This document discusses calculating the present value and future value of multiple uneven cash flows. It provides the formulas for present value (PV) and future value (FV) of uneven cash flows. As an example, it calculates the PV of a cash flow of Rs. 1000, Rs. 1500, Rs. 800 and Rs. 400 over 4 years with an interest rate of 8%. It also provides an example to calculate the FV of deposits of Rs. 500, Rs. 1000, Rs. 1500, Rs. 2000, Rs. 2500 over 5 years with an interest rate of 5%.

1. MULTIPLE UNEVEN
CASH FLOW

2. Cash Flow Time Line
 Future Value(FV):The amount to which a cash
flow or series of cash flows will grow over a given
period of time when compounded at a given
interest rate.
 Present Value(PV):The value today of a future
cash flow or series of cash flows.
 Compounding : The process of going to future
values (FVs) from present values (PVs) is called
compounding.

3. Present Value of Multiple Uneven
Cash Flow
 Investment made do not yield constant periodic
cash flow
 Most cases firm receives stream of uneven cash
flows
 Where
 Ct is Cash flow in period t,
 i is rate of interest
 n= number of years

4. Example
 Consider that an investor has an opportunity of
receiving Rs 1000, Rs 1500, Rs 800 and Rs
400 respectively at the end of one year
through five years
Find out the present value of this stream of
uneven cash flow.
The investor’s required interest is 8%

5.  The Present Value can be calculated as
follows
PV=1000/(1.08)+1500/(1.08)2+800/(1.08)3+1
100/(1.08)4+400/(1.08)5 = 3927.60
PV=C1/(1+i)+C2/(1+i)2+C3/(1+i)3
+………+Ct/(1+i)t=∑CFt/(1+i)t

6. Future Value of Multiple Uneven
Cash Flow
 The future value (FV) compounding interest
formula for each period and then sum them all
together.
• Where
CFt is the cash flow occurring at time t
i is the interest rate per period
n is the number of period

7. Example
 Suppose Mr X deposits each year Rs 500, Rs
1000, Rs 1500, Rs 2000 and Rs 2500 in his
saving bank account.
The interest rate is 5% yearly.
He wishes to find the future value of his
deposits at the end of 5th year.

8.  FV=500 X (1.05)5+1000 X (1.05)4+1500 X
(1.05)3+2000 X (1.05)1+2500 X (1.05)0 =
8020.5
End of
year
Amount
deposited
Number of years
compounded
Compound
interest factor
Future
Value
Col (1) Col(2) Col(3) Col(4) (2) X (4)
1 500 4 1.216 608
2 1000 3 1.158 1158
3 1500 2 1.103 1654
4 2000 1 1.05 2100
5 2500 0 1 2500

10. Thank You