RAJARATA UNIVERSITY OF SRI LANKAFACULTY OF MANAGEMENT STUDIES

POSTGRADUAATE DIPLOMA IN MANAGEMENT (PGDM) LEADING TO THE DEGREE IN MBA.

PGDM 1213 – FINANCIAL MANAGEMENT

VALUATION CONCEPTSESSION 05

KGA UDAYA KUMARA

SENIOR LECTURER

DEPT. OF ACCOUNTANCY & FINANCE

FACULTY OF MANAGEMENT STUDIES

RAJARATA UNIVERSITY OF SRI LANKA

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Session Objectives

To understand

• The valuation of bonds

• The valuation of preferred stocks

• The valuation of common stocks

• The stock valuation models

• The characteristics of different types of stocks

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Fundamental Rule of Valuation

Value/Price = Present Value of the Future Cash Flows

The fundamental asset valuation model (FVM) defines the value of an asset in terms of the present value of all its expected future cash flows discounted at an appropriate rate of return.

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To construct a valuation model for any asset three critical components are required:

1 Estimates of the size or volumes of the expected future cash flow returns which the asset is expected to generate, and the bigger the expected cash flows are the better.

2 Estimates of the timings of the future cash flows as this will also affect their respective values—the sooner cash flows are received the more valuable they will be. Cash flows may occur over any time period, days, weeks, months or years and their patterns may be regular or erratic.

3 An estimate of the investor’s required rate of return from the prospective investment. This is the minimum rate of return that will entice the investor to undertake an investment given its level of risk. Required rates of return, as we know, can be determined using the capital asset pricing model (CAPM).

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Assumptions:

All the cash flows are known before handAll the cash flows will occur with certaintyThere are no information asymmetriesThere is no default

The value of an asset can be expressed in present value equation form as:

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V0 = value of the asset at the present time, time zero CFtt = cash flow expected at end of year tt = any year (t=1, 2,…, n)r = required rate of return/appropriate discount raten = asset’s expected life

Which from the time value of money concept you will remember is the same as:

V0=[CF1×(PVIFr,1)]+[CF2×(PVIFr,2)]+[CF3×(PVIFr,3)] +...+ [CFn×(PVIFr,n)]

Characteristics of Bond

• A bond is a security that obligates the issuer to make specified interest and principal payments to the holder on specified dates.– Coupon rate– Face value (or par value or redemption price)– Maturity date(or term)– Term to maturity (remaining time period to redeem)

– Required rate of return (expected return = r = k = Kb)

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Bond Valuation

It is understood that the value of an asset is the present value (PV) of the future cash flows

Cash flows of a bond; Coupon Payments Maturity PaymentHence value of bond/debenture is based on the PV of its coupon

payments and maturity value ( redemption payment)

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Bond Valuation Cont.

PVCF

kt

bt

t

n

( ),

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where n = Number of periods to maturity, CFt = Cash flow (interest and principal) received in period t, kb = Required rate-of-return for bond.

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Bond Valuation (Redeemable Bonds) .

It = Coupon payment, coupon rate X face value,

P = Principal amount (face value) of the bond,

n = Number of periods to maturity.

Kb = Required rate of return

PVI

k

P

kt

bt

bn

t

n

( ) ( ),

1 11

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Example

• Suppose a 20% coupon bond with par value of Rs. 1,000 is trading for Rs. 1,100. It matures in six years from now and pays the coupon annually. What would be the Bond price today if the annual expected rate of return on similar investment is 16%, 20% and 24%

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13

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Bond with semiannual coupon

What would be the price of the bond, if the bond receives its coupon semiannually in the above example ?

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16

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Bond Valuation (Irredeemable Bonds)

PV = I/ Kb

where,

PV = Value of the bond at time zero

I = Annual interest or coupon payment in time period t (t=1, 2, …, n.)

Kb = required rate of return/appropriate discount rate

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Example 1 —Valuing an irredeemable bondIf a bond has a par value of Rs.100, pays a coupon interest rate of 10per cent per year and the return currently required by investors in themarket on similar risk bonds is 8 per cent, the bond’s value will becalculated as:

Why bond prices vary?

• Bond prices can and do change frequently over their life spans• Bond prices can fluctuate quite dramatically• Most corporate bonds frequently traded in the markets• Buying and selling activities and market expectations will

cause prices and yields to change.

The price or value of bonds is influenced by two main factors:

1. Changes in the required rate of return which are in turn related to changes in the general level of interest rates; and

2. The time to maturity of the bond.

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Bond values and the required rate of return

Inverse relationship between a bond’s price and the required rate of return;

• as the required rate of return decreases, the bond’s value increases and

• as the required rate of return increases, the bond’s value decreases

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Graphical Illustration: Bond values and the required rate of return

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Relationship between bond value and the required rate of return

Coupon rate (%) Required rate of return (%)

Bond value (Rs.) (Trading position)

12 14 87.70 (Discount)

12 12 100.03 (Par)

12 10 115.17 (Premium)

12 09 124.23 (Premium)

Bond values and the time to maturity

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Required Rate of Return Time Time to Maturityto Maturity

10 15 20

(1) 9% 124.23 119.22 111.68

(2) 12% 100.00 100.00 100.00

(3) 14% 87.70 89.59 93.10

(4) Change in Value (1) – (2)

36.53 29.63 18.58

Graphical Illustration: Bond values and the time to maturity

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Yield To Maturity (YTM)

The yield to maturity is that interest rate that equates the present discounted value of all future payments to bondholders to the market price.

Ex: Suppose the price of a bond with Rs. 1,000 par value, which matures in 10 years with a coupon of 8%, is Rs. 875. What is YTM?

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If an investor buys a bond today at a quoted price in the secondary market and holds it until maturity, the compound rate of return the investor would earn on the investment is known as the bond’s yield to maturity (YTM).

Trial and error methodIf the bond is selling at a discount, YTM >coupon rateIf the bond is selling at a premium, YTM < coupon rate

• Since selling at a discount, YTM > coupon rate

Try 10%,

PV of Interests = 491.56

PV of Par value = 385.54

Price = 877.10

Try a higher rate, say 11%,

PV of Interests = 471.14

PV of Par value = 352.18

Price = 849.83

Repeat rate, between 10 and 10.5%27