Notesale: Turn your study into money

Document Preview

Extracts from the notes are below, to see the PDF you'll receive please use the links above

---

See discussions, stats, and author profiles for this publication at: https://www
...
net/publication/354961751

INTRODUCTION TO BUSINESS FINANCE OR MANAGERIAL FINANCE LECTURE
NOTE
Preprint · September 2021

CITATIONS

READS

0

1,786

1 author:
Anu Toriola
Olabisi Onabanjo University
44 PUBLICATIONS   7 CITATIONS   
SEE PROFILE

Some of the authors of this publication are also working on these related projects:

Gender equality and sustainable education in nigeria View project

Gender equality and sustainable education in ogun state View project

All content following this page was uploaded by Anu Toriola on 30 September 2021
...


INTRODUCTION TO BUSINESS FINANCE OR MANAGERIAL FINANCE
LECTURE NOTE

TORIOLA, Keshiro
...
com

ʺ Copyright © 2021 by Toriola Anu
All rights reserved
...
Interested Publishers can contact the correspondence
...
meaning, nature and functions of finance
2
...
MATHEMATICS OF FINANCE
a
...
compound interest and discontinuity
c
...
CAPITAL BUDGETING DECISION OR INVESTMENT APPRAISAL TECHNIQUES
a
...
Discounting techniques:
i net present value (NPV)
ii profitability index (PI) or Benefit Cost Ratio (BCR)
iii Internal rate of return
5
...
Cost of capital
b
...
Cost of debt
6
...
Financial system institutions
b
...
Money market and participant with instrument
d
...
Dividend theory

MEANING, NATURE AND FUNCTIONS OF FINANCE
2

The activities of management have been identified to include finance, accounting, production,
marketing, personnel, management, research development, quality control among others
...
Management must
therefore be concerned not only with production and marketing but also with finance
...
Finance can be seen as the monetary and capital resources used by the business in the
acquisition of other resources or investment assets
...
Finance is also considered as the management of the monetary resources of organization and
this aspect is better referred to as financial management
...
The objective of financial
management is to increase shareholder’s wealth by maximizing returns and minimizing risks
...

BASIC CONCEPTS IN FINANCIAL MANAGEMENT
To further appreciate the concepts of financial management is necessary to highlight its concepts,
which include: capital, working capital and dividends
...
Capital: This is the financial resources used n business for investment purposes
b
...

c
...

Functions of Finance
According to pandey, finance functions are categorized into two, which are: managerial finance
functions (Assets acquisitions) and Routine finance function (working capital acquisition)
...
Investment decision
3

b
...
Dividend decision
d
...
Investment Decision: This involves the allocation of funds on cometing projects whether new
or existing ones
...
Investment decision is
called capital budgeting and it requires the estimate of the cost of capital (Interest rate), risks,
as well as expected cash flows from the project
...
Financing Decision: After the identification of profitable projects, it is necessary to determine
the source(s) of finance for the project, this decision therefore is concerned with the
determination of the least costs source of finance which would guarantee maximum return to
owners of the business, since different sources have different costs and maturity period
...
Dividend decision: This involves the determination of the dividend policy which balances the
expectation of dividends and growth through retained earnings
...
Anyh profit not declared as dividends are ploughed back
into the business as retained earnings which inevitably generate further profit
...

d
...
Hence, the firm must determine the proportion of her total assets to hold in short-term
assets
...

SOURCE OF FINANCE
The sources of finance can be categorized on the basis of providers of funds and the form of
financing
...

4

1
...
They include:
a
...
Leasing
c
...
Sales and leased back
2
...

They include:
a
...
Trade credit
c
...
Hire purchased
e
...
Preference shares
g
...
Venture financing
3
...

They include:
a
...
Trade credit
c
...
Loan from friends or relatives
e
...
Accrued expenses
4
...
They include:
a
...
Leasing
c
...

5
...

