Financial Management

Unit 4

Unit 4
4.1 Introduction 4.2 Valuation of Bonds Types of Bonds 4.2.1 Irredeemable or Perpetual Bonds

Valuation Of Bonds And Shares

4.2.2 Redeemable or Bonds with Maturity Period 4.2.3 Zero Coupon Bond Bond­yield Measures 4.2.1 Holding Period Rate of Return 4.2.2 Current Yield 4.2.3 Yield to Maturity (YTM) 4.2.4 Bond Value Theorems 4.3 Valuation of Shares 4.3.1 Valuation of Preference Shares 4.3.2 Valuation of Ordinary Shares 4.4 Summary Solved Problems Terminal Questions Answers to SAQs and TQs

4.1

Introduction

Valuation is the process of linking risk with returns to determine the worth of an asset. Assets can be real or financial; securities are called financial assets, physical assets are real assets. The ultimate goal of any individual investor is maximization of profits. Investment management is a continuous process requiring constant monitoring. The value of an asset depends on the cash flow it is expected to provide over the holding period. The fact that as on date there is no method by which prices of shares and bonds can be accurately predicted should be kept in mind by an investor before he decides to take an investment decision. The present chapter will help us to know why some

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securities are priced higher than others. We can design our investment structure by exploiting the variables to maximize our returns. Ordinary shares are riskier than bonds or debentures and some shares are more risky than others. The investor would therefore commit funds on a share only if he is convinced about the rate of return being commensurate with risk.

Learning Objectives: After studying this unit, you should be able to understand the following. 1. Know the meaning of value as used in Finance Theory. 2. Understand the mechanics of Bond valuation, and 3. Understand the mechanics of valuation of equity shares.

Concept of Intrinsic value: A security can be evaluated by the series of dividends or interest payments receivable over a period of time. In other words, a security can be defined as the present value of the future cash streams – the intrinsic value of an asset is equal to the present value of the benefits associated with it. The expected returns (cash inflows) are discounted using the required return commensurate with the risk. Mathematically, it can be represented by:
1 2 3 n V0=C1/(1+i) + C2/(1+i) + C3/(1+i) + Cn/(1+i) n = Cn/(1+i)

Where V0=Value of the asset at time zero (t=0) P0=Present value of the asset Cn=Expected cash flow at the end of period n i=Discount rate or required rate of return on the cash flows n=Expected life of an asset.

Example: Assuming a discount rate of 10% and the cash flows associated with 2 projects A and B over a 3 year period, determine the value of the assets.

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Year 1 2 3 Solution:

Cash flows Cash flows of A(Rs.) of B(Rs) 20000 20000 20000 10000 20000 30000

Value of asset A= 20000 PVIFA(10%,3y) =20000*2.487 =Rs. 49470 Value of asset B=10000PVIF(10%,1) + 20000PVIF(10%,2) + 30000PVIF (10%,3) =10000*0.909 + 20000*0.826 + 30000*0.751 =9090+16520+22530 =Rs. 48140 Example: Calculate the value of an asset if the annual cash inflow is Rs. 5000 per year for the next 6 years and the discount rate is 16%. Solution: n Value of the asset= Cn/(1+i) 6 =5000/(1+0.16)

Or

=5000PVIFA(16%, 6y) =5000*3.685 =Rs. 18425

4.1.1 Concepts of Value Book value: Book value is an accounting concept. Value is what an asset is worth today in terms of their potential benefits. Assets are recorded at historical cost and these are depreciated over years. Book value may include intangible assets at acquisition cost minus amortized value. The book value of a debt is stated at the outstanding amount. The difference between the book value of assets and liabilities is equal to the shareholders’ net worth. (Net worth is the sum total of paid­up capital and reserves and surplus). Book value of a share is calculated by dividing the net worth by the number of shares outstanding.
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Replacement value is the amount a company is required to spend if it were to replace its existing assets in the present condition. It is difficult to find cost of assets presently used by the company. Liquidation value is the amount a company can realize if it sold the assets after the winding up of its business. It will not include the value of intangibles as the operations of the company will cease to exist. Liquidation value is generally the minimum value the company might accept if it sold its business. Going concern value is the amount a company can realize if it sells its business as an operating one. This value is higher than the liquidation value. Market value is the current price at which the asset or security is being sold or bought in the market. Market value per share is generally higher than the book value per share for profitable and growing firms. 4.2

Valuation of Bonds

Bonds are long term debt instruments issued by government agencies or big corporate houses to raise large sums of money. Bonds issued by government agencies are secured and those issued by private sector companies may be secured or unsecured. The rate of interest on bonds is fixed and they are redeemable after a specific period. Some important terms in bond valuation: Face value: Also known as par value, this is the value stated on the face of the bond. It represents the amount that the unit borrows which is to be repaid at the time of maturity, after a certain period of time. A bond is generally issued at values such as Rs. 100 or Rs. 1000. Coupon rate is the specified rate of interest in the bond. The interest payable at regular intervals is the product of the par value and the coupon rate broken down to the relevant time horizon. Maturity period refers to the number of years after which the par value becomes payable to the bond­holder. Generally, corporate bonds have a maturity period of 7­10 years and government bonds 20­25 years. Redemption value is the amount the bond­holder gets on maturity. A bond may be redeemed at par, at a premium (bond­holder gets more than the par value of the bond) or at a discount (bond­holder gets less than the par value of the bond).

