

Financial
Management MGT201
VU
Lesson
04
TIME
VALUE OF MONEY
Learning
Objectives:
After
going through this lecture,
you would be able to have an
understanding of the following
concepts.
·
Main
Concepts of FM.
·
Time
Value of Money
·
Interest
Theory and its
determinants
·
Yield
curve theory and its
dynamics
FM
Concepts:
There
are certain financial
management concepts that
should be kept in mind,
while making an analysis
of
a financial decision. The
oneliners given here would
help you in committing these
concepts to your
memory.
·
A rupee today is worth more than a
rupee tomorrow.
Time
Value of Money &
Interest
·
A safe rupee is worth more
than a risky rupee.

Risk
and Return
·
Don't compare apples to
oranges

Discounting
& NPV
·
Don't put all your
eggs in one basket.

Portfolio
Diversification
·
Get insurance because you
will break some
eggs.

Hedging
& Risk Management
Time
Value of Money:
The
first concept, time value of
money, says that a rupee in
your hand today is worth more
than
the
rupee that you are
going to get tomorrow or the day
after. This is because if
you have a rupee in
hand,
you can put it into a
bank (invest it) and can
earn interest (return) on it, and
tomorrow you are
going
to have more than rupee one, which of
course, is more desirable than having
just one rupee.
Risk
and Return:
Investors
want to earn maximum return
on their investment; however,
risk is a constraint to
this
objective.
Investors dislike riskbearing,
unless they are adequately
compensated for that. Now
the risk
and
return concept states that a
safe rupee in your hand is better
than a risky rupee which is
not in your
hand.
This may imply that the
investors would be willing to bear
risk if they are offered
more than a
rupee
i.e., a certain premium for
risk bearing. However, in the
absence of this additional
compensation,
a
safe rupee is better than a
risky rupee. The details
about the concepts of risk and
return would be
discussed
in the middle of the course.
Discounting
& Net Present Value
(NPV):
The
third concept is of discounting and net
present value of money. This
is a fundamental
mathematical
concept and students need to
practice it to perfection. Whether
discounting for an asset
or
a
company, we have to see what
cash flow would it generate
during its future life
and then we bring
back
those future cash flow to
the present, i.e., we discount the
future cash flows to obtain
their present
value.
This exercise is done to make comparison
of cash flows occurring in
different time periods,
i.e.,
comparing
apples to apples, rather than
oranges. This concept is
relentlessly used throughout the
course
in
comparing different investment
options in different time
periods.
Portfolio
Diversification:
The
fourth concept is of portfolio
diversification i.e. how to
select different investment
options
so
as to reduce risk of losing the
invested money. For instance
if an investor has a million
rupees and he
invests
his total wealth in a single
company's share, he would be
exposed to greater risk. If the
company
goes
out of business or faces
serious loss, the investor is
likely to lose all his
investment. However, if
that
investor puts his total
wealth into shares of ten
different companies, the chances
that all the ten
companies
would face loss is
comparatively lesser and hence the
risk for the investor is
diversified and
reduced.
The rule of finance says do
not put all your
eggs in one basket, because
if you drop the
basket
accidentally,
you are likely to lose
all the eggs.
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Financial
Management MGT201
VU
Hedging
& Risk Management:
Finally,
there is this fifth concept of
hedging and risk management.
Hedging is a strategy of
risk
management that is employed by investors
to reduce or minimize the chances of
loss. Insurance is
said
to be an effective tools used to
manage risk. The concept of
hedging and risk management
says that
whether
you put your eggs in one
basket or in different baskets,
chances are there that you
will break
your
eggs so it is better to get the eggs
insured Insurance is the best way to
avoid loss so that even if
the
loss
occurs you may get a claim
on your damages.
Now,
let's discuss the concept of interest in
detail, first major &
technical area in
financial
management.
Remember, that the basic objective in
financial management is to maximize
shareholders
wealth.