They include:
a
...
Sales and leased-back
c
...
Preference shares
e
...
Venture financing
NOTES ON SOURCES OF FINANCE
1
...
It is a shot
5

term sources of finance suitable for working capital (or short term asset) because the repayment
is on demand
...

2
...
The costs pf
making use of this facility is the difference between the cash price of the goods and the price on
credit basis since the selling company must have consider the risks of repayment or delay in
repayment
...

3
...

4
...

5
...

6
...
In return for a regular specified payment known as lease
rental
...
Ordinary shares: These are issued by firm on incorporation to provide them risks capital
...


6

8
...
It is a long term promising note for raising
capital
...

MATHEMATICS OF FINANCE
INTEREST AND ANNUITIES
1
...

Principal is the sum borrowed
Numbers of years is the length of time for which the principal is borrowed
...
If the
principal is “P”, the interest rate per period is “r”, and the number of years is “n” and “SI”
represents the interest, them:
SI=Prn
Principal plus interest is called the accumulated value (fr) of simple interst
Fv=P+SI=P+Prn
Fv=P (1+rn)
In practice, interest is often paid periodically so that only interest due at the end of the term is that of
the last period
...
Find the interest and accumulated value id N460 is borrowed for 15 months at 14%per annum
...
14)
n= number of years (15/12=13/12=1
...
14 1
...
50
The accumulated value:
Fv=P+SI
Fv=460+80
...
50
It is a common practice among tending institution to count the exact number of days in term of a
loan when n
Fv=p(1+r)n where:
Fv =accumulated value (4500)
P=present value (3250)
r=rate of interest (0
...
06)n
4500/3250 =(1+0
...
3846=(1
...
3846 = nlog 1
...
06
n= log 1
...
06
n=0
...
023059
n=5
...
9 years
or use the formula:
n=log fv-log p/log (1+r)
COMPOUND INTEREST
8

Interest of compound interest
we can solve fv = p (1+r)n for r by use of logarithms or radicals or by tables and interpolation
...
5460 = (1+r)27
take 27th root of both sides
273
...
5460 -1
r=10
...
048-1
r1
...
048-1
r=4
...
g
...

9

Illustration
a

what is the end of the years value of #/m investment if interest rate 12% is payable monthly for

a year?
Solution
Fv=p(1+r/m)nm where:
Fv= end of the year value (?)
P=present value (1000000)
r=compounding rate (0
...
12/12)1x12
fv=1000000(1+0
...
10)12
Fv=#1000000(1
...

Continuous Compounding
The limiting case of compounding would be to compound every infinitesimal instant
...
The value at the end of n years with continuous
compounding is expressed as:
Fv=Per n where:
Fv=accumulated value
P=principal
E=exponential value (2
...
7183)
r=annual rate (008)
n=number of years (2)
fv=1000(2
...
08x2
fv=1000(2
...
16
fv=1000(1
...
5
Effective annual rate versus nominal annual rate
If the conversion period in compound interest differs from a year, the stated annual rate is called the
nominal rate
...
The symbol rm is often used to
represent annual rate and m represents the number of times per year
...
If p is invested at an effective rate of EAR for a year, it
accumulated to p (1+EAR)
...

Illustration
What is the effective rate if the nominal rate is 6% compounded quarterly?
EAR= (1+r/m)m-1
=(1+0
...
15)4-1
=1
...
0614 =6
...

4
...
The length of time between consecutive payments is called payment period and sum paid
periodically is known as the periodic payment or installment
...

Type of Annuity
a
...
Annuity due
Ordinary Annuity, Annuity at the End or Annuity in Arrears
Ordinary annuity is sequence of equal payments or receipts at the end of equal interval lasting for a
fixed numbers of periods
...
g
...


