Finance:- The Economics of allocating resources across time or
reallocation of recourses in time, Such as borrowing and Lending
money raising capital. Financial Investment:- Borrowing / Lending /
Buying shares etc ( Needs provision of funds) *Real Assets
Investment Building factories, buying equipment to be used in
production. (needs information) that financial markets provide to
interested investors. *Financial Markets allow participants to
reallocate resources across time Slide 2 The Present Value
(Discount value) : amount of money you must invest or lend at the
present time to end up with a particular amount of money in the
future. M.B. finding a present value of future cash flow is called
discounting cash flow. -Present value is an accurate representation
of what the financial market does when it sets a price on a
financial asset. *Opportunity costs : alternative to buying certain
security or doing certain investment. Slide 3 (The Cost OF Doing
This Instead) Of Something Else (Opportunity Foregone) *Present
Wealth:- Present value of all present and future resources (cash
Flow). Slide 4 Investing Investing Investing in real assets:
productive machinery, product line... Etc to create new future cash
flows that did not previously exist. - We must give up some
resources in order to undertake investment. -If the present value
of the amounts we give up is greater than the present value of what
we gain from investment (i.e Bad investment ) the investment will
decrease our present wealth. Investment decision depends on the
effect on present value of wealth Slide 5 Net Present Value. Net
Present Value. Present value of difference between an investments
cash inflows and outflows. a) Net present value 770/1.10 -550 = 700
550 = 150 770/1.10 -550 = 700 550 = 150 which is = change in
present wealth b) NPV is a reflection of how much investment
differs from its opportunity cost or NPV is the present value of
the future amount by which the returns from the investment exceed
opportunity cost of the investor. Slide 6 In Our Example:- The
investment cost ( @10%) = 550 X 1.1 = 605 The investment cost (
@10%) = 550 X 1.1 = 605 While investment returned 770 i.e
difference is 770 - 605 = 165.00 PV of difference = 165/1.1 =
150.00 Which is once again the NPV Slide 7 NPV of Investment 1-
Present value of all investment present and future cash flow
discounted at the opportunity cost of cash flow 2- Is the change in
present wealth of investor who choose a positive NPV investment. 3-
Is the discounted value of the amount by which the investment cash
flow differs from those of its opportunity cost. Slide 8 Internal
Rate of Return (IRR) Internal Rate of Return (IRR) 1- IRR is the
average per-period rate of return on money invested. 2-IRR is
calculated by finding the discount rate that would cause NPV of
investment to be Zero. 3-To use IRR, we compare it with the return
available on an equal Risk investment of comparable cash flow
timing. Slide 9 In Our Example:- NPV = O = - 550 + 770 / (1 + IRR)
( 1 + IRR) = 770 / 550 ( 1 + IRR) = 1.4 ( 1 + IRR) = 1.4 IRR = 0.4
i.e. 40% IRR = 0.4 i.e. 40% IRR is larger than opportunity cost
which is 10% from comparable Risk and timing investment. Slide 10 1
+ IRR = 594/ 550 = 1.08 = 1.08 IRR= 0.08 or 8% (i.e. Less the
opportunity cost of 10%) Investment should be rejected Slide 11
Multiple Period Finance t0 Period 1 t1 period 2 t2 Cf2 = CF0(1+i) 2
CF2= 100 (1.21) = 121.00 PV = CF2 / (1+i) 2 = 121/(1.10) 2 = 100 I
