ACCA F9 2018
FINANCIAL
MANAGEMENT

Chapter – 3
Investment appraisal – Discounted cash flow
techniques
DCF TECHNIQEQ
 Time value of money
• Interest
• Inflation
• Risk
• Compounding
• Discounting (PV of a single amount, Annuities, perpetuities,
delayed and advanced annuities)
 NPV
• Gives the net surplus earned for investors
• Absolute technique
• All cash flow considered
• Superior method
• But complex method
 IRR
• Gives the return earned on the project
• Is the rate at which NPV =0
• Find through interpolation
• A quick method for annuities and perpetuities
• DCF technique
• % means a relative return
• Easy to understand
• The disadvantage in estimation, complex, mislead in
choices when cash flows are unusual

 Some basic Mathematical Calculations are involved in the
chapter. Since the project involves cash flows for more than
a year, so time value of money is important. So we have to
develop the concept of Time value of Money. Money has a
time value that is Rs. 100 today are more valuable than the
same Rs.100 sometime from now. Why? because of three
factors:
a) Due to inflation (inflation premium).
b) Sacrificing the present consumption against future (Real
Return).
c) Risk Premium.
These three factors are different in different countries and they
are different in different investment proposal. Suppose in a
particular investment proposal risk premium is 5%, real return in
the market is 2 % and inflation in the market is 6%. The effective
interest rate is not 13% because simple Interest calculation is not
allowed. In Finance compound Interest calculation is essential.
According to Fisher`s Equation, the effective interest rate after
incorporating all the three factors, that is risk adjusted nominal
interest rate = ( 1 + risk free real rate ) ( 1 + inflation) ( 1 + risk
premium)- 1
= (1.02) (1.06) (1.05) - 1
= 0.13526
= 13.526 %
Suppose in the above example the investment is in government
securities. So risk premium is not to be taken into consideration.

So after incorporating real return and inflation it is risk free
nominal rate of return.
= (1 + real) * (1 + inflation) - 1
= (1.02) * (1.06) - 1
= 0.0812
= 8.12%
For example
Nominal Return is - 15%
Real Return - 3%
Inflation - 7%
Find out the risk premium
Answer:
(1+0.03) * (1+0.07) + (1 + risk %) - 1 = 0.15
= (1.03) * (1.07) * (1 + risk) = 1.15
= 1.1021 + 1.1021 risk = 1.15
Risk premium =
1.15−1.1021
1.1021
= 4.35%
The risk-free nominal rate is also called MONEY RATE OF
RETURN. Some basic calculations relating to interest rate are:-

Q1. Calculation of FUTURE VALUE of a given sum
For eg: Mr. A deposits 1, 00,000 in the bank @ 9 % for 5 years.
Find out the total amount receivable to Mr. A at the end of the 5
years.
Future Value = Present Value (1 + i) n
= 1, 00,000 * (1 + 0.09)5
= 1, 53,862.
Suppose in the above example interest rate is 9 % p.a.
compounded semi-annually. Then the total amount receivable at
the end of the fifth year.
Future Value = 100000 (1 + 0.09/2)5 * 2
= 1, 55,296
So in future value calculation, interest (i) is the interest % for each
compounding period and `n` is the number of times compounding
in that period.
To calculate FUTURE VALUE, (1 + i) n
is called Future Value
interest Factor (FVIF Factor) for different combinations of i and n.
Using Table given behind Future value = P.V (FVIFi, n)
= 1, 00,000 (FVIF 0.045, 10)
= 1, 55,296.

Q 2 – Calculation of the PRESENT VALUE of a given Sum.
Present Value = Future Value
(1 + i) n
For eg: Mr. B requires Rs 30,00,000 at the end of 20yrs. The
interest rate is 8% per annum compounded quarterly. Find out the
amount to be deposited today.
P.V = 30, 00,000
(1 + 8/4)20 * 4
= 30, 00,000/ (1.02)80
= 615329.
P.V= F. V ∗
1
(1+i)
n = present value interest factor
P.V = F.V * (PVIF i,n).
Calculation of Future Value of Annuity.
Annuity means a series of cash flows in which amounts are the
same and gap between the amounts are also the same. So future
value can be calculated by application of an arithmetical formula.
FVA = A/i [(1 + i) n - 1]
For eg. Mr. A will deposit 10000 in the bank at the end of every
month. If the interest rate on deposit is 12% p.a. for 5 years