Future value of ordinary annuity (end)

If A is received or paid at the end of each periods for n periods and if money is worth r per
period
...
i
...
+ A(1+r)n-1
Multiply although by (1+r)
12

Fv(1+r)=A(1+r) +A(1+r)2 +A(1+r)3 + …………………A(1+r)n+1
Subtract equation 2 from equation 1
Fv-Fv(1+r)=A-A (1+r)n+1
Fv[1-(1+r)]=A[1- (1+r)n+1]
Fv[1-(1+r)]=A[1- (1+r)n+1]
Fv[-r]=A[1-(1+r)n+1]
Fv[1-(1+r)]=A[1-(1+r)n+1/-r]
Multiply inside by -1
fv= A [(1+r)n+1-1/r]
fv=Accumulated value
A=periodic installment or investment
n=term of the annuity
=Annuity rate
Illustration
1
...
If an installment deposit of #5000 at 13% is made at the end of each month over the next 9
months, (a) determine the compound value of the installment
b) installment (A) of Annuity: sometimes the sum that must be paid, received or deposited
on each occasion of series of equal installment for a fixed period to accumulate to future amount
is required
...
i
...

Determine the sum that must be deposited on each occasion
...
+ A / (1+r)n+1
pv-pv/ (1+r) = A / (1+r)-A/ (1+r)n+!
d period at the end of each period
...
+ A/ (1+r)n
Divide all through by (1+r)
Pv/(1+r)=A/(1+r)2+A /(1+r)3 + …………… + A / (1+r) n+1
Subtract at equation 2 from 1
Pv-pv/(1+r)=A/(1+r)-A/(1+r)n+1
Pv[1-1/(1+r)]=A[1/1+r-A(1+

r)-(n+1)]

Pv[1+r-1/1+r]
Pv=A[(1+r)-1-(1+r)-(n+1)]×(1+r)/r
Pv=A[(1+r)-1+1-(1+r)-n-1+1/r]
Pv=A[(1+r)0-(1+r)-n/r]
Pv=A[1-(1+r)-n/r
Illustration
1
...
The first payment is due in a
year time
...

a future value of annuity due is the future value of annuity due is the value at period n of a
constant sum paid or received at the beginning of each year starting from year 1 to the last,
compounded annually at a specified rate
...
+ A (1+r)n
Multiply the equation all through by (1+r)
Fvn(1+r)=A(1+r)2+ A (1+r)3+ ……………
...


Calculate the future value of #10,000 deposited at the beginning of each of the next 5 years
compounded at 10% interest rate
...


If an installment deposits of #500 at 13% is made at the beginning of every month over the
next 9 months, determine the compound value of the installment
...

0

1

2

3

A/ (1+r)2
A/ (1+r)1
A/ (1+r)0
PVn= A/ (1+r)0 + A/ (1+r)1 + A/ (1+r)2 ………………
...
+ A /(1+r)n+1
Subtract equation 2 from equation 1
PVn – PVn/ (1+r)= A / (1+r)0- A / (1+r)n
PVn (1-1/ (1+r)]=A –A (1+r)-n
Pvn [1+r-1/1+r]=A[1-(1+r)-n]
PVn [r/(1+r)]=A[1-(1+r)-n]
FVn=A[1-(1+r)-n] x 1+r/r
PVn = A [1=r-(1+r)-n+1/r]
How much must be deposited in a savings account now if you are to fulfill a debt obligation of
#10000 at the beginning of each of the next 5 years and interest rate is 10% payable annually
CAPITAL BUDGETING DECISION
One of the four functions of finance is investment decision, which involves the commitment of funds
(and other resources) today for the purpose of enjoying the returns in the funds
...

16

Efficient allocation ensures that management allocates the scarce financial resources of the firm on
projects with the highest return, lowest risk and cost
...

Investment decision procedure
In order to achieve this inevitable management exercise, the following procedures are undertaken:
a
...
Identify alternative investment
c
...
Estimate the company’s weighted average cost of capital
e
...
Evaluate the alternative, investments opportunity
g
...