Interest
Theory:
·
Economic
Theory:
Interest
rate is an equilibrium price, expressed
in percentage terms, at which
demand and
supply
of funds (or capital) meet,
i.e., the rate at which the lenders are
ready to lend and buyers
are
ready
to buy. But equilibrium
price (Interest rate) varies from one
market to another. For
example,
the
"price" of capital in the
property market is different
from the "price" of capital
in the cotton
market.
Markets have different interest rates
guided by the supply & demand of
funds in that market.
Although
the interest rates in different markets
may differ, however, all the
markets in the country
and
the interest rates prevailing there are
interlinked.
Now,
we come to the factors that determine the interest
rates. It is important to understand
the
factors
that make up an interest rate in the
present day business
environment. In business when we
talk
about
the interest, we usually refer to nominal
rate of interest which is determined with
the help of
following
factors.
Factors
i
= iRF + g + DR + MR + LP + SR
i is the nominal interest rate generally
quoted in papers. The "real"
interest rate = i g
Here
i = market interest rate
g
= rate of inflation
DR
= Default risk
premium
MR
= Maturity risk
premium
LP
= Liquidity preference
SR
= Sovereign Risk
The
explanation of these determinants of interest
rates is given as
under:
Risk
Free Interest Rate (RF):
Factually
speaking, there is no such thing as a
riskfree rate of return because no
investment can
be
entirely riskfree. All the investments
and securities include a certain amount
of risk. A company
may
go bankrupt or close down.
However, if we talk about the
relevant risk involved in
different
securities,
the governmentissued securities are considered as
riskfree, since the chances of
default of a
government
are minimal. These
government issued securities provide a
benchmark for the
determination
of interest rates. Internationally the US
TBills are considered as risk
free rate of return.
In
Pakistan, Government of Pakistan TBills
can be used as a proxy for
risk free rate of return,
however,
since
Pakistan faces some sovereign
risk, the Tbills would not
be considered entirely riskfree in
the
true
sense.
Inflation
(g):
The
expected average inflation over the
life of the investment or security is
usually inculcated in
the
nominal interest rate by the issuer of
security to cover the inflation
risk. For instance, consider
a
bond
with a maturity of 5 years. If the
inflation rate in Pakistan is 8 % and the bond is
also offering 8%
percent
interest rate, the investors would not be
willing to invest in the bond
since the gains from the
interest
rate would be exactly offset by the
inflation rate which is actually
eroding the wealth of the
investor.
To secure the investor against inflation
the issuers, while quoting
nominal interest rates, add
the
rate of inflation to the real interest
rate.
Default
Risk Premium
(DR):
Default
risk refers to the risk that the company
might go bankrupt or close
down & bonds, or
shares
issued by the company may collapse.
Default Risk Premium is charged by the
investor, as
compensation,
against the risk that the company might
goes bankrupt. Companies may
also default on
20
Financial
Management MGT201
VU
interest
payments, something not very unusual in the corporate
world. In USA, rating
agencies like
Moody's
and S&P grade securities (debt
and equity instruments) according to
their financial health
and
thus
identify those companies
which have a good ability to
pay off their principal
lending and interest
charges
and those which might
default on the payments. The rating
from best to worst is: AAA,
AA, A,
BBB,
BB, B, CCC, CC, C. In Pakistan, Pakistan Credit
Rating Agency (PACRA) and
Vital Information
Services
(VIS) are actively
conducting analysis of corporate securities and
grading them.
Maturity
Risk Premium
(MR):
The
maturity risk premium is
linked to the life of that
security. For example, if
you purchase the
long
term Federal Investment Bonds issued by the
government of Pakistan, you are
assuming certain
risk,
because changes in the rates of
inflation or interest rates would
depreciate the value of your
investment.
These changes are more
likely in the long term and
less likely in the short term.
Maturity
Risk
Premium is linked to life of the
investment. The longer the
maturity period, the higher the
maturity
risk
premium.