compounded monthly, Find out the total amount receivable at the
end of 5 yrs.
A = annuity amount that is 10000.
i = interest rate for each annuity period
.
. . interest % for 1 month = 12% / 12 = 1%
n = no .of Annuities = 60.
So total amount receivable at the end of 5 years
10000[(1 + 0.01)60
- 1)
0.01
= (10,000 / 0.01) ((1.01)60
- 1).
= 816696.
Future value interest factor for annuity.
= 10000 * FVIFA (i,n)
= 10000 * FVIFA (1%., 60)
There are two types of Annuities,
- Regular Annuity
- Annuity Due
In the case of Regular Annuity, Annuity arises at the end of each
period and in the case of an Annuity due, annuity arises at the
beginning of each period. So suppose in the above example

10000 is deposited at the beginning of each period, which is the
beginning of each month, the total Future value at the end of 5th
year.
= 816696 * (1.01)
= 824862.
The problem remaining silent, the annuity is treated as a regular
annuity
Calculation of present value of Annuity.
Suppose Mr. B will do business. The business will run for 5 years.
Cash inflow in the business for coming 5 years 100000 every
year. If Mr. B requires a 12% return from the business, what is the
maximum amount which B can invest today?
PVA = A/i [(1 - 1/ (1 + i) n
]
= 1, 00,000/0.12 [1 - 1/ (1.12)5
]
= 3, 60,477
= 1, 00,000 * PVIFA (12%, 5)
It annuity is annuity due, then present value will also be 360477 *
1.12 = 4, 07,766

Present Value of Perpetuity
Perpetuity means an annuity, which will continue for ever.
Suppose in the above example, Mr. B will receive 1, 00,000 p.a.
for every year Present value = 1, 00,000/0.12 = 8, 33,333.
Q Suppose Mr. X invests 5, 00,000 in business. The business will
be conducted for 5 years.
Cash flow in 5 years will be
Year Cash flow
1 100000
2 80000
3 30000
4 100000
5 260000
If Mr. X requires a 15% return from the business, whether the
business should be started by Mr. X or not.
Answer
Mr. X will invest 500000 in the business and he requires a 15%
return. So the P.V of all the cash inflows @5% should be 500000
or> 500000, then only the business or project should be done
otherwise not.

Year Cash Flow PV factor
(Discountingfactor)[1/1.5]
Present
Value
1 10000 0.870 87000
2 80000 0.756 60480
3 30000 0.657 19710
4 100000 0.572 57200
5 260000 0.497 129220
TOTAL 353610
Net Present Value (NPV)
= P.V of inflow - outflow.
= 353610 - 5, 00,000
= (146390)
So a project should be accepted when NPV is Zero or positive.
Inflation effect on the Project
Nominal Cash flows should be discounted by the nominal
discount rate, and real cash flows should be discounted by real
rate. Problem remaining silent it is assumed that cash flows are
nominal and the discount rate is nominal.
To solve the problem there are two options:

1. Convert Real Cash flow into Nominal Cash flow by adjusting
inflation and then find out NPV by the nominal discount rate.
2. Convert the nominal discount rate into the real discount rate
and then find out NPV by the real discount rate.
Note - if inflation is different on sales, raw material, labor,
and overhead etc. then to solve the problem we have only
one option that is converting real cash flows and then finds
out NPV.
Methods to Decide About a project
There are two types of Methods for taking a decision about a
project.
A. Discounting Methods /Criteria.
Those who consider the time value of money. These includes
1. Net Present Value Method.
2. Internal Rate of Return Method
3. Profitability index or Benefit Cost Ratio method
4. Annual Capital Charge Method.
5. Discounted Payback Period Method.
Calculation of Internal Rate of Return
IRR is the rate of return which the organization is getting from the
project. This can be calculated by equating the present value of
cash inflows with the outflows. So if the internal rate of return is
greater than the required rate of return than the project should be
accepted otherwise not.

