# Lec 03 ```CORPORATE FINANCE
VALUATION OF FUTURE CASH FLOW
SCHEME OF STUDIES
THIS MODULE INCLUDES:
• TIME VALUE OF MONEY - BASICS
• DISCOUNTED CASH FLOW VALUATION
• BOND VALUATION
• COMMON STOCK VALUATION
CORPORATE FINANCE - MODULE # 2
VALUATION OF FUTURE CASH FLOW
TIME VALUE OF MONEY
FUTURE VALUE
PRESENT VALUE
ANNUITIES
PERPETUITIES
CORPORATE FINANCE - MODULE # 2
VALUATION OF FUTURE CASH FLOW
FUTURE VALUE
Depends on three factors
– Size of Investment
– Time Period
– Interest Rate
CORPORATE FINANCE - MODULE # 2
VALUATION OF FUTURE CASH FLOW
FUTURE VALUE
TIME VALUE DEFINED
– A dollar or Rupee received today is better than a
dollar or rupee to be received after a year. Why?
– Because the dollar or rupee received today will start
earning profit right from today
CORPORATE FINANCE - MODULE # 2
VALUATION OF FUTURE CASH FLOW
FUTURE VALUE
FV = (Investment, Time, Interest Rate)
This can be written as
FV = PV x (1 + r)t
(1 + r) t is known as Future Value Interest Factor
(FVIF)
r = Rate of Interest
t = Time period
CORPORATE FINANCE - MODULE # 2
VALUATION OF FUTURE CASH FLOW
Example
You invest Rs. 1000 today and will get Rs. 1100 at
the end of one year, if interest rate is 10% p.a.
= 1000 X (1 + 0.10)= 1100
At the end of second year your investment is worth:
1100 x (1 + 0.10) = 1210
Alternatively:
1000 x (1 + 0.10)2 = 1210
CORPORATE FINANCE - MODULE # 2
VALUATION OF FUTURE CASH FLOW
COMPOUND INTEREST
• After One year:
– 1000 X (1.10) = 1100
• After two years:
– 1100 X (1.10) = 1210
At the end of 2nd year total Investment 1210 that means
we earned 210 in terms of Interest.
210 = 100+100+10
10 is basically Compound Interest
CORPORATE FINANCE - MODULE # 2
VALUATION OF FUTURE CASH FLOW
COMPOUND INTEREST
This 1210 has four parts:
– 1000 original investment
– 100 interest – 1 year
– 100 interest – 2 year
– 10 interest on Year 1 interest
Earning interest on interest is know as compounding
Interest over period is reinvested to earn more
interest.
CORPORATE FINANCE - MODULE # 2
VALUATION OF FUTURE CASH FLOW
LONG PERIOD EXAMPLE : (Future Value)
An investment opportunity pays 12% pa and a business
entity intends to invest 500,000. What will be the worth
of this investment in 7 years time? How much interest
will the company earn in this period? What portion of
total interest represents compound interest?
CORPORATE FINANCE - MODULE # 2
VALUATION OF FUTURE CASH FLOW
Solution
Worth after 7 years:
FV = PV x (1 + r)t
FV =500000 x (1.12)7 =1105350
(1.12)7 = 2.2107
CORPORATE FINANCE - MODULE # 2
VALUATION OF FUTURE CASH FLOW
2nd Question: How much Interest will the
Company earn in this period?
Total interest earned:
1105350 – 500000 = 605350
Compound Interest:
500000 x 12% x 7 = 420000
=605350 – 420000 = 185350
CORPORATE FINANCE - MODULE # 2
VALUATION OF FUTURE CASH FLOW
PRESENT VALUE
You know that you will get 10000 at the end of 3rd
year from now. The interest rate is 10%. What is the
PV of 10000 now?