Sovereign
Risk Premium
(SR):
Sovereign
Risk refers to the risk of
government default on debt
because of political or economic
turmoil,
war, prolonged budget and trade
deficits. This risk is also
linked to foreign exchange
(F/x),
depreciation,
and devaluation. Nowadays the
individuals as well as institutions
are investing
billions
of
rupees globally. If a bank
wants to invest in Pakistan, it will have
to take view of Pakistan's
political,
economic,
and financial environment. If the bank
sees some risk involved it
would be willing to lend
at
a
higher interest rate. The interest rate
would be high since the bank
would add sovereign risk
premium
to
the interest rate. Here it may be
clarified that Pakistan is not considered
as risky as many
other
countries
of Africa and South
America.
Liquidity
Preference (LP):
Investor
psychology is such that they
prefer easily encashable securities.
Moreover, they charge
the
borrower for forgoing their
liquidity. A higher liquidity preference
would always push the
interest
rates
upwards.
Yield
Curve Theory:
Term
Structure and Yield
Curve:
Interest
rates for any security
vary across time horizon.
The supply & demand for
funds vary
depending
on how long the funds are
required. Normally, short term interest
rates are lower than
long
term
rates, or we can say that
the interest rates depend on their term structure.
Based on the maturity, the
securities
can be classified into three
categories, although, these
classes have been loosely
defined.
Short
Term: Short
term means for the period of one
year or less.
Medium
Term: For
the period of any where between one
year to five years.
Long
Term: Any where between
15 years to 20 years some
people say that medium term
is
from
5 year to ten years and long term
from 10 years to 20 years and
plus.
Nominal
or upward sloping yield
curve:
The
supply & demand of funds or
capital varies depending upon
how long funds are
required. For
example,
today the supply and demand
for short term money might be
different from supply
and
demand
of the long term money. In another words, the number
of borrowers to take loan
for one week
may
be different from the borrowers of
loan for one year. Short
term interest may be different than
the
long
term interest; normally, short term interest
rates are lower than
long term than interest
rates
because
investors think that inflation is
going to increase. This phenomenon
results in nominal
or
upward
sloping yield
curve.
Abnormal
or downward sloping yield
curve:
Sometimes,
the reverse is true. This is
known as the Abnormal (or
Downward Sloping)
Yield
Curve.
It is the case where the short term raters
are higher than long term
interest tares. You can
also
16
have
a mixed or Humped Back
Curve.
12
N
o rm a l
8
A
bno rm a l
4
0
Yr
1
Yr
3
Yr
5
Y
r 10
Yr
20
21
Financial
Management MGT201
VU
Now,
we go into the reason why the
curves have either upward slope or
downward slope. Following
are
some
of the factors that determine the slope of the
yield curves.
Expectations
Theory:
Investors
normally expect inflation (and interest)
to rise with time thereby
giving rise to a
normal
shaped yield curve.
Liquidity
Preference Theory:
Investors
prefer easily encashable securities
with short maturities. The
only problem is that
short
term securities are easy to encash
but at maturity there is no guarantee
that you can renew it
.so,
you
can find a security today
which will give you 25
%or 30% per annum they are
not always
renewable
hence unpredictable.
Market
Segmentation:
The
demand/supply for Short Term
securities is different from that of
Long Term securities.
This
can easily give rise to an
Abnormal Yield Curve.
Now
let's talk about the
practical types of interest there three kinds of
interest we will talk
about
1simple
interest
2discrete
compound interest
3continuous
compound interest
1.
Simple Interest (or Straight
Line):
Simple
interest incurs only on the principal.
While calculating simple interest we keep
the
interest
and principal separately,
i.e., the interest incurred in one year
is not added to the principal
while
calculating
interest of the next period. Simple
interest can be calculated using the
following formula.
F
V = PV + (PV x i x n)
Example:
Assume
that you have Rs 100 today
and you want to invest the
amount with a bank for
five
years.
The bank is offering an interest
rate of 7 percent. We can obtain the
simple interest on the
investment
using the aforementioned
formula
F
V = PV + (PV x i x n)
Here
FV is the simple interest accrued
for the term of the investment
PV
is the amount invested, i.e., Rs 100 in
our example
i
stands for the interest rate offered by
the bank, i.e., 7 % =
0.07
n
is the term of the investment, which is
assumed to be 5 years
Putting
these values in the formula, we
get
FV
= 100 + (100 x 0.07 x
5)
FV
= 100 + (7 x 5)
FV
= 100 + (35)
FV
= Rs 135
Here
Rs 135 is the future value of
investment after five years
and Rs 35 is the interest accrued
during
five
years on the initial investment of Rs
100.
