# Financial Management

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Financial Management ­ MGT201
VU
Lesson 06
PRESENT VALUE AND DISCOUNTING
Learning objectives:
After studying this lecture, you would be able to have a better understanding of the following.
·  Present Value and Discounting
The Topics of this lecture are covered in the chapter 6 of our text book called Financial
Management theory and practice by Eugene F. Brigham & Louis C. Gapenski.
Objectives of present value:
The objective of calculating the present value is to translate the future cash flows in to present
terms. The basic principle is to compare apples with apples. For instance, if you have Rs.10 in your
pocket today and then you have may as many rupees ten years after, how can you compare the two. You
can do it only by comparing both amounts at the Present time.
We choose the present (today) as the most convenient point in time where we could compare all
the cash flows taking place at various points in time in future. We must compare everything at the
SAME point in time otherwise; we would be neglecting the Time Value of money concept.
For example, Rs 105 is more than Rs 100 BUT; Rs105 after 1 year may not necessarily be
more than Rs100 today! We first have to first bring all cash flows to the Present, or Discount them, and
then compare them. The concept of present value says that we can compare both the amounts in the date
of today we will bring back future cash flows to the present
Discounting:
"Discounting is defined as bringing the future cash flow to the present time".
Before answering which amount is greater in the aforementioned example, we need to have
some concept of interest rates or the cost of money. An interest rate can also be understood as an
opportunity cost.
One of the simple ways of estimating what opportunity cost or interest rate should be for our
discounting calculations, we can use interest rate given on the PLS accounts by the banks. For example,
if money is deposited in a bank and getting 10% per annum then it is interest or opportunity cost for you.
This interest on PLS account becomes minimum rate of return which any investment should be able to
generate. Therefore, the investment project should offer higher rate of return than the returns on the PLS
account.
Now let's see the answer of the question that Rs.105 will be more one year later or Rs.100 today,
and for this, we need interest or opportunity cost. It is important to understand why interest rate is called
opportunity cost? Because, opportunity cost essentially means the cost of taking up one option while
sacrificing the other. For instance, when you deposit your money in the bank and get interest, you are
sacrificing by
(1) Not consuming the money to buy something for yourself and
(2) Not investing your money elsewhere at a higher return than the bank interest.
Usually when an investment option is taken up, investors forgo the option of depositing the
money in a bank account and earn interest on that. The opportunity lost in this case is the opportunity
cost. Now the question is that what kind of interest rate should we use? There are many interest rates
quoted in the schedules of the bank but for discounting, the most commonly used rate is the nominal
interest rate, or APR.
Interest Rates for Discounting Calculations
·  Nominal (or APR) Interest Rate = i nom
·  It is usually published in newspapers .Annual Nominal Interest Rate is quoted for 1
year by Credit Card Companies and Leasing Companies because it understates the
actual (or Effective) interest you have to pay, these companies want to create an
impression that the interest charged by them is the minimum in the market.
·  Periodic Interest Rate = i per
Periodic interest rate is used in FM for Discounting and Present Value (PV) calculations.
It is defined as
iper = ( i nominal Interest rate) / m
Where
m = no. of times compounding takes place in 1 year i.e.
If semi-annual compounding then m = 2
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Financial Management ­ MGT201
VU
·
Effective Interest Rate = i eff
It is very useful to compare securities and investments with different life or
compounding cycles but not used for Discounting and PV.
i eff = [1 + ( i nom / m )]m ­ 1
Where m = no. of times compounding takes place in 1 year, the compounding cycle. The shorter the
compounding cycle more frequently money compounded & faster the money grows.
Coming back to our earlier example where we were trying to figure out whether or not Rs 100 of
today are worth more than Rs 105 a year after, while the periodic interest rate is 10 percent per annum. The
interest rate used here would be the nominal interest rate, i.e., 10 percent. When we are going to solve for
the present value we are discounting from the future to the present
PV=FV/(1+i)n
Where, i=interest rate
N=no. of years if we plug in the values
PV=105/(1+0.10)1=Rs.95.45
Now we can see that if we discount Rs.105 from future to the present that is only the worth of
Rs.95.45 which is less than Rs.100. The amount offered in the future is seemingly more but when
converted to present value, the worth it has today, it come out to be less than Rs 100. Thus, it is clear
that Rs100 today worth more to Rs. 105 one year later. This conclusion is drawn on the assumption that
interest rate is 10%, but if we change the interest rate, the answer might be different.
With the help of the following diagram, we can observe the effect of discounting the cash flows.
Now the point to understand is that if we discount back this money from 2 years back we would have
only approximate Rs.87 in other words if Rs 105 are to be received after two years, the present value of
would be even lesser
If you discount Rs 105 two years from now, you will have lesser amount than you have one
year from today. It is clear from the slide that as more future cash flow occurs distant in time, the more
its present value decreases.
