P 3 GHS 84.2 GHS 55.404 PV(P 3 ) = P 3 (PVIF 15%, 3 ) = GHS 84.2 (0.658) = GHS 55.404 intrinsic value of UT Bank  Finally, we calculate the intrinsic value of UT Bank by summing up the Present Value of all the Cash Flows  Value = 3.532 + 3.561 + 3.593 + 55.404 = GHS 66.09 = GHS 66.09 38

39. Security's Yield The intrinsic value of a long-term security is estimated by capitalising the security’s income stream by a discount rate appropriate for the security’s risk (i.e. investors’ required rate of return). To get the price of a long-term security, one has to discount the security’s income stream by a discount rate (security's market yield). The security’s market require rate of return (yield) is the discount rate at which the present value of the security’s income stream is equal to the security’s market price. Note that when the intrinsic value of a security is equal to the market price, then investors’ required rate of return is equal to security’s market yield. 39

40. Bond’s Yield to Maturity (YTM) YTM is the expected rate of return on a bond if bought at its current market price and held to maturity. YTM is the discount rate that sets the P.V. of the bond’s income stream equal to the bond’s current market price. YTM is also referred to as the bond’s Internal Rate of Return (IRR). 40

41. Bond YTM Equation With Po, MV, and n given one can solve the following equation for YTM: Bond Price, Bond Price By interpolation, Deriving YTM by Interpolation 41

42. Bond YTM Equation Where, C = Coupon Payment, FV = Face Value, P = Price, n = Years to Maturity Notice that the formula shown is used to calculate the approximate yield to maturity. To calculate the actual yield to maturity requires trial and error by putting rates into the present value of a bond formula until P, or Price, matches the actual price of the bond 42

43. YTM, Coupon Rate and Behaviour of Bond Price YTM Vs Coupon RateImplication Behaviour of Bond Price When the YTM is more than stated coupon rate. The price of the bond will be less than its face value. The bond will be selling at a discount. When the YTM is equal to the stated coupon rate. The price of the bond will be equal to its face value. The bond will be selling at par value. When the YTM is less than the stated coupon rate. The price of the bond will be more than its face value. The bond will be selling at a premium. 43

44. Interest Rate and Behaviour of Bond Price If interest rate rise such that the YTM increases, the bond’s price will fall. If interest rates fall such that YTM falls, the bond’s price will rise. Bond is affected by volatility in interest rates and thus, the price of the bond is exposed to interest rate risk ( measure of variation in market price of a security caused by changes in interest rates). The investor will incur a loss due to interest rate risk only when a security is sold before its maturity and the level of interest rate has changed since the security was purchased. 44

45. Changes in YTM and Behaviour of Bond Price For a given change in YTM, the price of a bond will change by greater proportion, the longer its maturity. That is bond price volatility is directly related to maturity. The Maturity Effect For a given change in YTM, the price of a bond will change by a greater proportion, the lower the coupon rate. That is bond price volatility is inversely related to coupon rate. The Coupon Rate Effect 45

46. Effective Annual Yield Bond interests may be paid semi-annually. In this case, the bond valuation equation is modified thus: Effective Annual YTM = [1+(annual YTM/2)] 2 - 1 46

47. Yield on Preference Shares By replacing intrinsic value (V) by current market price (P0) in the preference share valuation equation we get the price equation: Preference share price is given by:P 0 = D p /k p The discount rate (kp) that sets the share’s income stream equal to its current market price is the market required return (yield) for the share. Yield on preference share:k p = D p /P 0 47

48. Yield on Ordinary (Common) Stock By replacing intrinsic value (V) by market price (P0) in the ordinary share valuation equation we get the price equation: Ordinary share price is given by:P 0 = D 1 /(k e – g) The discount rate (kp) that sets the share’s income stream equal to its current market price is the market required return (yield) for the share. Yield on ordinary share:k e = (D 1 /P 0 ) + g 48

49. Sources of Ordinary Share Yield 49

50. Illustration of Ordinary Share Yield D1 = 2 pesewas Dividend growth rate = 10% Current market price per share = 4 cedis Assumptions Compute the yield Compute dividend yield Compute capital gains yield Required 50

51. Assignment AB Julika Inc is selling a new issue of bonds to raise money. The bonds will pay a coupon rate of 8% and will mature in 10 years. The face value of the bond is GHS 1000, coupon is paid annually. The market rate of interest is 12% for similar bonds. 1. What is the price of the bond? 2. What is the current yield on the bond? 3. If a price of GHS 980 was paid for the bond, find its YTM. 51

52. Assignment 2 P.K Bet Ltd is selling a new issue of bonds to raise money. The bond will pay a coupon rate of 10% and will mature in 6 years. The face value of the bond is GHS 1000, Coupon is paid semi-annually. Market rate of interest is currently 8% for similar bonds. 1. What is the price of the bond? 2. Is it sold at par, premium or discount? 52

53. Assignment 3 You have 100 shares in company, which is expected to grow at 20% for the next 4years, then 10% for another three (3) years and finally settle down to a growth rate of 5% for the indefinite future. The company currently pays dividend of GHS 50 per share and this is expected to grow in line with the growth of the firm. You require 10% return on your investment. RQD: i.What value will you place on one share ii.If a friend wants to buy 40% of your ownership in the company, what is the minimum amount you will charge him 53