i =10% m =2 CF0 = 100 FV = PV (1 + i) n PV = FV/ (1 +i) n Slide 12
- Compound Interest Exchange rate between two time points where
interest is not only earned on original investment (principle) but
also on interest earned. Example : CF2= CF0 +CF0 (i1) + CF0 (i2) +
CF0(i1)(I2) i.e. 121 = 100 + 100 (10%)+ 100 (10%)(10%) Or CF2
=CF0(1+i) 2 121 = 100 (1 +10%) 2 121 = 100 (1 +10%) 2 - -The
general arithmetic of interest compounding (for number of times per
period) =CF0 (1+ /m) mt Where m number of times per period And t-
isnumber of periods Slide 13 Multiple Period Cash Flow The Present
Value of Stream of future cash flow is the sum of present values of
each of the future cash flow. PV = CF 1 + CF 2 + CF 3 (1+i 1 ) 1
(1+i 2 ) 2 (1+i 3 ) 3 (1+i 1 ) 1 (1+i 2 ) 2 (1+i 3 ) 3 Multiple
period Investment Decision Multiple period Investment Decision NPV
= (CF0) + CF 1 + CF 2 + CF 3 (1 + i 1 ) 1 (1+i 2 ) 2 (1+i 3 ) 2 (1
+ i 1 ) 1 (1+i 2 ) 2 (1+i 3 ) 2 NPV must include all present and
future cash flow associated with investment Slide 14 As IRR is the
discount rate that causes NPV to equal Zero. Solving for IRR is the
technique called Trial & Error NPV = 0 = (CF0) + C C C CF1 + +
C CF2 + + CF3 (1+IRR)1 (1+IRR)2 (1+IRR)3 Slide 15 Using Financial
Table PV=FV (factor) PVA=PMT (factor) FV=PV (factor) PVA Due=PMT
(factor ) X (1+i) Present value of perpetuity *Perpetuity: PV = F F
F FV Constant per period cash flow i Constant interest (discount)
rate. *Limitation: Value Error. if cash flow is to cease by 40
years 100/0.10/(1.10)40= 22.10 A value of error of t 22.10 out of
1000 = or 2.21 percent Slide 16 Perpetuity valuation can be
convenient in long- lived assets Growth Perpetuity present-value
calculation. PV = CF / (i- G) Example : 100/0.10-0.05 = 2000.00
Limitation: (Equation does not work if growth rate is equal or
larger than the discount rate) Slide 17 Slide 18 *The yield to
Maturity It is the IRR of the Bonds promised cash flow used to
discount promised cash flow to equal market price of the Bond. -The
coupon effect on the YTM Government Bonds Coupon
rateMaturityPriceYield 8% t110295%A 8% t210395.96%B 8% t310296.90%C
4% t39836.9%D 12% t311366.85%E The yield curve yield at various
maturities Slide 19 Interest Rate Risk & Duration Effect of
Interest Rate Risk; variability of values and therefore in wealth
due to changes in interest rates. Reasons of interest rate changes
*Change in inflation *changes in creditworthiness of bond issuer
*changes in return available on real asset investment. Duration:
extent bond is subject to interest rate risk. i.e. how much bond
value will go up and down as interest change. Or exposure of the
value of a bond to changes in interest rates. Slide 20 Duration
number of periods into future where bonds value, on average is
generated. The greater duration of bond the more it react to
changes in interest rates. Calculation by weighting the time points
from which cash flow is generated by proportion of total value
generated at each time. Slide 21 Example: Cash Flow price t0 t1t2
t3 Bond c 1029 80 80 1080 Bond D 923 40 40 1040 Interest 5% 6% 7%
Duration Bond c =1 [80/(1.05)/1029)+2[80/(1.06)2/1029]+ 3
[1080/(1.07)3/1029]=2.78 Duration Bond D =1
[40/(1.05)/923)+2[40/(1.06)2/923]+ 3 [1040/(1.07)3/923]=2.88 Slide
22 Relationship between risk and return The higher the Risk, The
higher the required return. SML can be used to generate
risk-adjusted discount rates to be used in Financial decisions.
