valuation of securities
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Valuation of Securities – Part ONE
By,Kaushal Mandalia
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Time Value of Money
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Simple Interest V/s Compound Interest
• Simple Interest• Compound Interest : Interest on Interest.• E xample• Fixed Deposit : Rs 5,00,000• Tenure : 3 Years• Interest Rate : 10% • Find Maturity Value in case of Simple and Compound
Interest
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Four Important Calculation
• Future Value of Single Amount• Present Value of Single Amount• Future Value of Annuity• Present Value of Annuity
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Future Value of Single Amount• How much something is worth in future….
• E xample• Mr Shah has invested Rs 10
Lac in Fixed Maturity Plan for 2 years which give s guaranteed return of 12% compounded annually. What is the maturity value of Mr Shah’s Investment?
Ans : Rs 12,54,400S
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Excel Sheet Calculation
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Present Value of Future Sum
• Present Value is a synoname for Valuation
Example Mr Sharma wants Rs 1 Crore when he turns 55 years. He wishes to invest in Reliance Industries Share which is going to give 25% compounding annualized return. Mr Sharma’s current age is 51 years. Find out the amount that Mr sharma need to Invest Today.
Example Mr Ambani invested in a bond whose Valuation After one year is Rs 15000. The interest rate on the bond is 10%. Find out the amount Mr Ambani has invested today.
Ans : 40,96,000
Ans : 13,636
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Future Value of Annuity
Rs 10,000 Rs 10,000 Rs 10,000 Rs 10,000 Rs 10,000 Rs 10,000 Rs 10,000 Rs 10,000
Future ValueOf Annuity
Annuity
Future value of Series of Equal Payment at definite interval.
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Future Value of Annuity
Example Mr. Nair is a government servant and expected to get retired at the age of 58. His contribution to Provident Fund (PF) Account every year at the end of year is Rs 70000. He is getting 9% Compounded annualized return on his PF Account. What is the Future Value (Maturity Value) of this account when Mr. Nair is retired. Currently Mr. Nair is 42 Years old.
Example Mr. Lakhani wishes to Invest 10 Lacs every year for next two years at the end of each year. He is expecting 15% interest (compounded annualized). What is the future value of this investment? Ans : 21,50,000
Ans : 23,10,238
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Future Value of Annuity
NperIt is the total no of payment periods in the investment
PmtIt is the payment made each period. It cant change over the life of investment
PV : Assume as ZERO
Type 1 : Payment at the beginning of period0 : payment at the end of the period.
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Future Value of growing Annuity
Example Find the Future value of Rs 1 lac which is growing at a rate of 5% every year. The expected interest rate is 10% and tenure of investment is 8 years.
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Present Value of Annuity
• It is used in the valuation of Bond, Securities and Preference Shares.
ExampleFind Present Value of Annuity whereMr Sharma is investing 1 lac every year for next 8 years at the end of year.Assumed Interest rate is 10% compounded annually.
Ans : 533492
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PV : Excel Calculation
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PV : examples
ExampleFace Value of 10% Annual, 2 year bond is Rs 100. Find the valuation of Bond if discount rate is 6%. At the end of 2 years, bond will be redeemed at face value.
ExampleMr Sharma is investing in share of Wipro Ltd. Current Market Price of Wipro is Rs 500, Face value is Rs 10. Analyst has estimated that wipro will give 250% dividend every year and share price at the end of 8 years will be Rs 650. Should Mr Sharma invest in Wipro for 8 years? Assume discounting rate as 7%
Ans : 107.33
Ans : Yes, 527.59
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PV : examples
1. As a General Manager, Gujarat Venture Finance Ltd (GVFL), you have received a project from Suzlon Pvt Ltd to open a wind farm at Rajasthan. They wish to have 10 windmills. Each windmill is costing about 5 Crore. Each windmill generates electricity worth Rs 10 Lacs every month. The life of each Windmill is 8 years. The scrap value of each Windmill is Rs 50 Lacs. Suzlon Pvt Ltd requested GVFL to become his investment partner and invest Rs 50 crore. As a general manager of GVFL what should be your decision assuming 7% as discount rate?