FV = PV x (1+r)3
10000= PV x (1.10)3
PV = 10000/ (1.10)3= 7513.14
CORPORATE FINANCE - MODULE # 2
VALUATION OF FUTURE CASH FLOW
We can find PV the other way too:
PV = FV / (1 + r)t
1 / (1.10)3 = known as PVDF
PV = FV X PVDF
PV = 10000 X 0.7513*
= 7513
* From table A-3
CORPORATE FINANCE - MODULE # 2
VALUATION OF FUTURE CASH FLOW
Comparison between two options
Option 1= Pay 4000 today and 6000 after 2 years to buy a
computer
Option 2= Pay all today and get a credit of 500. (Net price
today is 9500)
• Interest rate is 10% at present.
• Which option is better?
CORPORATE FINANCE - MODULE # 2
VALUATION OF FUTURE CASH FLOW
Option 1:
Finding PV:
PV = 4000 + (6000 / (1.10)2
PV = 4000 + 4958.68 = 8958.68
It means that 4958.68 invested today @ 10% will
yield 6000 at the end of year 2, enabling you to pay
CORPORATE FINANCE - MODULE # 2
VALUATION OF FUTURE CASH FLOW
Option 2:
PV = 9500
Option 1 is better because it cost 8958.68 as
compared to 9500 of option 2.
CORPORATE FINANCE - MODULE # 2
VALUATION OF FUTURE CASH FLOW
• So far we come across four factors of Time
•
•
•
•
Value of Money:
PV
FV
Interest factor or discount factor
Time period
• Given three we can find the fourth.
CORPORATE FINANCE - MODULE # 2
VALUATION OF FUTURE CASH FLOW
Finding interest rate
• An opportunity requires 1000 investment today
that will double at the end of 8th year. What is
the implicit interest rate?
PV = FV / (1 +r)8
1000 = 2000 / (1 +r)8
(1 +r)8 = 2000/1000
(1 +r)8 = 2
CORPORATE FINANCE - MODULE # 2
VALUATION OF FUTURE CASH FLOW
Finding interest rate
(1 +r)8 = 2
1+ r = (2)1/8
1+r = (2)0.125
1+r = 1.09
r = 1.09 – 1
r = 0.09 or 9%
CORPORATE FINANCE - MODULE # 2
VALUATION OF FUTURE CASH FLOW
Three Ways to Solve:
– Mathematical Equation
– Financial Calculator
– Time Value of Money Tables
• Look FV table 8 year row select and move
towards right unless under the interest Rate
%age you read 2 or nearest to 2.
• Implicit Interest Rate = 9%
CORPORATE FINANCE - MODULE # 2
VALUATION OF FUTURE CASH FLOW
PERPETUITY
Defined: Stream of equal cash payments equally
spaced that continues for ever.
If you wish to help a welfare trust by providing
100,000/- per annum forever and the interest rate is
10%, how much amount must be set-aside today?
Formula:
PV of Perpetuity = C/r
= 100000/0.10
= 1,000,000/-
CORPORATE FINANCE - MODULE # 2
VALUATION OF FUTURE CASH FLOW
• And if you wish to start payments after 3rd year,
then what is the PV of this delayed Perpetuity?
• PV of Delayed Perpetuity = C/r (1+r)^t
=100,000 / 0.1(1.10)3
= 751,315
CORPORATE FINANCE - MODULE # 2
VALUATION OF FUTURE CASH FLOW
ANNUITIES
Series of equal amount and equally spaced payments for
limited period of time but not unlimited.
Valuation of Annuities:
• Using FV/PV tables
• Using formula
CORPORATE FINANCE - MODULE # 2
VALUATION OF FUTURE CASH FLOW
Example:
cost you 4000 per year for next three years.
Assume interest rate of 10%. Find out the PV of this
annuity?
Using table
4000 x 1/(1.10)
4000 x 1/(1.10)2
4000 x 1/(1.10)3 = 9947.41
CORPORATE FINANCE - MODULE # 2
VALUATION OF FUTURE CASH FLOW
Using Formula:
PV= Annuity x 1/0.1 – 1/ 0.10(1.10)3
PV = 4000 x {10 – 1/0.1331}
PV = 4000 x {10 – 7.513}
= 4000 x 2.4869 = 9947.60
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