Return Return i Risk i SML Risk Slide 23 Risk and Rate of Return
Portfolio Rate of Return : Average weighted return on the portfolio
as a whole. Standard deviation : reflection of risk inherent in the
portfolio. It measures the extent of possible outcomes are likely
to be different from the mean outcome Slide 24 Risk, Return and
Diversification Return Probability Assets A 10%45% 20%55% 20%55%
Assets B 7%65% 12%35% Slide 25 Asset A average return 0.10 X0.45
+0.20X0.55 = 15.5% Standard deviation of Return (0.10-0.155 ) 2
X0.45+(0.20-0.155) 2 X0.55 Variance = 0.00247 standard deviation =
0.00247 =4.97% Asset B average Return 8.75 Standard Deviation 2.39%
Slide 26 The correlation coefficient, the covariance Direct way to
find portfolio risk by dealing with the interrelatedness of Assets
returns. It is a number that can take values from -1 (perfect
negative relatedness) to +1 ( perfect positive relatedness). (
perfect positive relatedness). *The more positively related
securities in portfolio, the less gain from diversification. Slide
27 Summery Portfolio Risk 1- Portfolio risk is not likely the
average risk of underlying Assets. 2-Measurment of relatedness of
individual Assets returns is the correlation coefficient of paired
return of assets within the portfolio. Slide 28 Diversifiable &
Un-diversifiable Risk Number of Securities in Portfolio Risk of
Average Portfolio Risk (M) Slide 29 Beta Coefficient ( Regression
coefficient) B coefficient express relationship between the return
expected from security and that expected from the market as whole j
= Standard deviation Correlation of j Standard deviation
Correlation of j of return j X with the Market of return j X with
the Market Standard deviation of Market Return Slide 30 i.e = j Pjm
m m Same as j m Pjm 2 m 2 m j = j m Covariance j with Market 2 m
variance of Market 2 m variance of Market Slide 31 Example: If
Market return move from 12% to 14% a security with return of 15%
and of 1.3 will move to 15% +1.3 (14%-12%) = 17.6% Slide 32
Security Market line (SML) the Market Model Security Market line
(SML) the Market Model Objective : having quantitative mechanism
for setting risk adjusted returns necessary for co. investment
decision -SML allows estimating discount rates and opportunity cost
for co. investment E ( rj) = rf +{ E(rm) rF } X j ERj SML 1.0 M Er
(M) Slide 33 Learning Points 1- Total risk can be separated to
diversifiable and systematic (Market) Risk. 2- Un-diversifiable
Risk is related to underlying market factors that is common to all
assets and securities. 3- Systematic Risk is measured by Beta
coefficient (standard deviation X Correlation with Market) 4-SML
dictate set of risk adjusted returns available in the market 5- SML
from basis for evaluating internal co. investment where it should
offer returns in excess of capital supplier opportunity. Slide 34
Market Terminology -Spot Rate Interest Rate Cross Rate. - FX
Forward - Options Swap Hedging Slide 35 Exchange Rate & Low OF
One Price (Purchasing Power Parity) Same thing can not sell for
different prices at the same time. Impact of Demand & Supply
Factors on currencies for different prices quoted across countries
for same thing Exchange rates : Portray relationship in wealth
exchanges across national borders (Now) Interest Rates: Portray
wealth exchanges across time (in Future) Slide 36 * Spot &
Forward Exchange Rates Example: FX Quotation on July 22,1997 /$ $/
0,6266_____ 1.5960 Spot 0,6337 _____ 1.5780 Forward 180 days
Sterling is at forward discount or dollars is at forward premium
*Forward Exchange Rates & Interest Rates Interest rate parity
interact with forward exchange market in order for no arbitrage
opportunities to exist. Example: $i = 6.5%spot $/ 1.5960 i = 8.94%
/$ 0,6266 Slide 37 1- amount borrowed ( six month $ 100.000 @ 6.5%)
= 100 000 = $ 96900,00 (PV) = 100 000 = $ 96900,00 (PV) (1.065)
(1.065) 2- purchase spot = $ 96 900 X 0,6266 = 60717.00 3- invested
6 month @ 8.94% =60717X(1.894) = 63373.00 Review $ 100.000
(Borrowed) should equal 63373 in 6 month period i.e Forward
exchange rate should be /$ 0,6337 Slide 38 FX Forward Example :
Spot$1.2750/55 FWD points 50/60 FWD Buying FWD Selling 1.27501.2755
50 60_______ ________ 1.28001.2815 Slide 39 Currency Swap
Simultaneous spot buying/selling against opposite forward
selling/Buying of a foreign Exchange. Example: * /$ spot 1.2850/55
*Swap cost 30/35 -at 55&30 we buy and sell against $ i.e on
same date we buy spot at 1.2855 and sell FWD at 30
____________________________ 1.2885 Slide 40 Interest Rate Swap
(IRS) An interest rate swap is an exchange of interest flows in the
same currency for maturities of over one year. These swaps never
involve an exchange of principal amounts. The common type of
interest rate swap is one in which fixed Rate payments are exchange
for floating rate payments (based on reference rate such as Libor )
Swaps can also be arranged. In which one floating rate is swapped
for an other (e.g 3 month Libor against 6 month Libor) the notional
principal amount should be at least US $ 5 Million. Slide 41
Interest rate swaps are available for a Varity of periods from one
year up to a maximum of ten years. All interest rate swap
transactions between the customers and the bank is governed by
single standard agreement( the ISDA) Slide 42 Example:- A company
has taken out a bank loan for Swiss Franc 10 Million at a fixed
rate of 7 percent for 5 years. This money is used to buy a floating
rate note at ( Libor +3/8 percent) with a 6 month rollover. ( if
the floating rate investment is left unhedged, the company stand to
make a loss as soon as Libor fall below 6 5/8 percent.) Making an
interest rate swap in which the company pays a floating rate and
receives a fixed rate can cover this risk. Let us assume that the
bank quotes (7.5-7.6%) against 6 month Libor for the 5 years swap
in our example. This means that banks is prepared to pay 7.5% in
return for receiving flat Libor If the bank were the floating rate
payer, it would demand a rate of 7.6%. Slide 43 IRS Example I CO.
