Share and Bond Valuations

Learning Objectives:

• Explain efficient capital markets and their importance.
• Describe the corporate bond market and bond types.
• Calculate bond value and understand its inverse relationship with interest rates.
• Differentiate and calculate coupon rate, yield to maturity, and effective annual yield.
• Understand preference shares as a special type of bond.
• Explain the dividend-valuation model for ordinary shares.
• Understand why $g$ must be less than $R$ in the constant-growth dividend model.
• Value preference shares with and without a stated maturity date.

DCF Technique in Valuations:

• Applies present value techniques to find intrinsic price/fair value.
• Focuses on specific financial instruments (Bonds, Ordinary Shares, Preference Shares).
• Emphasizes present valuing and timing of cash flows for each instrument.

Introduction to Valuations:

• Security markets connect buyers and sellers.
• Organized markets reflect supply and demand.
• A security’s true value is the present value of expected future cash flows.
• New information adjusts cash flow estimates and security prices.

What is Valuation?

• Valuation determines an asset's worth, fair value, or intrinsic value.
• It involves discounting future cash flows to determine intrinsic value.
• Valuation helps determine if an asset is overvalued or undervalued.
• Techniques include Discounted Cash Flow (DCF).

Market Price (MP) vs. Intrinsic Price (IP):

• MP is the observed market consensus price.
• IP is a self-assigned value from estimation models.
• Investment decisions:
• MP < IP: BUY (security is underpriced).
• MP > IP: SELL (security is overpriced).
• MP = IP: HOLD (security is correctly priced).
• Value investors seek underpriced assets.

Role of Valuation:

• Assist investors in making investment decisions.
• Examples:
• Intrinsic value > Market price: Buy.
• Intrinsic value < Market price: Sell.
• Intrinsic value = Market price: Hold.

Market Conditions:

• Efficient Markets: Market prices reflect all information, knowledge, and expectations.
• Low costs and easy transactions.
• Market price = intrinsic price.
• Inefficient Markets: Market prices deviate from intrinsic prices.
• Over and underpriced securities.
• Efficient Market Hypothesis: Information is incorporated into security prices.

Techniques of Valuing Financial Assets:

• Discounted Cash Flow (DCF) technique: Present value of future benefits (cash flows).
• $PV = \frac{CF<em>1}{(1+r)^1} + \frac{CF</em>2}{(1+r)^2} + \frac{CF<em>3}{(1+r)^3} + \frac{CF</em>4}{(1+r)^4}$
• Discount rate = Required rate of return (RRR).

Discounted Cash Flow Variations:

• Perpetuity: $V_0 = \frac{C}{r}$
• Annuity + Lump Sum: $V<em>0 = C \times PVIFA</em>{n,r} + P \times PVIF_{n,r}$
• Growing Perpetuity: $V<em>0 = \frac{C</em>1}{r-g}$
• Lump Sum: $V_0 = C \times \frac{1}{(1+r)^n}$
• Two-Stage Cash Flow: $V<em>0 = \sum</em>{t=1}^{n} \frac{C<em>0(1+g</em>1)}{(1+r)^t} + \frac{C<em>1(1+g</em>2)}{(1+r)^t} + \frac{C_3}{r-g} \times \frac{1}{(1+r)^n}$

Share Valuation:

• Preference Shares
• Ordinary Shares

The Market for Shares:

• Secondary Market: Shares are traded among investors.
• Efficient markets reflect all available information.
• Types of Secondary Markets:
• Direct search: Costly, infrequent trading.
• Broker: Brings buyers and sellers, increases efficiency.
• Dealer: Provides continuous bidding, improves efficiency.

Preference Share Valuation:

• Regarded as fixed income securities with a fixed dividend.
• Preference shareholders have rights over ordinary shareholders.
• Receive dividends before ordinary shareholders.
• Preference in liquidation before ordinary shareholders.
• No voting rights.
• Ranked ahead of ordinary shares but behind debt.

Preference Share Transaction:

• Companies issue prefs to investors for finance.
• Investors buy prefs seeking investment opportunities.
• Secondary trading is common.

Redeemable and Non-Redeemable Preference Shares:

• Preference in Perpetuity/Non-Redeemable Preference Shares:
• Normal perpetuity.
• Non-redeemable + cumulative/non-cumulative preference shares.
• Redeemable Preference Shares

Valuation of Preference Shares:

• Discount future cash flows (dividends) using the required rate of return.
• $PS_0 = PV \ of \ dividend \ payments + par \ value$

Preference Share in Perpetuity:

• Non-redeemable, a permanent financing form.
• Pays infinite series of equal, periodic cash flows.
• Valued using perpetuity formula: $PS<em>0 = \frac{D</em>p}{i}$, where $D_p$ is the annual dividend and $i$ is the yield to maturity.

Redeemable Preference Shares:

• $PS_0 = D \times \frac{1-\frac{1}{(1+i)^n}}{i} + P \times (\frac{1}{(1+i)^n})$
• $D$ = annual dividend, $P$ = stated (par) value, $i$ = yield to maturity, $n$ = years to maturity.