2. Mr Suri is planning to buy a dream home. The cost of the home is Rs 30 Lacs. Before applying to loan Mr Suri has analyzed his cash flow and found that he is comfortable paying rs 25000 as EMI for next 15 years. The interest rate on the loan is 9%. Find out how much loan amount Mr Suri can afford?
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Bond Valuation.
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Terminology
Par ValueThe Value Stated on the face of Bond is called as Face Value.
Coupon RateBond carries a specific interest rate which is called the coupon rate.
Maturity PeriodThe maturity of a bond indicates the length of time until the bond issuer returns the par value to the bond holder and terminates or redeems the bond.
Current YieldThe current yield on a bond refers to the ratio of the annual interest payment to the current market price .
Yield to MaturityThis is the rate of return that investors earn if they buy the bond at a specific price and hold it until maturity.
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Type of Risk Associated with Bond
Interest Rate Risk The interest rate in market changes over time, and an increase in interest rate leads to a decline in the value of outstanding bonds. This risk of a decline in bond values due to rising interest rate is called Interest Rate Risk.
Reinvestment Rate RiskAs Interest rate in market changes over time, any decrease in interest rate may cause a company to exercise its call option for the bonds issued with call option. The bond holders will have to replace his high income bonds with low income bonds. This risk of fall in income due to fall in market interest is called as Reinvestment Rate Risk.
Default RiskThis risk occur when issuer of bonds default either in payment of Interest or Principal amount.
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Accrued Interest
C1 C2 C3 C4
Accrued Interest =C
m
Dj
Td
C = Coupon Paymentm = No of coupon payment in a yearDj = No of days since last coupon paymentTd = Total no of days between two coupon payment
Accrued interest is that part of the interest which is yet to be paid to bondholders, but has been earned since the last payment date
ExamplesEssar Oil pays 12 percent per annum quarterly interest rate due every
March, June, Sept and Dec end. The quoted price in the market is Rs 86 on Jan 24, 2003. Determine the accrued interest as on this date?
Ans : 0.74
Hotel Lee’s 10% per annum half yearly interest rates are due every March and SEpt end and has a current quoted price of Rs 44 on Feb 3. What should be the price at which the debenture will be exchanged in the market on this date?
Ans : 3.46
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Yield to Maturity
YTM = C + F - P
P n X P
C = coupon paymentF = face value of bondP = clean pricen = No of years to maturity
Example1. Kanika buys 5 year, 7% bond at Rs 99.48. What is the simple yield to maturity?
Face value of bond is Rs 100. Ans: 7.15%
2. What is simple yield to maturity for 10 year, 9% bond bought at Rs 108.32? Face value Rs 100. Ans : 7.54%
3. Find YTm for 15 year, 12% bond which is bought at Rs 112.45 with 5 years maturity. Ans : 8.46%
4. Deepa buys 10 year, 8% bond with six months to maturity at Rs 99.89. Find YTm. Ans : 8.23%
Examples
1. A rs 100 par value bond bearing a coupon rate of 12% will mature after 5 years. What is the value of bond, if discount rate is 15%?
2. The market price of Rs 1000 par value bond carrying coupon rate of 14% and maturing after 5 years is Rs 1050. What is YTM?
3. A Rs 100 par value bond bears a coupon rate of 14% and matures after 5 years. Interest is payable semi annually. Compute the value of bond if the required rate of return is 16%?
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LAns1) 89.922) 12.6%3) 93.27
Stock Valuation.