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Market value is the price at which the bond is traded in the stock exchange. Market price is the price at which the bonds can be bought and sold and this price may be different from par value and redemption value. Types of Bonds Bonds are of three types: (a) Irredeemable Bonds (also called perpetual bonds) (b) Redeemable Bonds (i.e., Bonds with finite maturity period) and (c) Zero Coupon Bonds. 4.2.1 Irredeemable Bonds or Perpetual Bonds Bonds which will never mature are known as irredeemable or perpetual bonds. Indian Companies Acts restricts the issue of such bonds and therefore these are very rarely issued by corporates these days. In case of these bonds the terminal value or maturity value does not exist because they are not redeemable. The face value is known; the interest received on such bonds is constant and received at regular intervals and hence the interest receipts resemble a perpetuity. The present value (the intrinsic value) is calculated as: V0=I/id If a company offers to pay Rs. 70 as interest on a bond of Rs. 1000 par value, and the current yield is 8%, the value of the bond is 70/0.08 which is equal to Rs. 875 4.2.2 Redeemable Bonds : There are two types viz.,bonds with annual interest payments and bonds with semi­annual interest payments. Bonds with annual interest payments; Basic Bond Valuation Model: The holder of a bond receives a fixed annual interest for a specified number of years and a fixed principal repayment at the time of maturity. The intrinsic value or the present value of bond can be expressed as: n n n V0 or P0=∑ t=1 I/(I+kd) +F/(I+kd)

Which can also be stated as folloows V0=I*PVIFA(kd, n) + F*PVIF(kd, n) Where V0= Intrinsic value of the bond
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P0= Present Value of the bond I= Annual Interest payable on the bond F= Principal amount (par value) repayable at the maturity time n= Maturity period of the bond Kd= Required rate of return Example: A bond whose face value is Rs. 100 has a coupon rate of 12% and a maturity of 5 years. The required rate of interest is 10%. What is the value of the bond? Solution: Interest payable=100*12%=Rs. 12 Principal repayment is Rs. 100 Required rate of return is 10% V0=I*PVIFA(kd, n) + F*PVIF(kd, n) Value of the bond=12*PVIFA(10%, 5y) + 100*PVIF(10%, 5y) = 12*3.791 + 100*0.621 = 45.49+62.1 = Rs. 107.59 Example: Mr. Anant purchases a bond whose face value is Rs. 1000, maturity period 5 years coupled with a nominal interest rate of 8%. The required rate of return is 10%. What is the price he should be willing to pay now to purchase the bond? Solution: Interest payable=1000*8%=Rs. 80 Principal repayment is Rs. 1000 Required rate of return is 10% V0=I*PVIFA(kd, n) + F*PVIF(kd, n)

Value of the bond=80*PVIFA(10%, 5y) + 1000*PVIF(10%, 5y) = 80*3.791 + 1000*0.621 = 303.28 + 621 =Rs. 924.28

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This implies that the company is offering the bond at Rs. 1000 but is worth Rs. 924.28 at the required rate of return of 10%. The investor may not be willing to pay more than Rs. 924.28 for the bond today. Bond Values with Semi­Annual Interest payment: In reality, it is quite common to pay interest on bonds semi­annually. With the effect of compounding, the value of bonds with semi­annual interest is much more than the ones with annual interest payments. Hence, the bond valuation equation can be modified as: n n 2n V0 or P0=∑ t=1 I/2/(I+id/2) +F/(I+id/2)

Where V0=Intrinsic value of the bond P0=Present Value of the bond I/2=Semi­annual Interest payable on the bond F=Principal amount (par value) repayable at the maturity time 2n=Maturity period of the bond expressed in half­yearly periods kd/2=Required rate of return semi­annually. Example: A bond of Rs. 1000 value carries a coupon rate of 10%, maturity period of 6 years. Interest is payable semi­annually. If the required rate of return is 12%, calculate the value of the bond. Solution: n n 2n V0 or P0=∑ t=1 (I/2)/(I+kd/2) +F/(I+kd/2) 6 6 =(100/2)/(1+0.12/2) + 1000/(1+0.12/2)

=50*PVIFA(6%, 12y) + 1000*PVIF(6%, 12y) =50*8.384 + 1000*0.497 =419.2 + 497 =Rs. 916.20 It is to be kept in mind that the required rate of return is halved (12%/2) and the period doubled (6y*2) as the interest is paid semi­annually. 4.2.3 Valuation of Zero Coupon Bonds. In India Zero coupon bonds are alternatively known as Deep Discount Bonds. For close to a decade, these bonds became very popular in India because of issuance of such bonds at regular intervals by IDBI and ICICI. Zero­coupon bonds have no coupon rate, i.e. there is no interest to be