Ordinary Share Valuation:

• Listed Ordinary Shares

Valuing Ordinary Share: Dividend Discount Model (DDM):

• Intrinsic value of stock price equals PV of all future dividends.
• General Formula: $P_0 = PV(All \ future \ dividends)$
• Valuation process:
• Project future dividends.
• Determine the RRR (Required rate of return).
• Discount dividends to valuation date.

DDM Versions:

• Zero Growth in dividend
• Constant Growth Model/Gordon Growth Model
• Non-Constant Growth Model/2-Stage Model

Ordinary Share: Zero Growth Model:

• Assumes dividend has zero growth.
• Dividend payment remains constant.
• Formula: $P_0 = \frac{D}{R}$

Ordinary Share: Constant Growth Model:

• Dividends grow at the same average rate from period to period.
• Formula: $P<em>0 = \frac{D</em>1}{R-g} = \frac{D_0(1+g)}{R-g}$
• $D<em>1$ = next year’s dividend, $D</em>0$ = last dividend paid, $R$ = required rate of return, $g$ = constant growth rate.

Constant Growth Model Considerations:

• Determine if dividend given is $D<em>0$ or $D</em>1$.
• Growth rate may be positive, negative, or zero.
• Compute growth rate using the sustainable growth formula.
• Calculate RRR using CAPM.

Corporate Bonds: What is a Bond?

• Financial securities issued to borrow from the public.
• Long-term debt instrument.
• Two parties: Borrower/issuer/seller and Lender/Investor/Buyer.
• Borrower pays periodic interest and principal at a specific date.
• Interest paid is a coupon payment.
• Safer than shares but with lower returns

Types of Corporate Bonds:

• Plain Vanilla/Straight Bonds: Fixed coupon payments, principal paid at maturity.
• Zero-Coupon Bonds: No coupon payments, single payment at maturity.
• Convertible Bonds: Converted into ordinary shares at a predetermined ratio.
• Callable, Puttable, and Perpetual Bonds: Issuer can redeem the bond at a present price.

Basic Bond Features:

• Face Value: Principal amount owed at maturity.
• Coupon Rate/Payment: Determines coupon payments.
• Time to Maturity: Lifespan of the bond.
• Yield to Maturity: Return required by investors, used as a discount rate.
• Price: Amount investor pays for the bond.

Bond Interpretation:

• Par-Value Bonds: Coupon rate equals the market rate.
• Discount Bonds: Sell below face value.
• Premium Bonds: Sell above face value.

Valuation of Corporate Bonds:

• Redeemable and Non-Redeemable bonds

Bond Types Mathematical expression:

• **Bond in Perpetuity/Non-Redeemable Bond: $P_B = \frac{C}{i}$
• Redeemable Bond: $P_B = C \times \frac{1-\frac{1}{(1+i)^n}}{i} + F \times (\frac{1}{(1+i)^n})$

Bond Valuation

• To determine the intrinsic value of a bond, discount all future coupons using yield to maturity as the discount rate

Bond in Perpetuity/Non-Redeemable bond Formula, Variables and Definition:

• Formula to use: $P_B=\frac{C}{i}$
• C = Coupon payment ( face value * coupon rate)
• i = required rate

Redeemable bond Annual Compound Formula and Variables

• Formula to use: $P_B = C \times \frac{1-\frac{1}{(1+i)^n}}{i} + F \times (\frac{1}{(1+i)^n})$
• C= Coupon = face Value * coupon rate
• n = the number of years to maturity
• i = required rate
• F = Face value, principal amount

Redeemable bond: Semi-annual compounding:

• Formula to use: $P_B = C \times \frac{1-\frac{1}{(1+i)^n}}{i} + F \times (\frac{1}{(1+i)^n})$
• C= Coupon rate, coupon amount
• I = Intrest rate or required rate of return
• N = term period, bond term
• F = Face value

Relationship between Yield to Maturity and Bond Price:

• Inverse relationship between bond price and YTM.
• When YTM = coupon rate, bond price = face value (trading at par).
• When YTM < coupon rate, bond price > face value (trading at a premium).
• When YTM > coupon rate, bond price < face value (trading at a discount).

Non-Mathematical Explanation: Negative Relationship Bond Price & YTM

• The negative relationship exists to ensure that existing bonds continue to offer the return that is demanded by investors/the return equal to similar bonds.

Preference Share Features vs Bonds:

• Preference shares are an equity position (like a bond).
• Receive a fixed dividend (can be postponed).
• Rank second priority.
• Bonds are a debt position.
• Receive fixed interest/coupon.
• Rank first priority.

Ordinary Share Features vs Bonds:

• Ordinary shares are an equity (ownership) position.
• Rank last on dividend & liquidation proceeds.
• No fixed cash flow or lifespan.
• Bonds & preference shares: debt positions, fixed cash flow, fixed term.

Bond Markets and Bond Ratings:

• Bond markets are where participants buy and sell debt securities.
• Rated by independent agencies for creditworthiness.
• Ratings affect coupon rates.
• Lower risk, lower return.

Factors influencing Bonds Returns:

• Return an investor obtains as comensation for the risk they are prepared to take:
• Real interest rate and expected inflation rate
• Interest Rate and Time to Maturity
• Default risk
• Lack of liquidity.