Time & Arrow Diagram
1 Year Discounting of Future Value
Time & Arrow Diagrams are important in visualizing the concept of Discounting
FV = Rs. 105
PV = Rs 95.45
Interest: 10% pa
Time (Years)
Yr 1
Yr 0
Today
Present
Discounting
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Financial Management ­ MGT201
VU
Time & Arrow Diagram
2 Year Discounting of Future Value
Notice how Discounting Rs 105 (FV2) from Year 2 gives a smaller Present
Value (PV2 = Rs 87) than Discounting Rs 105 from Year 1
FV1 = Rs. 105
FV2 = Rs. 105
PV1= Rs 95.45
PV2= Rs 87
Interest: 10% pa
Interest: 10% pa
Time (Years)
Yr 1
Yr 2
Yr 0
Today
Present
Discounting
Cash inflows (Income, other income & cash profits) shown with upward pointing arrow
Cash outflows (expense) shown with downward pointing arrow
Discounting Cash Flows of a Business, Investment, or Project:
Let's talk about the discounting cash flow of the business as to how we would estimate the cash
flow business can generate? How can we calculate the market value and intrinsic value of a business or
working asset? There are two steps involved
1) Forecast future cash flows of any business, investment, or project by using percent of sales
method.
2) Discount the net cash flows back to the present time.
The two-step process here can be elaborated by the following hypothetical example.
Cafe Case Study:
Suppose you are thinking about starting a small café or canteen inside a university campus. You
make a simple feasibility report showing the estimated initial investment and the forecasted cash flows
for the first Year (based on expected cash receipts from sales and cash payments for expenses).
The Key Financial Data is as follows:
·  Initial Investment = Rs 100,000
·  Forecasted Cash Receipts (end Year 1) = Rs 200,000
·  Forecasted Cash Payments (end Year 1) = Rs 50,000
·  Forecasted Future Investment (end Year 1)=Rs30,000
·  Periodic Interest Rate (Opportunity Cost) = 10% p.a.
First step is to represent the phenomenon through a diagram in the form of cash out flows.
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Financial Management ­ MGT201
VU
Cash Flow Diagram
Café Example
Use Downward Pointing Arrows to show Cash Outflows (Cash
Payments or Investments). Use Upward Pointing Arrows to show
Cash Inflows (Cash Receipts)
Receipts = Rs. 200,000
Interest: 10% pa
Yr 0
Yr 1
Future Investment = Rs 30,000
Payments = Rs 50,000
Initial Investment = Rs 100,000
First of all, we can see the initial investment represented by the downward arrow. We have also
forecasted the sales one year from now that is Rs.200, 000. This is a cash inflow for the business and is
represented by an upward arrow; similarly, the expenses and investments (cash outflows) that we expect
in future, will be shown by the downward arrows. In the diagram there are three arrows, the upward one
is showing forecasted sales (cash inflow) and two arrows downward show expenses of Rs.50, 000 and
invest outlay of Rs.30, 000 respectively. Now the combined effect of the three arrows can be
represented by a single arrow. We can see that cash inflow of Rs.200,000 is having a +ve sign and
expenses of Rs.50,000 and investment out lay of Rs.30,000 have ­ve signs and finally, by deducting the
negative signed figures from the positive one we can arrive at the net effect of the cash inflows and
outflows, which is given as under
200,000-50,000-30,000 =Rs 120,000.
These different arrows can be added or subtracted because they are occurring at the same point
of time and Rs.120, 000 can be shown by one arrow sign. In order to calculate the present value of
Rs.120, 000, rate of interest as discount factor should be 10% per year.
Simplified Cash Flow Diagram
Café Example
Net Cash Receipts = CF1 = FV1
=200,000­50,000­30,000 = Rs 120,000
Interest: 10% pa
Yr 1
Yr 0
After combining all Cash Flows
for Year 2 into one Net Cash
Flow Figure (CF1), you are
ready to now Discount it to the
Initial Investment = Rs 100,000
Present...
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Financial Management ­ MGT201
VU
Calculating the NPV
of the Café Business for 1st Year:
NPV = Net Present Value (taking Investment outflows into account)
NPV = -Initial Investment + Sum of Net Cash Flows from Each Future Year.
NPV = - Io +PV (CF1) + PV (CF2) + PV (CF3) + PV (CF4) + ...+
Note that PV (CF1) means the Present Value of Future Net Cash Flow (CF) taking place at the
end of Year 1. CF is like the FV in our interest formulas. Our compounding cycle is 1 year so the
Periodic Interest Rate is 10%.
Present Value of Net Cash Flow from Year 1 =
PV (CF1) = CF1 / (1+ i) n = 120,000 / (1+0.1)1 = Rs 109,000
The value of money has shrink from Rs.120, 000 to 109,000 as the concept of time value of the
money suggests and now we are in position to calculate the net present value of the money:
NPV = - Io + PV (CF1) = -100,000 + 109,000 = + Rs 9,000
The NPV of our Business after 1 Year is Positive Rs 9,000 which is a good sign. We will
discuss this topic in more detail in capital budgeting.
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