Valuation of Long Term Securities

Presented by:

Ashra Rehmat

Bond valuation

– Important Terms– Types of Bonds– Valuation of Bonds– Handling Semiannual Compounding

Important Terms Important Terms

• A bond is a long-term debt instrument issued by a corporation or government.

• The maturity value (MV) [or face value] of a bond is the stated value. In the case of a US bond, the face value is usually $1,000.

• The bond’s coupon rate is the stated rate of interest; the annual interest payment divided by the bond face value.

• The discount rate (capitalization rate) is dependent on the risk of the bond and is composed of the risk-free rate plus a premium for risk.

Bonds:

Different types of bonds

A perpetual bond is a bond that never matures. It has infinite life.

V = I / kd

Example:

Bond P has a $1,000 face value and provides an 8% annual coupon. The appropriate discount rate is 10%. What is the value of the perpetual bond?

Types of bonds:

• A non-zero coupon-paying bond is a coupon paying bond with a finite life.V = I (PVIFA kd, n) + MV (PVIF kd, n)

Bond C has a $1,000 face value and provides an 8% annual coupon for 30 years. The appropriate

discount rate is 10%. What is the value of the coupon bond?

Coupon Bond Example

TYPES:

• A zero coupon bond is a bond that pays no interest but sells at a deep discount from its face value; it provides compensation to investors in the form of price appreciation

(1 + kd)n

V=MV

= MV (PVIFkd, n)

Bond Z has a $1,000 face value and a 30 year life. The appropriate discount rate is 10%. What is the value of the

zero-coupon bond?

Semiannual compounding

A non-zero coupon bond adjusted for semi-annual compounding..

(1) Divide kd by 2

(2) (2) Multiply n by 2

(3) Divide I by 2

= I/2 (PVIFAkd /2 ,2*n) + MV (PVIFkd /2 ,2*n)

EXAMPLE:-

Bond C has a $1,000 face value and provides an 8% semi-annual coupon for 15 years. The appropriate discount rate is 10% (annual rate). What is the value of the coupon bond?

Preferred Stock Valuation

Common Stock Valuation

Preferred Stock is a type of stock that promises a (usually) fixed dividend, but at

the discretion of the board of directors.

V = DivP / kP

(1 + kP)1 (1 + kP)2 (1 + kP)¥V = + + ... +

DivP DivPDivP

Stock PS has an 8%, $100 par value issue outstanding. The appropriate discount rate is 10%. What is the value of the preferred

stock?

Example:

Common stock• Common stock represents a residual

ownership position in the corporation.• Dividend Valuation Model

Basic dividend valuation model accounts for the PV of all future dividends.

= S¥t=1 (1 + ke)t

DivtV

Divt: Cash Dividend at time t

ke: Equity investor’s required return

Dividend Growth Pattern Assumptions

The dividend valuation model requires the forecast of all future dividends. The

following dividend growth rate assumptions simplify the valuation process.

Constant Growth

No Growth

Growth Phases

The constant growth model assumes that dividends will grow forever at the rate g.

The constant growth model assumes that dividends will grow forever at the rate g.

The growth phases model assumes that dividends for each share will grow at two or

more different growth rates.

The zero growth model assumes that dividends will grow forever at the rate g = 0.

Zero Growth Model

Growth Phases Model

Constant Growth Model

Example

James Consol Company currently pays a dividend of $1.60 per share on its common stock. The company expects to increase the dividend at a 20 % annual rate for the first four years and at a 13 % rate for the next four years, and then grow the dividend at a 7 percent rate thereafter. This phased-growth pattern is in keeping with the expected life cycle of earnings. You require a 16 % return to invest in this stock. What value should you place on a share of this stock?

SolutionPHASES 1 and 2: PRESENT VALUE OF DIVIDENDS TO BE RECEIVED OVER FIRST 8 YEARS

END OF PRESENT VALUE CALCULATION PRESENT VALUE

YEAR (Dividend × PVIF16%,t ) OF DIVIDEND

Phase 1

1 $1.60(1.20)1 = $1.92 × 0.862 = $ 1.66

2 1.60(1.20)2 = 2.30 × 0.743 = 1.71

3 1.60(1.20)3 = 2.76 × 0.641 = 1.77

4 1.60(1.20)4 = 3.32 × 0.552 = 1.83

Phase 2

5 3.32(1.13)1 = 3.75 × 0.476 = 1.79

6 3.32(1.13)2 = 4.24 × 0.410 = 1.74

7 3.32(1.13)3 = 4.79 × 0.354 = 1.70

8 3.32(1.13)4 = 5.41 × 0.305 = 1.65

= $13.85

PHASE 3: PRESENT VALUE OF CONSTANT GROWTH COMPONENT

Dividend at the end of year 9 = D8 ( 1 + g )

$5.41(1.07) = $5.79

Value of stock at the end of year 8

D9 $ 5.79 $64.33

ke – g (0.16 – 0.07)

Present value of $64.33 at end of year 8 = V8 = FV (PVIF16%,8) =($64.33)(PVIF16%,8)

= ($64.33)(0.305) = $19.62

PRESENT VALUE OF STOCK

V = $13.85 + $19.62 = $33.47

YIELD TO MATURITY (YTM)

DEFINITION:-

The expected rate of return on a

bond if bought at its current market price and

held to maturity.

Internal rate of return

(IRR)

It is also known as the bonds internal rate of

return.

Calculating Rates of Return (or Yields)

Calculating Rates of Return (or Yields)

1. Determine the expected cash flows.

2. Replace the intrinsic value (V) with

market price (P0).

3. Solve for the market required rate of return

That equates the discount cash flows to the

market price.

1. Determine the expected cash flows.

2. Replace the intrinsic value (V) with

market price (P0).

3. Solve for the market required rate of return

That equates the discount cash flows to the

market price.

Steps to calculate the rate of return (or Yield).

Determining Bond YTMDetermining Bond YTM

Determine the Yield-to-Maturity (YTM)

for the annual coupon paying bond with a finite life.

Determine the Yield-to-Maturity (YTM)

for the annual coupon paying bond with a finite life.

P0 = Sn

t=1(1 + kd )t

I

= I (PVIFA kd , n) + MV (PVIF kd , n)

(1 + kd )n

+ MV

kd = YTM

Bond Price - Yield Relationship

Bond Price - Yield Relationship

Discount Bond – The market required rate of return exceeds the coupon rate (Par > P0 ).

Premium Bond – The coupon rate exceeds the market required rate of return (P0 > Par).

Par Bond – The coupon rate equals the market required rate of return (P0 = Par).

Discount Bond – The market required rate of return exceeds the coupon rate (Par > P0 ).

Premium Bond – The coupon rate exceeds the market required rate of return (P0 > Par).

Par Bond – The coupon rate equals the market required rate of return (P0 = Par).

Yield to maturity

Interest rate (or yield) risk

Interpolation:-

Estimate an unknown number that lies

somewhere between to unknown numbers.

For example:-

For example:-

The variation in market price of a security caused by changes in interest rates.

Determining the YTMDetermining the YTMJulie Miller want to determine the YTM for an issue of

outstanding bonds at Basket Wonders (BW). BW has an

issue of 10% annual coupon bonds with 15 years left to

maturity. The bonds have a current market value of $1,250.

What is the YTM?

Julie Miller want to determine the YTM for an issue of

outstanding bonds at Basket Wonders (BW). BW has an

issue of 10% annual coupon bonds with 15 years left to

maturity. The bonds have a current market value of $1,250.

What is the YTM?