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Share Valuation1. Earning Valuation
• Price Earning Ratio2. Revenue Valuation
• Price to Sales Ratio = MCAp / One yr total revenue3. Cash Flow Valuation
• EBDIT• Free Cash Flow = Operational cash Flow – Capital
Exp4. Asset Valuation
• Book Value• Price to Book Value• Return on Equity
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Valuation of Equity Share
Equity share valuation is comparatively a difficult task because of following reasons –
1. Rate of dividend is not known and certain. Dividend payment is discretionary. Therefore the forecast of cash flows is not certain and difficult to make.
2. Earnings & Dividends on equity shares are expected to grow.
Valuation Models for Equity Share Valuation
Dividend Discount ModelUnder this model ,the price paid for shares today will be the present value of dividend stream receivable in Future and any amount which will be realized after sale of shares.
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Single Period Valuation Model
ASSUMPTIONS• Dividends are paid annually.• The first dividend will be received one
year after the equity share is purchased.• The share is held only for one year.
P0D1
(1+r)
P1
(1+r)+=
P0 = Current Price of Equity ShareD1 = Dividend expected a year henceP1 = Price of the share expected a year henceR = rate of return required on equity share
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Example• Prestige’s equity share is expected to
provide a dividend of Rs 2.00 and fetch a price of Rs 18.00 a year hence. What price would it sell for now if the investor’s required rate of return is 12%
Ans : Rs 17.86
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Constant Growth Model
• What happens if the price of the equity share and dividend is expected to grow at a rate of g percent annually? The formula is…..
P0D1
r - g=
• Example – The expected dividend per share of XYZ Ltd is Rs 2.00. The dividend per share has grown over the past five years at the rate of 5% pa. This growth will continue in future. The market price of the equity share is also expected to grow at the same rate. What is a fair estimate of the intrinsic value of the equity share if the required rate of return is 15%
Ans : Rs 20.00
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Expected Rate of Return
rD1
P0 + g=
• Example – The expected dividend per share of Vaibhav Ltd is Rs 5.00. The dividend is expected to grow at the rate of 6%pa. If the price per share now is Rs 50.00, what is the expected rate of return?
Ans : 16%
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Multi Period Valuation Model
With no fixed ,pre determined maturity period
dividend stream may be of infinite duration. In
this case P0 will be computed differently.
P0 =
t = 1
n
D1
(1+r) tPn
(1+r) n+
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Zero Growth Model
Dividend Remains same throught the period perpatually..
P0
D
r=
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Multi Period Growth Model
• Normally applicable to relatively young and fast growing firms who do not pay steady dividend. The dividend profile looks like below..
Example
• Lets imagine that a high tech firm’s earnings are growing @ 50% a year, which is not uncommon for such companies, if this rate is assumed to last forever, what should be the fair valuation of stock if the discount rate is 25% and Dividend at the end of year 1 is Rs 10 per share.
P0
D1
r - g=
Negative price is not realistic…… hence some correction is needed.
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Limitation of earlier models
• No firm can sustain high growth rate until infinity since competition will soon jump in and erode sales growth and profitability.
• Little or no dividend in early years. • In order to handle this situation, researchers relaxed the
constant growth assumption and came up with multi period growth model for stock valuation
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Multi Period Valuation Model
• Since no firm can grow at an extraordinarily high rate forever, the model splits the life of firm into two phases
1. The early Years,2. The maturity or steady state years.
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Multi Period Valuation Model
Multi Period Valuation Model
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Example• Pepsico Beverage has just introduced a new flavor in the
market. Pepsico’s earning and dividend is expected to grow at 30% pa during next four years, after which they are expected to stabilize at 6% a year. The most recent dividend paid was Rs 3 per share. Analysts have estimated that given the risk of the stock, a discount rate of 14% is appropriate for discounting Pepsico’s future dividends. What is the fair value of stock?
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Example• XYZ Ltd, has just been listed on NYSE. They went public
this year only. XYZ is not expected to pay any dividend for next three years. It is expected to pay Rs 0.50 in forth year and 0.75 in fifth year. Beginning sixth year, its dividend will grow at a constant 5% annually. Given a discount rate of 18% what is the fair value of stock today?
Ans : Rs 3.24
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