Steps to calculate IRR.
Step 1. Assume any rate find out the present value of cash
inflows
Let the rate is 10%
So present value of cash inflow @10%
P.V
200*0.409 =181.8
150*0.826 =123.9
100*0.751 =75.1
100*0.683 =68.3
120*0.621 =74.52
523.62
Step - 2
It Present value in step 1 is higher than initial outflow then take a
higher rate and vice versa.
Let IRR is 15%
200 0.869 173.8
150 0.756 113.4

100 0.657 65.7
100 0.572 57.2
120 0.497 59.64
469.74
Step – 3
Apply interpolation or extrapolation to find out IRR
i PV
10% 523.62
15% 469.64
i% 0
If `i` will be within two rates then it is treated as interpolation and if
`i` is outside the two rates it is treated as extrapolation
15−10
𝑖−10
=
469.64−523.62
450−523.62
5
𝑖−10
=
−53.98
73.62
= 16.8

Note: IRR will be different for different students in the same
project because it depends upon those two rates which you
have assumed. So in IRR, the methodology of computation is
important.
Note - If the annual cash inflows are equal, then exact IRR
can be calculated with the help of annuity factor table like in
Page 481 illustration.
700000 * PVIFA (I,3) = 15,00,000
PVIFA (I,3) = 15,00,000/7,00,000
PVIFA (i, 3) = 2.14.
So from the annuity factor table, in front of 3 yrs. at 19% annuity
factor is 2.140. So IRR of the above project is 19%.
The conflict between NPV and IRR
a) Generally, those project whose NPV is higher, generally, their
IRR will also be higher, but sometimes NPV of one project is
higher and IRR of another project is higher. This can be explained
in two ways.
1. Due to the timing of cash flows like in page 284 in project A
all the Cash flow arises at the end of the life of the project
that is at the end of the second year, whereas in project B,
Some cash flow arises in the first year also. So, IRR is
higher for project B because of earlier cash flows, but the
total cash flow is higher in project A. So NPV is higher for

project A. So NPV gives importance to total cash flow
and IRR gives importance to the timing of cash flow.
2. The discount rate is lower than the rate of return where NPV
of both the projects is equal. In the above example, the
discount rate is 10%. Whereas NPV of both the projects will
be equal at a rate higher than 10%.
REFER DIAGRAM ON PAGE NO. 118 slide /86 book page
If this scenario arises in any two projects, the decision should
always be based on NPV. Because organizations have the cost of
funds 10% in both the projects and project A is giving higher NPV
at 10%. So project A should be accepted.
CHANGE IN DISCOUNT RATES
Suppose the cash flows of a project are.
year 0 1 2 3 4
Cash
flow
(100) 20 50 30 80
Dis % 10 12 13 11
Dis factor 1 1 0.909 0.812 0.718
1.1 1.12 1.13 1.11
0.909 0.812 0.718 0.647
(100) 18.18 40.6 21.54 51.76
NPV = Inflow - 100
= 132.08 - 100 = 32.08
(In relation with illustration in page 505 changes in rates)

Advantages and disadvantages of using NPV
Advantages:
Theoretically, the NPV method of investment appraisal is superior
to all others. This is because of it:
• considers the time value of money
• is an absolute measure of return
• is based on cash flows, not profits
• considers the whole life of the project
• should lead to the maximization of shareholder wealth.
Disadvantages:
• It is difficult to explain to managers
• It requires knowledge of the cost of capital
• It is relatively complex.
Advantages and disadvantages of IRR
Advantages:
The IRR has a number of benefits, e.g. it:
• Considers the time value of money
• Is a percentage and therefore easily understood
• Uses cash flows, not profits
• Considers the whole life of the project
• means a firm selecting projects where the IRR exceeds the cost
of capital should increase shareholders' wealth

Disadvantages
• It is not a measure of absolute profitability.
• Interpolation only provides an estimate and an accurate
estimate requires the use of a spreadsheet program.
• It is fairly complicated to calculate.
• Non-conventional cash flows may give rise to multiple IRRs
which mean the interpolation method can't be used.