3. Simple Interest V/s Compound
Interest
• Simple Interest
• Compound Interest : Interest on Interest.
• Example
• 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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4. 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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5. Future Value of Single Amount
• How much something is worth in future….
• Example
• Mr Shah has invested Rs 10
Lac in Fixed Maturity Plan for
2 years which gives
guaranteed return of 12%
compounded annually. What
is the maturity value of Mr
Shah’s Investment?
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7. Present Value of Future Sum
• Present Value is a synoname for Valuation
Example
Mr Sharma wants Rs 1 Crore
Example
when he turns 55 years. He
Mr Ambani invested in a bond
wishes to invest in Reliance
whose Valuation After one
Industries Share which is going
year is Rs 15000. The interest
to give 25% compounding
rate on the bond is 10%. Find
annualized return. Mr Sharma’s
out the amount Mr Ambani
current age is 51 years. Find out
has invested today.
the amount that Mr sharma
Ans : 13,636
need to Invest Today. L
Ans : 40,96,000 M LEARNING
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8. 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
Annuity Future
Value
Of
Future value of Series of Equal Payment at definite interval. Annuity
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9. Future Value of Annuity
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
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.
Ans : 23,10,238
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10. Future Value of Annuity
Nper
It is the total no of payment
periods in the investment
Pmt
It 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
period
0 : payment at the end of the
period.
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11. 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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12. Present Value of Annuity
• It is used in the valuation of Bond,
Securities and Preference Shares.
Example
Find Present Value of Annuity
where
Mr 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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13. PV : Excel Calculation
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14. PV : examples
Example
Face 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.
Ans : 107.33
Example
Mr 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 : Yes, 527.59
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15. 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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17. Terminology
Par Value
The Value Stated on the face of Bond is called as Face Value.
Coupon Rate
Bond carries a specific interest rate which is called the coupon rate.
Maturity Period
The 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 Yield
The current yield on a bond refers to the ratio of the annual interest
payment to the current market price .
Yield to Maturity
This 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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18. 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 Risk
As 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 Risk
This risk occur when issuer of bonds default either in payment of Interest or Principal
amount.
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19. Accrued Interest
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
C1 C2 C3 C4
C Dj C = Coupon Payment
Accrued Interest = m = No of coupon payment in a year
m Td Dj = No of days since last coupon payment
Td = Total no of days between two coupon payment
20. Examples
Essar 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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21. Yield to Maturity
C = coupon payment
F = face value of bond
YTM = C + F-P P = clean price
n = No of years to maturity
P nXP
Example
1. 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%
22. 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%?
Ans
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24. Share Valuation
1. Earning Valuation
• Price Earning Ratio
2. Revenue Valuation
• Price to Sales Ratio = MCAp / One yr total revenue
3. Cash Flow Valuation
• EBDIT
• Free Cash Flow = Operational cash Flow – Capital
Exp
4. Asset Valuation
• Book Value
• Price to Book Value
• Return on Equity
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25. 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 Model
Under 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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26. 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.
D1 P1 P0 = Current Price of Equity Share
P0 = + D1 = Dividend expected a year hence
(1+r) (1+r) P1 = Price of the share expected a year hence
R = rate of return required on equity share
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27. 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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28. 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…..
• 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 D1
the rate of 5% pa. This growth will continue in future. The market
P0 =
price of the equity share is also expected to grow at the same r-g
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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29. Expected Rate of Return
D1
r =
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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30. 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.
n
D1 Pn
P0 = +
(1+r) t (1+r) n
t=1
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31. Zero Growth Model
Dividend Remains same throught the period perpatually..
D
P0 =
r
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32. 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..
33. 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.
D1
P0 =
r-g
Negative price is not realistic…… hence some correction is needed.
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34. 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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35. 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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38. 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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41. 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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42. LearningMadeSimpleTM
Learning Made Simple is initiative taken by few people
earlier related to the Corporate World whose aim is to
provide quality education and training to those who
wish to excel in their career path. Learning Made
Simple is an association who works on a no profit no
loss basis and provide training and development in the
era of Financial Planning, Financial Management,
AMFI, NCFM, Management Concepts, Soft Skills,
Leadership, Personality Development, Goal Setting,
Marketing Management, Behavioral Science, NLP and
various other segments. You can get in touch with us
by sending email on
kaushal@thefinancialplanners.in
