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

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INTRODUCTION TO BUSINESS FINANCE OR MANAGERIAL FINANCE
LECTURE NOTE

TORIOLA, Keshiro
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com

ʺ Copyright © 2021 by Toriola Anu
All rights reserved
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Interested Publishers can contact the correspondence
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meaning, nature and functions of finance
2
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MATHEMATICS OF FINANCE
a
...
compound interest and discontinuity
c
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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
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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
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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
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Ordinary shares: These are issued by firm on incorporation to provide them risks capital
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6

8
...
It is a long term promising note for raising
capital
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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
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3846=(1
...
3846 = nlog 1
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06
n= log 1
...
06
n=0
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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
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5460 -1
r=10
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048-1
r1
...
048-1
r=4
...
g
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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 savin
project excludes the acceptance of the other, select the project with the least payback period
...
It does not consider the timing of the flows within the payback period
2
...
Arbitrary determination of cut-off rate
4
...
It is not consistent with the objective of maximization of shareholder’s wealth because
company’s share is not a function of function of the payback period of investments projects
...
Simple to understand and easy to calculate
2
...

3
...

4
...
It recognizes risks and uncertainty by requiring early payment
Return on investment (ROI)or Accounting Rate of Return (ARR)
It is also known as Accounting Rate of Return (ARR) or Return on Investment (ROI)
...

ARR or ROI= Estimated average profit/ Estimated average investment x 100 / 1= EAP/EAI X 100 /1
Estimated average profit: this is the estimated earning from the project, after taxes and depreciation
divide by the life span of the project
...
e
EAR = Total profit-Depreciation-Taxes/life span = PAT/life span
Estimated average investment : this is the average of the initial capital outlay and the scrap value of
the project
...
ARR or ROI=EAP/EAI X 100/1
ARR or ROI = PAT / life span / Initial outlay + scrap value/ 2
Note: Depreciation = Initial cost-Scrap value
19

Depreciation = initial cost/ life span
Illustration
Antokel Nig
...
Advice on which of the machines to choose
if the required rate is 21% when the tax rate is 40%
(Answer: x = 19
...
5%)

Accounting Rate of Return Rule
For mutually exclusive project, select the project with the highest ARR or whose ARR is greater
than or equal to the predetermined rate for independent project
...
It does not consider time value of money
2
...
It uses the accountant’s net income figures and look value of investment which is wrong
Advantages of ARR
1
...
It is consistent with the return on investment which most managers are conversant with
...
It makes use of all profit figures over the life of the project
4
...

20

2
...
Techniques under this categories include:
a
...
Internal rate of return (IRR)
c
...
The emanated present values
of cash flows are then compared with the initial outlay
...
The method is rooted on the
concept of time value of moey
...
If Npv is negative, the project
is investment and such project would erode the shareholders wealth
...

Inputs of NPV method
There are four informational inputs required for obtaining Npv of project and they are:
1
...

2
...

3
...

Note : Sunk costs and the cost for evaluating a project and are irrelevant to the cash flows
...
Side effects interest expenses, depreciation and
operating costs are irrelevant
...
e, Co, C1 and C2 the mathematical formula is suitable but
when it is more than two year, tabular method should be used
...


Another profits in a project of 2 years are #1500 and #2000, if the rate is 10% find the Npv
if the initial investment is 5000
...
1 +2000 / (1+0
...
1 +2000 / (1+0
...
1 – 5000
Npv = 5500 / 1
...
1 -5000
2
...
The following cash flows relate to the projects:

Year

Project A

Project B

0

(18000)

1

2500

10000

2

6000

4000

3

10000

6000

4

12000

5500

(16000)

22

Using the Npv method:
a
...

b
...
Hence, advise the company on which project to select
Assume WACC of 10% as the relevant discount rate
...
This fact determines the reason why firms would endeavor to
obtain the minimum cost of capital from the combined sources of finance
...
That is larger cash flows are preferable to smaller ones
...
It rests on the ability to forecast future cash flows which is difficult in practice given the
ariability in the market
...
Determination of appropriate discount rate is difficult especially for unquoted companies
3
...
It is not suitable for mutually exclusive projects with unequal life span
...
Npv uses cash flows
2
...
Its discounts cash flows to their present value
4
...

B
...
t
...
IRR is the closest to Npv in terms of reliability
...
The IRR aim
to determine a single rate which summaries the merits of a project which is a rate independent of the
market rate
...

Step 1: Use the cash flow given and rate of return to obtain an Npv

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