# Lec 04-1

```CASH FLOW VALUATIONS
Means that at the end of every time period the cash
flow level or cash flow amount is different.
Example:
An investment returns 10000 after first year, 13000,
15000 & 18000 after 2nd to 4th year respectively. If the
prevailing interest is 10% what is the present value of
cash flow.
Equations:
FV = PV x (1 + r)t
PV = FV / (1 + r)t
YEAR
1
CASH
FLOW
10000
FVIF @
PV=
10%
Cash Flow / FVIF
=1.10
9,090.91
2
13000
=1.21
10,743.80
3
15000
=1.331
11,269.72
4
18000
=1.4641
12,294.24
TOTAL
56000
43,398.68
Effective Annual Rate – EAR
 EAR basically depend on Compounding
 More period of Compounding total interest
will be more
Effective Annual Rate – EA
Example:
Bank A pays 15% interest on deposit, that is
compounded monthly.
Bank B pays 15% interest on deposit, which is
compounded quarterly.
Bank C pays 15% interest on deposit, which is
compounded half yearly.
Formula to find EAR
Bank A (Monthly Compounding)
EAR = 1 + i/n
n
-1
Bank A = 1 + .15/12
12
=1.16075 – 1
= 16.075%
-1
• Bank B (Quarterly Compounding)
4
Bank B = 1 + .15/4 - 1
=(1.0375) 4 – 1
= 1.15865 – 1
= 15.865%
Bank C (Half Yearly Compounding)
Bank C = (1 + .15/2) 2 - 1
= (1.075) 2 - 1
= 1.155625 – 1
= 15.5625%
Example:
A bank offers 12% compounded quarterly. If you place
1000 in an account today, how much you have at the
end of two years?
What is EAR (Effective Rate of Interest)?
Solution:
EAR =(1 + i/n)
n
-1
EAR = (1 + .12/4)4 – 1= 12.55%
= (1.1255)2 X 1000 = 1266.75
OR
Quarterly interest is 12/4 = 3%
=(1.03)8 X 1000 = 1.2667 X 1000 =1266.77
BOND VALUATION
• It’s a debt security
• Whenever Company needs Capital, different sources
to raise Capital
IPO’s of Shares in Primary Market
Bank Loan
Bond Debt Financing (Different from bank loan)
• Bonds have maturity date
• Normally Bonds are Long Term like 10 years, 20
years & 30 years
Main Characteristics:
– How much Interest will be paid?
– How many times?
– Maturity
Terminologies:
• Coupon Payments: stated annual interest amount
e.g. A Bond which pays Rs. 100 every year. So
Coupon payment i.e. Rs. 100 per year.
• Coupon Rate:
• Coupon Interest Rate = Coupon Payment / Bond’s
face value
• Face value: Also Par value, shows the nomination
value.
• Maturity Date: date on which Companies pay back the
principal Investment.
• Discount Bond: A bond which is sold less than the
face or par value is discount bond. Also called Zero
Coupon Or Zeros.
• Premium Bond: A bond which has a price over and
above its face value or its par value is Premium Bond.
• Yield to Maturity (YTM): Interest rate required in
market on a bond.
Or
• A Market phenomenon, Interest rate on particular
Investment
• Current yield: Annual coupon payment(s) divided by
bond market price.
```