The document outlines key concepts in investment evaluation including payback period, time value of money, and internal rate of return (IRR). It emphasizes the importance of understanding payback periods for both even and uneven cash flows, as well as the decision-making criteria for investments. Additionally, it discusses the implications of time value on future and present cash flows, demonstrating how these concepts can impact investment decisions.

1. Payback Period,
Time Value of
Money &
Internal Rate of
Return
Presented By:SUBHASH ROHIT

2. Payback Period
Def i ni t i on:
The Payback
peri od i s t he amount
of t i me t hat i t t ake
t o recover your cos t s
i n a proj ect .

3. FORMULA: Payback
Period Even Or Uneven
 Even:
Payback Period = I nit ial I nvest ment /
Annual Cash f lows
 Uneven:
Paybeck Period=A+(B/ C)
Where; A=The Last period wit h a negat ive
cumulat ive cash f low
B=The absolut e value of cumulat ive cash

4. Example
Even Cash Flow:
Company Cis planning to undertake a project requiring initial
investmentof$105million. Theprojectisexpectedtogenerate
$25millionperyearfor7years. Calculatethepaybackperiodof
theproject.

5. Cont..
Payback Period = I nit ial
I nvest ment / Annual Cash f lows
=$105/ $25
=4.2 year

6. Cont..
Uneven Cash Flows.
CompanyCisplanningtoundertakeanotherprojectrequiringinitial
investmentof$50millionandisexpectedtogenerate$10million
inYear1, $13millioninYear2, $16 millioninyear3, $19
millioninYear4and$22 millioninYear5. Calculate the
paybackvalueoftheproject.

7. Cont..
Payback Period
= 3 + (| -$11M| ÷
$19M)
= 3 + ($11M ÷
$19M)
(cash flows in millions)
Year Cash Flow
Cumulative
Cash Flow
0 50 -50
1 10 -40
2 13 -27
3 16 -11
4 19 8
5 22 30

8. Payback Period Rule
The Decision Rule: t he act ual
payback is compared wit h a
predet ermined pay back, t hat
is, t he pay back set by t he
management in t erms of t he
maximum period during which
t he invest ment must
recovered.

9. Advantage of
Payback PeriodI t is very simple. I t is easy t o
underst and and apply
 I t is cost ef f ect ive
The payback per iod measures
t he direct relat ionship bet ween
annual cash inf lows f rom
Proposal and t he net invest ment
r equir ed

10. Disadvantage Of
Payback Period
The pay back period ent irely
ignores t he cash inf lows t hat
occur af t er t he pay back
period
The pay back period also
ignores salvage value and
t ot al economic lif e of t he

11. Drawbacks of
Payback PeriodDoes not consider all of t he
proj ect ’s case f lows.
This proj ect is clearly
prof it able, but we would

12. Time Value Of Money
The concept modern f inance
and management .
We say t hat money has a t ime
value because t hat money can
be invest ed wit h t he
expect at ion of earning a
posit ive rat e of ret urn

13. Calculations based on the
time value of money
Present Value - An amount of
money t oday, or t he cur rent
value of a f ut ure cash f low
Future Value - An amount of
money at some f ut ure t ime
per iod
‘n’ is t he number of periods
‘r ’ is t he rat e at which t he

14. Cont…
PV(A) t he value of t he annuit y
at t ime = 0
FV(A) t he value of t he annuit y
at t ime = n
‘A’ t he value of t he individual
payment s in each compounding
per iod
‘n’ is t he number of periods

15. Formulas
Present value of a future sum
/ Future value of a present
sum.

16. Example
 Consider 2 sit uat ions
 Opt ion A: You receive Rs.
10,000 t oday.
 Opt ion B: You receive Rs.
10,000 in 3 years t ime
 Assume no inf lat ion
 Assume int erest rat e 10%

17. Future Value
Calculation
Consider Opt ion B
Let ’s calculat e t he f ut ure value
of Rs. 10,000 received at t he
present t ime.

18. Cont..

19. Present Value
Calculation
Similarly using t he equat ion as

20. Cont..
t he present value of Rs. 10,000
received in 3 years when t he
int erest r at e is 10% can be

21. Cont..

22. (Internal Rate of
Return) IRRThe I RR should be applied only
f or very simple invest ment s.
I nt ernal rat e of r et urn (I RR) is
t he discount rat e at which t he
net present value of an
invest ment becomes zero. I n
ot her words, I RR is t he
discount rat e which equat es t he

23. Cont…
Decision Rule
 St and-alone Proj ect s
 I f I RR >cost of capit al
(k) ⇒ accept
 I f I RR <cost of capit al
(k) ⇒ rej ect

24. IIR Calculation
 Formula

25. Cont..
FindtheIRRofaninvestmenthavinginitialcashoutflowof
$213,000. Thecashinflowsduringthefirst, second, thirdand
fourthyearsareexpectedtobe$65,200, $96,000, $73,100and
$55,400respectively.
Assumethatris10%.

26.  NPV at 10% discount rat e =
$18,372
Since NPV is great er t han zero
we have t o increase discount
rat e, t hus
NPV at 13% discount rat e =
$4,521
But it is st ill great er t han zero
we have t o f urt her increase t he
discount rat e, t hus
NPV at 14% discount rat e = $204

27. Cont…
First , imagine a sit uat ion in
which you invest $1 million
t oday and t hen receive
$500,000 per year f or t he next
4 years. That invest ment gives
an I RR of 35%, which would be
pret t y good by t oday’s
st andards. Now let ’s change

28. I f inst ead you had t o invest only
$500,000 up f ront f or t he same
amount of ret urn, t he I RR
improves t o 93%.For t hose of you
unf amiliar wit h t he t erminology, a
proj ect wit h an I RR of 93% is bot h
r ar e and ver y desirable t o pursue.
The reduct ion in t he up-f r ont
invest ment caused t he ret urn t o
skyrocket .

29. CONCLUSION
Any t ime you ar e evaluat ing an
invest ment over t ime, use t ime-
value-of -money.
I n f inancial modelling, allow f or
bot h t ime-value-of money
calculat ions as well as
uncert aint y t o impr ove your
proj ect ions and t he decisions on

30. Thank
You…!