PRESENT VALUE AND RATE OF RETURN - 3

8/7/2019 PRESENT VALUE AND RATE OF RETURN - 3

1/29

IN THE NAME OF ALLAHTHE MOST BENIFICIAL AND MERCIFUL


2/29

PRESENT VALUE AND RATE OF

RETURN

We normally come across while

reading news papers that supposeyou deposit rupees 1,000/= today

and get twice the amount in 7 years,

or pay us rupees 100/= for 10 years

and we will pay rupees 100/= a year

thereafter in perpetuity and so on.


3/29

In such situation you would be interested

to know that what rate of interest beingoffered by the advertiser. You can use the

concept of present value to find out the

interest rate of return of these offers. Let

us take some examples.


4/29

A bank offers you to deposit Rs. 1000/= and

promise to pay Rs. 1,762/= at theend of five

years, what rate of interest you areearning? You

can set your problem as follows:

Rupees 1000/= is the present value of rupees

1762/= due to be received at theend of fifth yearThus

P= Rs. 1000 = Rs. 1762 (PVF5 . i)

PVF5, i= 1000 = .576

1762


5/29

Now we refer to tableCwe note that since

.567 is a PVF at i rate of interest for 5

ye

ars, look across the

row for pe

riod 5years and interest rate column until you

find this value. You will notice factor in 12

percent column. You will thus earn 12

percent on your amount Rs. 1000.


6/29

Let us take anotherexample, assume you

borrow Rs. 70000/= from theexisting

financial institution for mee

ting youremergent capital shortfall. You are

required to give some acceptable security

to the ban and agree to pay Rs. 11,396.93

annually for a period of 15 years. Whatinterest rate you will be paying?


7/29

Notice that Rs. 70,000/= is the present

value of 15 years annuity of rupees

11,396.93 that is: P = Rs. 70000 =

Rs. 11396.93 X PVAF15. i

PVAF15.i = 70,000 = 6.142 11,396.93


8/29

This time look across in tableD the row for

period 15 and interest rate column until

you will get the value 6.142 you find this

value in the 14 percent column, thus the

financial institution is charging 14 percent

rate of interest from you on the borrowed

amount of Rs. 70,000/=


9/29

Uneven series of cash flow

Now finding the rate of return on uneven

series of cash flow is little difficult. Bypractice and by using trial and error

method you can find it. Let us suppose

that your customer want to borrow rupees

1600 today and would return back to youRs. 700, Rs. 600, and


10/29

Rs. 500 in year 1 through year 3 as

principal plus interest. What rate of interest

would you beearning? You can again

recognize that Rs. 1600 is the present

value of Rs. 700, Rs. 600, and Rs. 500

receive respectively after one , two , and

three years. You feel that your customermust have perhaps paying you an interest

of 8 percent.


11/29

When you calculate the present value ofthe cash flow at 8 percent, you get the

following amount:


12/29

Years Cash flow

Rs.

PVF at 8% PV of Cash Flow

1. 700 .926 648.2

2. 600 .857 514.2

3. 500 .794 387.00

1,559.40


13/29

Since the amount is less than rupees 1600

therefore it seems that the rate of interestis lower than 8 percent. So you now have

to try at 6 percent and you obtain the

following results:


14/29

Years Cash flow

Rs.

PVF at 6% PV of Cash Flow

1. 700 .943 660.10

2. 600 .890 534.00

3. 500 .840 420.001,614.10


15/29

It seems that the approximate offer

interest rate is 6 percent. In fact the actual

rate of interest would be little higher than 6

percent. However at 7 percent the present

value of cash flow will be Rs. 1,586. Thus

you can interpolate as follows to calculate

the actual rate:


16/29

Difference

Required PV Rs. 1600

PV at 6% Rs. 1,614 Rupees 14

PV at 7% Rs. 1,586 Rupees 28

Thus the rate of interest is:

= 6% + (7% - 6%) X Rs.14

Rs.28

= 6% + .5% = 6.5%


17/29

PAYBACK (PERIOD)

The payback is one of the most popularand widely recognized traditional methods

ofevaluating investment proposals. It is

defined as the number of years requiredto

recoverthe original cash outlay invested in

a project.


18/29

If the project generates constant annual

cash inflow, that is:

Payback = Initial Investment = Co

Annual Cash inflow C


19/29

To Illustrate

Assume that a project requires an outlay

of Rs.50, 000 and yield annual cash inflowof Rs. 12,500 for 7 year. The payback

period for the project is:

Payback = 50,000 = 4 years

12,500


20/29

In case of unequal cash inflow thepayback period can be found out by

adding up the cash inflow until the total is

equal to the initial cash outlay.


21/29

To Illustrate

Suppose that a project requires cash outlay of

rupees 20,000 and generates cash inflowRs. 8,000, Rs. 7,000, Rs 4,000, and Rs 3,000 during

the next 4 years. When we add up the cash inflows

we find that in the first 3 years Rs. 19,000 of the

original of the outlay is recovered. In the fourth yearcash inflow generated is Rs. 3,000 and only Rs 1,000

out of the original outlay remains to be recovered.


22/29

Assuming that cash inflow occurs evenly

during the year, the time required torecover Rs. 1,000 will be ( Rs. 1,000/Rs.

3,000) X12 months = 4 months. Thus the

payback period is 3 years and 4 months.


23/29

AMORTIZATION

Amortizingof a Loan

An important use of present valueconcepts is in determining the paymentrequired for an installment-type loan. The

distinguishing feature of this loan is that itis repaid in equal periodic payment thatincludes both interest and principal.


24/29

These payments can be made monthly,

quarterly, semiannually or annually.Installment payments are prevalent in

mortgage loans, auto loans, consumers

loan and certain business loans.


25/29

To illustrative with the simplest case ofannual payment, suppose you borrowRupees 22,000/= at 12 percent compound

annual interest to be repaid over the nextsix years. Equal installment payments arerequired at theend ofeach year. Inaddition these payments must be sufficient

in amount to repay Rs. 20,000 togetherwith providing the lender with a 12 percentreturn.


26/29

In TableIVwe find that the discount factor for sixyears annuity with a 12 percent interest rate is4.111. Solving forRwe set up the problem as :

Rs. 22,000 = R ( 4.111 )

R= Rs. 22,000 / 4.111 = Rs.5,351

Thus annual payments of Rs. 5,351 will

completely amortize (extinguish) a Rs.22,000loan in six years. Each payment consists interestand partly of principal


27/29

End of

year

( 1 )

Installment

payment

( 2 )

Annual Interest(4) X .12

( 3 )

Principal

Payment

(1) (2)

( 4 )

Principal Amount

owing at the end

(4) (3)

0 - - - 22,000

1 5,351 2,640 2,711 19,289

2 5,351 2,315 3.036 16,253

3 5,351 1,951 3,400 12,853

4 5,351 1,542 3,809 9,044

5 5,351 1,085 4,266 4,778

6 5,351 573 4,778 0

32,106 10,106 22,000


28/29

Text boos recommended for studies:

Fundamental of Financial Management1. Ramesh K.S.RAO

2. James C.Van Horne / John M. Wachowicz, JR.

Essentials of Financial Management

1. I.M.Pandey


29/29

THE END

PRESENT VALUE AND RATE OF RETURN - 3

Documents

Transcript of PRESENT VALUE AND RATE OF RETURN - 3