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paid out. Instead, these bonds are issued at a discount to their face value, and the face value is the amount payable to the holder of the instrument on maturity. The difference between the discounted issue price and face value is effective interest earned by the investor. They are called deep discount bonds because these bonds are long term bonds whose maturity some time extends up to 25 to 30 years. Example: River Valley Authority issued Deep Discount Bond of the face value of Rs.1,00,000 payable 25 years later, at an issue price of Rs.14,600. What is the effective interest rate earned by an investor from this bond? Solution: The bond in question is a zero coupon or deep discount bond. It does not carry any coupon rate. Therefore, the implied interest rate could be computed as follows: Step 1. Principal invested today is Rs.14600 at a rate of interest of “r”% over 25 years to amount to Rs.1,00,000. n Step 2. It can be stated as A = P0 (1+r) 25 1,00,000 = 14,600 (1+r)

Solving for ‘r’, we get

25 1,00,000/14600 = (1+r) 25 6.849 = (1+r)

Reading the compound value (FVIF) table, horizontally along the 25 year line, we find ‘r’ equals 8%. Therefore, bond gives an effective return of 8% per annum.

4.2.4

Bond­yield Measures

4.2.4.1 Current Yield: Current yield measures the rate of return earned on a bond if it is purchased at its current market price and the coupon interest received. Current Yield = Coupon Interest / Current Market Price Example: Continuing with the same example above calculate the CY if the current market price is Rs. 920

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Solution: CY=Coupon Interest / Current Market Price =80/920 =8.7% 4.2.4.2 Yield to Maturity (YTM) It is the rate earned by an investor who purchases a bond and holds it till its maturity. The YTM is the discount rate equaling the present values of cash flows to the current market price. Example: A bond has a face value of Rs. 1000 with a 5 year maturity period. Its current market price is Rs. 883.4. It carries an interest rate of 6%. What shall be the rate of return on this bond if it is held till its maturity?

Solution: n n n V0 or P0=∑ t=1 I/(I+kd) +F/(I+kd)

OR V0=I*PVIFA(kd, n) + F*PVIF(kd, n) = 60*PVIFA(Kd, 10) + 1000*PVIF(Kd,10)=883.4 We obtain 10% for kd Example: A bond has a face value of Rs. 1000 with a 9 year maturity period. Its current market price is Rs. 850. It carries an interest rate of 8%. What shall be the rate of return on this bond if it is held till its maturity? Solution: n n n V0 or P0=∑ t=1 I/(I+kd) +F/(I+kd)

OR V0=I*PVIFA(kd, n) + F*PVIF(kd, n) =80*PVIFA(Kd%, 9) + 1000*PVIF(Kd%, 9)=850 To find out the value of Kd, trial an error method is to be followed. Let us therefore start the value of Kd to be 12% and the equation now looks like =80*PVIFA(12%, 9) + 1000*PVIF(12%, 9)=850 Let us now see if LHS equals RHS at this rate of 12%. Looking at the tables we get LHS as

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80*5.328 + 1000*0.361=Rs. 787.24 Since this value is less than the value required on the RHS, we take a lesser discount rate of 10%. At 10%, the equation is =80*PVIFA(10%, 9) + 1000*PVIF(10%, 9)=850 Let us now see if LHS equals RHS at this rate of 11%. Looking at the tables we get LHS as 80*5.759 + 1000*0.424=Rs. 884.72 We now understand that Kd clearly lies between 10% and 12%. We shall interpolate to find out the true value of Kd. 10% + {(884.72­850)/(884.72­787.24)}*(12%­10%) 10% + (34.72/97.48)*2 10% + 0.71 Therefore Kd=10.71% An approximation: The following formula may be used to get a rough idea about Kd as Trial and Error Method is a very tedious procedure and requires lots of time. This formula can be used as a ready reference formula. YTM={I+(F­P)/n} / {(F+P)/2} Where YTM =Yield to Maturity I=Annual interest payment F=Face value of the bond P=Current market price of the bond n=Number of years to maturity. Example: A company issues a bond with a face value of 5000. It is currently trading at Rs. 4500. The interest rate offered by the company is 12% and the bond has a maturity period of 8 years. What is YTM? Solution: YTM={I+(F­P)/n} / {(F+P)/2} = 600 + {(5000­4500)/8} / {(5000+4500)/2} ={600 + 62.5} / 4750 = 13.94%

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4.2.5 Bond Value Theorems The following factors affect the bond values: · · · Relationship between the required rate of interest (Kd) and the discount rate. Number of years to maturity. YTM

Relationship between the required rate of interest (Kd) and the discount rate: · · · When Kd is equal to the coupon rate, the intrinsic value of the bond is equal to its face value, that is, if Kd=coupon rate, then value of bond=face value. When Kd is greater than the coupon rate, the intrinsic value of the bond is less than its face value, that is, if Kd>coupon rate, then value of bond