Investment Appraisal Techniques
Investment appraisal techniques are generally grouped into: Non-Discounted cash flow method and
Discounted cash flow method
...
Non- Discounted cash flow methods: these are investment appraisal techniques which does
not distinguish between early cash flows and later ones
...
The techniques include:
a) Payback period method
b) Accounting rate of return
Payback period method (PBP): this is also known as pay off period (POP), Capital Recovery Period
(CRP) and Cash Recovery Period (CRP)
...
This traditional technique is used as one of the most popular
alternatives to the NPV
...
g
...
The notation can be used to represent the foregoing investment (#100,000, #60,000,
#40,000 & #30,000)
...
Thus the payback period of the project is 2 years
...
If a project has constant cash
flow, the PBP = Initial outlay/ One cash flow
...
A project requires an investment of #25,000 and is expected to generate an annual cash
flow of #5,000, #7,000, #9,000, #10,000, #2,000, #1,000, #10,000, #5,000, #2,500
respectively for each of its 10 years life’s span
...
XYZ Nig
...
The life’ span of each of project is 5 years
...
The profits from the projects are given below:
Year

Profit A

Profit B

0

400,000

400,000

1

160,000

390,000

2

160,000

130,000

3

160,000

140,000

4

160,000

130,000

5

160,000

100,000

Advice the company on which payback period rules to chose if the scrap value is #20,000
This requires a pre determined payback period or cut – off time, where two or more project can be
taken at the same time, any project with payback period equal to or less than this cut-off time is
selected otherwise it is rejected
...

18

Limitation of PBP
1
...
It does not consider payment offer payback period
3
...
It favour liquidity at the expense of profitability
5
...

Advantage of PBP
1
...
Its simplicity helps to minimize cost and time of data production
...
It helps to evaluate manager’s decision making ability because PBP helps to know of the
manager’s assessment of cash flows was correct in due course
...
It is suitable for making relatively small decision
5
...
The
accounting rate of return relates in percentage term, the estimated average profit of the project to the
estimated average investment
...
i
...

EAI=Initial outlay + Scrap value/2

...
Ltd wishes to require a new machine and has relating to two alternatives the
information below:
Machine X (#)
Initial cost

Machine Y (#)

20000

20000

Residual value

5000

4000

Estimated profit (Yr 1)

8000

7000

(Yr 2)

8000

7000

(Yr 3)

10000

11000

(Yr 4)

5500

9000

The profit figures where arrived at before depreciation
...
8% Y= 22
...

Limitations of ARR
1
...
Arbitrary determination of predetermine rate
3
...
Simple to compute and understand
2
...

3
...
Information for its calculation accounting records
...
Discounted Cash flow method
This include techniques that recognize time value of money on cash flows by discounting them to
their present value
...
Net present value (NPV)
b
...
Profitability index (PI) or Benefit Cost Ratio (BCR)
A Net Present Value Method (Npv): This is rightly consider as the best method of among the lot
because it is a process which involve the standardization of cash flows emanating from a project by
discounting them to their present values at the required discount rate
...
In light of this, the method presumes that all
inflows and outflows of funds would take place now by attaching different discounting factor to cash
flows based on timings to manage the limitations in this assumption
...

A positive Npv implies that the project is viable and can be accepted
...
If the first rate gives negative Npv, reduce the
rate (-40) to have a new rate (R1) to have a positive Npv (Npv1)
...
8 or -0
...
8
r=1-0
...
2
r=20%=IRR
when the cash flow is for multi period IRR is obtained by tabulation using trial and error to assume a
second rate
...
The amount is to be incurred at the
beginning of the project; the project is to last for 5 years with expected cash flows presented as
follows:
Year

#

1

8000

2

7000

3

5000

4

6000

5

11000

Determined the desirability of the project using IRR if the cut-off rate is 13%
IRR rule
Accept a project if IRR is higher than the firm’s opportunity cost of capital weighted average cost of
capital or the require rate of return for mutually exclusive project, the higher IRR, the better the
project
...
Additive principle does not hold i
...
Requires the forecast of cash flows, which may be different in practixe
3
...
It results in multiple rates when the cash flows are non-conventional
...

