Payback Period,

Time Value of Money &

Internal Rate of Return

Presented By: SUBHASH ROHIT

Payback Period

Definition:

The Payback period is the amount

of time that it take to recover your costs in a

project.

FORMULA: Payback Period

Even Or Uneven

Even:

Payback Period = Initial Investment/ Annual Cash flows

Uneven:

Payback Period=A+(B/C)

Where;

A=The Last period with a negative cumulative cash flow

B=The absolute value of cumulative cash flow at the end of the period A;

C=The total cash flow during the period after A

Example

Even Cash Flow:

Company C is planning to undertake a projectrequiring initial investment of $105 million.The project is expected to generate $25million per year for 7 years. Calculate thepayback period of the project.

Cont..

Payback Period = Initial Investment/ Annual Cash flows

=$105/$25

=4.2 year

Cont..

Uneven Cash Flows.

Company C is planning to undertake another project

requiring initial investment of $50 million and is

expected to generate $10 million in Year 1, $13

million in Year 2, $16 million in year 3, $19 million

in Year 4 and $22 million in Year 5. Calculate the

payback value of the project.

Cont..

Payback Period

= 3 + (|-$11M| ÷ $19M)

= 3 + ($11M ÷ $19M)

≈ 3 + 0.58

≈ 3.58 years

(cash flows in millions)Year Cash Flow

CumulativeCash Flow

0 50 -50

1 10 -40

2 13 -27

3 16 -11

4 19 8

5 22 30

Payback Period Rule

The Decision Rule:

If the pay back period is less than the predetermined

payback, then the project would be Accepted; if not, it

would be rejected

Advantage of Payback Period

It is very simple. It is easy to understand and apply

It is cost effective

The payback period measures the direct relationship

between annual cash inflows from Proposal and the net

investment required

Disadvantage Of Payback Period

The pay back period entirely ignores the cash

inflows that occur after the pay back period

The pay back period also ignores salvage value

and total economic life of the project

It ignores the time value of money

Drawbacks of Payback Period

Does not consider all of the project’s case flows.

This project is clearly profitable, but we would

accept it based on a 4 year payback criterion!

Time Value Of Money

The concept modern finance and management.

We say that money has a time value because that

money can be invested with the expectation of earning

a positive rate of return

In other words, “a rupee received today is worth more

than a rupee to be received tomorrow”

Calculations based on the time value of money

Present Value - An amount of money today, or the

current value of a future cash flow

Future Value - An amount of money at some future

time period

‘n’ is the number of periods

‘r’ is the rate at which the amount will be compounded

each period

Cont…

PV(A) the value of the annuity at time = 0

FV(A) the value of the annuity at time = n

‘A’ the value of the individual payments in each

compounding period

‘n’ is the number of periods

‘r’ is the rate at which the amount will be compounded

each period

Formulas

Present value of a future sum / Future value

of a present sum.

Example

Consider 2 situations

•Option A: You receive Rs. 10,000 today.

•Option B: You receive Rs. 10,000 in 3 years time

•Assume no inflation

•Assume interest rate 10% (Compound Interest)

•Assume no change in any other financial situation

Future Value Calculation

Consider Option B

Let’s calculate the future value of Rs. 10,000

received at the present time.

Cont..

Present Value Calculation

Similarly using the equation as

Cont..

The present value of Rs. 10,000 received in 3 years

when the interest rate is 10% can be calculated as Rs.

7513.1

Cont..

(Internal Rate of Return) IRR

The IRR should be applied only for very simple

investments.

Internal rate of return (IRR) is the discount rate at

which the net present value of an investment becomes

zero. In other words, IRR is the discount rate which

equates the present value of the future cash flows of

an investment with the initial investment.

Cont…

Decision Rule

•Stand-alone Projects

•If IRR > cost of capital (k) accept

•If IRR < cost of capital (k) reject

IIR Calculation

•Formula

Cont..

Find the IRR of an investment having initial cash

outflow of $213,000. The cash inflows during the

first, second, third and fourth years are expected to be

$65,200, $96,000, $73,100 and $55,400

respectively.

Assume that r is 10%.

NPV at 10% discount rate = $18,372

Since NPV is greater than zero we have to increase

discount rate, thus

NPV at 13% discount rate = $4,521

But it is still greater than zero we have to further

increase the discount rate, thus

NPV at 14% discount rate = $204

NPV at 15% discount rate = ($3,975)

Since NPV is fairly close to zero at 14% value of r,

therefore

IRR ≈ 14%

Cont…

First, imagine a situation in which you invest $1

million today and then receive $500,000 per year

for the next 4 years. That investment gives an IRR of

35%, which would be pretty good by today’s

standards. Now let’s change some of the key

variables.

If instead you had to invest only $500,000 up front for

the same amount of return, the IRR improves to 93%.For

those of you unfamiliar with the terminology, a project with

an IRR of 93% is both rare and very desirable to pursue.

The reduction in the up-front investment caused the return to

skyrocket.

Now let’s go back to the initial $1 million investment and

make the return only $350,000 for 4 years. This

manipulation causes the IRR to drop to only 15% from the

previous value of 35%.

CONCLUSION

Any time you are evaluating an investment over time,

use time-value-of-money.

In financial modelling, allow for both time-value-of

money calculations as well as uncertainty to improve

your projections and the decisions on which they are

based.