Swap Bank FRN Bank CHM 10mm @ 7% Libor +3/8 Loan 5 year Libor 7.5%
Slide 44 Example II A company that had borrowed $ 20 million on a
floating rate basis with interest at percent per annum over 6 month
Libor. The company is concerned the interest rates will rise and
wants to fix the rate on the loan for the balance of the term. The
company can enter into an interest rate swap and agree to pay a
fixed rate for remaining term of the loan and in return receive 6
month Libor on a floating basis. If the fixed rate was 7 percent,
then it has effectively created a fixed rate loan with a cost of 8
1/4percent. Slide 45 IRS Example 2 CO. Swap Bank LIBOR Fixed 7.75 %
$ 20 mm 6 month Libor +0.50 Cost id fixed 7.75+0.50=8.25% Slide 46
Options: having the right ( not the obligation) to buy or to sell
at certain agreed terms for a fixed period of time Options
terminology : *Contingent claim *Underlying Asset *Striking/
exercise price *Expiration date *Profitable option In the Money
Ex:- option to buy underlying asset @ 1.25 while market price is
1.50 @ 1.25 while market price is 1.50 Slide 47 Out the Money :
Example Call option by @ 1.50 while Market price is 1.25 *Option
Holder (Beneficiary ) *Option Writer (Issuer) *Covered option
(Covered call) option writer owns the underlying Asset. * Naked
option (naked call) Writer does not own the underlying asset. Slide
48 Put option allows holder to sell at fixed price for a fixed
period of time Put has a positive (+) exercise value if underlying
asset value is less than striking (exercise) price While call
option has a positive exercise value if underlying Asset value is
higher than the striking price. Slide 49 Value Of a Simple Option
Example;(A) *Current price of underlying security So= 1.50
*Probability of price increase q= 0.6 *Upward Multiplier of
underlying security U=2 *Downward Multiplier of underling security
d=0.5 d=0.5 Uso= 2X1.50 = 3.00 i.e 1.50 dso=0.5X 1.50 =0.75 q =0.6
1-q=0.4 Slide 50 (B) Value of Call Option : Co= Current Market
Value of the option Cu= option payoff if underlying security price
is up Cd= option payoff if underlying security price is down X =
Striking (exercise Price Cu=max =( 0.Uso-X) =max= (0.3-1.25) i.e
Co= =1.75 Cd= max (0.Dso-X) = max (0.75-1.25) =0 q =0.6 1-q=0.4
Slide 51 Result It the underlying Security X increase in price to
Uso 3.00 the 1.25 call option will have an exercise value (co) of
1.75 and no payoff if option is out of the money and the option has
60% chance of paying 1.75 and 40% chance of paying nothing Slide 52
(C) Option Valuation ( Binomial model Case) Technique of
calculating market value of an option 1- Get Y = Cu Cd = 1.75 - 0.0
= 0.7778 So (U-d) 1.50 (2-0.5) 2- Get Z = Ucd dcu = 2( 0.0) 0.5(
1.75) = 0.5303 (u-d)(1+rf) (2-0.5)(1+0.10) 3-Co =Y so + Z = 0.7778
X 1.50 - 0.5303 = 0.6364 Assuming European option. Y Purchased sold
shares Z Borrowed money or lent Money Slide 53 Forward Interest
Rates: Set of interest rates that begins at some future point other
than now (t0). PV = CF1 + CF2 (1+i1) (1+i2) 2 = 80 + 1080 (1.05)
(1.06) 2 = 76 + 961 = 1037 Slide 54 i.e. of the 1037 invested at t0
76.00 Produces t 80 at t1 for 5% 961 Produces t 1080 at t2 for 6%