PI or BCR=PV of Cash flow/ Initial Investment = Pv/Co
OR the PI may give wrong indication for mutually exclusive project where the scales of investment
of the different projects significantly of the differ
...

PI rule
For mutually exclusive project, select the project with higher PI or project that the PI is greater than
one for independent projects
...
It requires cash flow forecast
2
...
It contradicts the NPV in method in the event of difference in side of investment
...
It recognize time value of money
2
...
It is consistent except for scale problem and therefore consistent with the wealth maximization
objective
...

26

WORK EXAMPLE
WEIGHTED AVERAGE COST OF CAPITAL
Given that both private and public sector companies have several of capital it is therefore necessary to include this
consideration into the cost of capital
...
Ltd has the following capital structure:
Cost of capital calculate for each
6%
10%
17%
17%

12% debentured
#450,000
8%
preference shares
#200,000
Ordinary shares
#800,000
Returned earnings
#500,000
Calculate the weighted average cost of capital

Solution
Sources

Capital structure

Cost

Weighted cost

12% Debenture

500,000

0
...
1

20,000

Ordinary shares

800,000

0
...
17

85,000
= 271,000

WACC = 271,000/2,000,000 = 13
...
)
NET PRESENT VALUE METHOD
If a firm invest in a project with rates of return of 15% then it can “discount” future profits at 15% which becomes the
firms marginal investment rate
...
It can be calculated once the future streams of costs associated with the project are known
...

If the discounted value of net inflows is greater than the initial investment, the surplus is the Net Present Value (NPV) of
the project
...
e
...
Hence, the decision criterion when using NPV is:
Accept project if NPV>0
Reject project if NPV<0
Hence, NPV is the value today of the surplus that the firm makes over and above what it could make by investing at its
marginal rate
...
It is the discount rate that makes the present value of benefits equal to the present value of costs
...
An / (1+r)n – C = 0
Where A1, A2, A3 etc are the cash inflows at the end of the first, second and the third year respectively
...

For example
Antokel profits in a project of 2 years are 1500 and 2000 if the rate is 10%, find the IRR if the initial investment is 5000
Solution
1500 / (1+r)1 + 2000 / (1+r)2 – 5000 = 0
Let (1+r) = x
1500/x + 2000 / x2 – 5000 = 0
1500/x + 2000 / x2 = 5000
1500x + 2000 / x2 = 5000 / 1
1500x + 2000 = 5000x2
5000x2 – 1500x – 2000 = 0
divide through by 500
2
10x – 3x – 4 = 0
X = 0
...
5
Since 1+r = x
1+r = 0
...
8
r = 0
...
In this case, there is no single way to
find a solution to internal rate of return
...

IRR is a very useful measure of project worth and it is the measure which the World Bank uses to analyze all her
economic and financial analysis of prospects
...
For economic analysis: internal rate of return is
involved and financial analysis – internal financial return
...
First choose a discount rate that will make NPV greater that zero (i
...
positive)
...

The positive NPV is refer to as the NPV at lower discount rate
...
Then choose another discount rate that will make NPV negative
...
Approximate the value of IRR by substituting and interpolation in the formula below:
IRR = R1 + (R2 – R1)
NPV1 / NPV1 – (-NPV2)
Where
R1 = Lower rate
R2 = Higher rate
NPV1 = Positive NPV
NPV2 = Negative NPV
Decision Criterion
The decision to accept or reject a project using IRR is arrived at by comparing the calculated IRR with its cost of capital,
r*
...


The assumption that all cash flows are certain

2
...


It rely on the correct estimate of the cost of capital

Problems of IRR
1
...


The issue of negative capitals which appears in the cash flow as a result of cash outflows exceeding cash inflows
in any particular year
...


The problems of evaluating mutually exclusive projects involvin

---