2.
Discrete Compound
Interest:
Discrete
compound interest is the most commonly
used tool in Financial
Management
Discounting
and NPV calculations. Unlike
simple interest, compound interest
takes into account
the
principal
as well as interest accrued for a term,
while calculating interest incurred
during the next term.,
i.e.,
interest incurred for one year
would be added to the principal to
calculate the interest for the
next
period.
However, this compounding of interest
takes place in a discrete manner, i.e., the
compounding
takes
place yearly, semiannually, quarterly,
or monthly. For computing the
annual compounding, we
use
the following formula
Annual
(yearly) compounding:
F
V = PV x (1 + i) n
However,
a slight modification in the formula is
need if the compounding takes place
monthly.
Such
a compounding would be calculated
using the following
formula.
F
V = PV x (1 + (i / m) m x n
Here
`m' refers to the compounding intervals
during the term of the investment. In
order to
calculate
monthly compounding, the value of
`m' would be 12; however,
for quarterly
compounding
calculation
m would be equal to 4
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Financial
Management MGT201
VU
Example:
Assume
that the investor in our
previous example is offered a compound
return (interest) on his
same
investment,
at the same interest rate and term. The
future value of the investment is
given as under
F
V = PV x (1 + i) n
FV
= 100 x (1+0.07)5
FV
= 100 x (1.07)5
FV
= 100 x (1.40255)
FV
= 140.255
Here
the interest accrued on the five year
investment is more than what we
found out in simple
interest.
However
if the compounding is done every month
the future value of investment
would be
F
V = PV x (1 + (i / m)) m x n
FV
= 100 x (1 + (0.07/12)) 12 x 5
FV
= 100 x (1 + 0.005833)) 60
FV
= 100 x (1.005833) 60
FV
= 100 x 1.4176
FV
= 141.76
With
more frequent compounding, the wealth of
the investor increases to a greater
degree.
3.
Continuous (or Exponential) Compound
Interest:
The
other type of compound interest is
exponential compound interest. In this compound
interest an
infinite
number of times per year at intervals of
microseconds.
F
V (Continuous compounding) = PV x e
i
x n
Here
e is a constant the derived value of
which is 2.718
Example:
Assume
that the same investor has
now the opportunity of investing at
continuous compounding
with
the
same term and interest rate. His future
wealth after five years is
given as under
F
V = PV x e i x n
FV
=
100 x
2.718(0.07x5)
FV
= 100 x 1.419
FV
= 141.9
We
can see that the wealth of
the investor is the highest, when he
decided to invest in a scheme
which
offers
continuous compounding.
The
difference between simple and compound interest
can increase manifold if the term of
the
investment
is increased. As we see in the following
example
Example:
Suppose
you deposit Rs 10 in a bank
today. The bank offers
you 10% per annum (or per
year)
interest.
How much money will
you have in the bank after 15
years?
If
the bank is offering simple
interest:
F
V = PV + (PV x i x n) = 10+ (10x0.10x15)
= Rs. 25
If
the bank is offering discrete
compounding:
F
V = PV x (1+ i) n
= 10 x
(1+0.10)15
= Rs.
42
approx.
Banks
do not offer continuous
compounding but if they
did:
F
V = PV x e ixn
= 10 x
(2.718) 0.10x15
= Rs.
45
approx
23
Financial
Management MGT201
VU
Graphical
View of Compounding
The
miracle of compounding you
earn interest
on
interest
&
principal!
50
Simple
Amount
Discre
te
(Rupees)
25
Compound
Continuous
Compound
0
Yr
1
Yr
5
Yr
10
Yr
15
Note:
After 15
years, Continuous Compounding
gives you almost two
times more money
than
Simple Interest. Compound
Interest gives you about
oneandahalf times as
much!
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