Slide 55 Forward interest Rates Example: t0t1 t2 Bond 1037 80 1080
1037 invested at t0 @ 5 % The amount invested at t1 ( before
interest payment ) 1037 X 1.05 = 1089 after 80.00 payment at t1 the
amount invested is thus 1089 - 80 = 1009 amount invested in bond B
at t1 Value at t1* ( 1+ 12) = CF2 1009 ( 1 + 12) = 1080 12 = 7%
Slide 56 Relationship between spot interest rates and forward
interest rates i.e. (1+ spot Rate) = geometric means of (1+ Forward
Rates) Example : (1+ i3)3= (1+ 01 ) (1+ 12 )(1+ 23 ) (1.07)3=
(1.05)(1.07)(1+ 23 ) (1+ 23)= (1.07)3 /[(1.05)(1.07)] = 1.09 23= 9%
(1+ i 2) 2 =(1+ 0 1 ) (1+ 1 2 ) Slide 57 Conclusion of
Relationships PV = CF1/(1+i) + CF2/(1+i2)2 + CF3/(1+i3)3 = CF1/(1+
01) + CF2/(1+ 01)(1+ 12) + CF3/(1+ 01 )(1+ 12)(1+ 23) =CF1/1+YTM +
CF2/(1+YTM)2 + CF3/(1+YTM)3 Slide 58 923 = 40/(1.05) + 40/(1.06)2 +
1040/(1.07)3 923 = 40/(1.05) + 40/(1.05)(1.07) +
1040/(1.05)(1.07)(1.09) 923 = 40/(1.069) + 40/(1.069)2 +
1040/(1.069)3 Slide 59 Interest Rate Futures Undertaking a real
asset investment because of positive NPV could be badly affected if
actual future interest rate increase. Example: t0t1t2 - 1700 1000
1000 - 1700 1000 1000i1=10% And i2 =11% 1)NPV = (1700)+ 1000/(1.1)
+ 1000/(1.11) 2 = + 20.71 = + 20.71 Slide 60 And 2) (1+i2)2
=(1+i1)(1+ 12) (1+ 12) =(1+i2)2/(1=i1) (1+ 12) =(1.11)2/(1.10) 12
=12.009% Slide 61 Now, If Risk that 12 increase to 15% i.e. 1-
(1+i2)2 = (1+i1)(1+12) (1+i2)2 =(1.10)(1.15) (1+i2)2 = (1.265) i2 =
12.4722% 2-NPV = ( 1700) + 1000/(1.10) + 1000/(1.124722)2 NPV = -
0.40 i.e. The positive NPV of investment has become negative due to
the increased interest rate applicable to t2 cash flow N.B. : LOSS
WILL BE 20.71+0.40 =21.1 Slide 62 Hedge against interest Rate Risk
by selling interest Rate futures contract. Commit to sell at a
fixed price a security at t1. So IF 1 2 increases, the price of
such security will decline, but since we have a contract to sell
that security at a fixed higher price -the value of the contract
will increase to offset the decrease of the NPV of investment.
(i.e. avoiding risk of interest Rate changes) Slide 63 Interest
Rate Futures. Example: i1 =10%i2=11% T1 CF 1000t2 CF 1000 (1+i2)2 =
(1+i1)(1+12) 1+ 12 = (1+i2)2/(1+i1) 1+ 12 = (1.11)2 /(1.10) 12 =
12.009% t1 future price =1000/(1+ 12) =1000/1.2000 =892.79 Slide 64
To hedge against interest rate risk you commit to sell 1000t2 cash
flow at t1 for 892.79. N.B. no cash actually changed at t0 where
investment undertaken futures contract sold meaning you only made a
commitment to sell the security at t1. Slide 65 If 12 increases to
15% beside decline of NPV from 20.71 to (0.40) i.e. a wealth loss
of 21.11 However a) The new t1 value of t2 1000 is 1000/1.15 =
869.57 b) Contract value increase at t1 892.79 - 869.57 = 23.22 c)
Discounting that value increase to t0 @ 10% increase in contract
value at t0 23.22/1.10 = 21.11 Conclusion: increase in value of
interest rate futures contract at t0 equals the decrease in value
of investment NPV Slide 66 N.B : If 1 2 re to decrease the NPV
would increase while futures contract value would decrease to
offset NPV increase i.e.: Hedging means losing both bad and good
chances arising out of interest.
