Financial Analysis
MBA/MSL 643
Hall #7 Part 1
Time Value of Money
2
Biblical Foundation
Live right and you will eat from the life-giving tree. And
if you act wisely, others will follow.
PROVERBS 11:30
•Does “being” proceed “doing?”
•Can anything great be achieved alone? Why or why not?
3
Key Concepts
• Be able to compute:
▫ The future value of an investment made today
▫ The present value of cash to be received at some
future date
▫ The return on an investment
▫ The number of periods that equates a present value
future value given an interest rate
▫ The future value of multiple cash flows
▫ The present value of multiple cash flows
and a
• Be able to solve time value of money problems using:
▫ Formulas
▫ A financial calculator
▫ A spreadsheet
• Understand how interest rates are quoted
4
Key Concepts continued
• Be able to compute the future value of multiple
cash flows
• Be able to compute the present value of multiple
cash flows
• Understand how interest rates are quoted
5
Basic Definitions
• Present Value (PV)
▫ The current value of future cash flows discounted
at the appropriate discount rate
▫ Value at t=0 on a time line
• Future Value (FV)
▫ The amount an investment is worth after one or
more periods.
▫ “Later” money on a time line
6
Basic Definitions continued
• Interest rate (r)
▫ Discount rate
▫ Cost of capital
▫ Opportunity cost of capital
▫ Required return
▫ Terminology depends on usage
7
Time Line of Cash Flows
• Tick marks at ends of periods
• Time 0 is today;
• Time 1 is the end of Period 1
0
1
2
3
CF1
CF2
CF3
r%
CF0
+CF = Cash INFLOW -CF = Cash OUTFLOW
PMT = Constant CF
8
Future Value General Formula
FV = PV(1 + r)t
FV = future value
PV = present value
r = period interest rate, expressed
as a decimal
t = number of periods
• Future value interest factor = (1 + r)t
Note: “yx” key on your calculator
9
Example: Future Value
Suppose you invest $100 for one year at 10% per year.
What is the future value in one year?
▫ Interest = 100(.10) = 10
▫ Value in one year
= Principal + interest
= 100 + 10 = 110
▫ Future Value (FV)
= 100(1 + .10) = 110
Suppose you leave the money in for another
year. How much will you have two years
from now?
FV = 100(1.10)(1.10)
= 100(1.10)2 = 121.00
10
Effects of Compounding
• Simple interest
▫ Interest earned only on the original principal
• Compound interest
▫ Interest earned on principal and on interest received
▫ “Interest on interest” – interest earned on
reinvestment of previous interest payments
• Consider the previous example
▫ FV w/simple interest
= 100 + 10 + 10 = 120
▫ FV w/compound interest
=100(1.10)2 = 121.00
▫ The extra 1.00 comes from the interest of .10(10) =
1.00 earned on the first interest payment
11
Texas Instruments BA – II Plus
•
•
•
•
•
FV = future value
One of these MUST
be negative
PV= present value
I
/
Y*
= period interest rate (r)
N = number of periods
PMT = payment (but will equal 0 in
our examples of lump sums)
N
I/Y
PV
PMT
FV
*
I
/
Y= period interest rate (r)
Interest is entered as a percent, not a decimal
5% interest = “5”, not “.05”
12
Example: FV of Lump Sum
• Suppose you invest the $100 from the previous
example for 5 years. How much would you have?
• Formula Solution: FV=PV(1+r)t
=100(1.10)5
=100(1.6105)
=161.05
Calculator Keystrokes: 5, N; 10, I/Y; -100, PV; 0, PMT; CPT
FV = 161.05
Excel Solution: =FV(Rate, Nper, Pmt, PV)
=FV(.10, 5, 0,-100) = 161.05
NOTE: Rate = decimal
13
Present Value
• The current value of future cash flows discounted at the appropriate
discount rate
• Value at t=0 on a time line
• Answers the questions:
▫ How much do I have to invest today to have some amount in the future?
▫ What is the current value of an amount to be received in the future?
• Present Value = the current value of an amount to be received in the future
• Why is it worth less than face value?
▫ Opportunity cost
▫ Risk & Uncertainty
Discount Rate = ƒ (time, risk)
FV = PV(1 + r)t
• Rearrange to solve for PV
PV = FV / (1+r)t
PV = FV(1+r)-t
• “Discounting” = finding the present value of one or more future amounts.
14
What’s the PV of $100 due in 3 Years if r = 10%?
• Finding PVs is discounting, and it’s the reverse of
compounding.
0
10%
1
2
3
100
PV = ?
Formula: PV = FV/(1+r)t = 100/(1.10)3 = $75.13
Calculator: 3, N; 10, I/Y; 0, PMT;100,
FV;
CPT PV = -75.13
Excel: =PV(.10,3,0,100) = -75.13
15
The Basic PV and FV Equation for a Lump Sum
PV = FV / (1 + r)t
There are four parts to this equation
▫ PV, FV, r and t
▫ Know any three, solve for the fourth
• Be sure and remember the sign convention
+CF = Cash INFLOW -CF = Cash OUTFLOW
16
Present Value and Future Value of a Lump Sum
Recap
17
Future Value of a Series of Multiple Cash Flows
• You think you will be able to deposit $4,000 at the end of each of
the next three years in a bank account paying 8 percent interest.
• You currently have $7,000 in the account.
• How much will you have in 3 years?
• How much in 4 years?
• Find the value at year 3 of each cash flow and add them together.
▫ Year 0: FV = $7,000(1.08)3
= $ 8,817.98
▫ Year 1: FV = $4,000(1.08)2
= $ 4,665.60
▫ Year 2: FV = $4,000(1.08)1
= $ 4,320.00
▫ Year 3: value
= $ 4,000.00
▫ Total value in 3 years
= $21,803.58
• Value at year 4 = $21,803.58(1.08)= $23,547.87
18
Example: FV of a Series of Multiple CFs
with a Timeline
If you deposit $100 in one year, $200 in two years and $300 in
three years, how much will you have in three years at 7 percent
interest?
TIMELINE
0
1
2
3
-$100.00
-$200.00
-$300.00
4
5
7%
$300.00
200*(1.07) =
$214.00
100*(1.07)^2 = $114.49
$628.49
Total interest = $628.49-600=28.49
* (1.07)^2 =
$719.56
19
Example: FV of a Series of Multiple CFs
Using Excel
If you deposit $100 in one year, $200 in two years and $300 in
three years, how much will you have in three years at 7 percent
interest?
Rate
7%
Year Nper CF
FV
Function
1
2
-100 $114.49 =FV(0.07,2,0,-100)
2
1
-200 $214.00 =FV(0.07,1,0,-200)
3
0
-300 $300.00 =FV(0.07,0,0,-300)
Total FV at Year 3
Total FV at Year 5
$628.49
$719.56 =(628.49)*(1.07)^2
20
Example: FV of a Series of Multiple CFs
• Suppose you plan to deposit $100 into an account in one year
and $300 into the account in three years.
• How much will be in the account in five years if the interest
rate is 8%?
FV = $100(1.08)4 + $300(1.08)2 = $136.05 + $349.92 =
$485.97
0
1
$100
2
3
$300
4
5
300*(1.08)2 =
$349.92
100*(1.08)2 =
$136.05
$485.97
21
PV of a Series of Multiple Cash Flows
You are offered an investment that will pay
$200 in year 1,
$400 the next year,
$600 the following year, and
$800 at the end of the 4th year.
You can earn 12% on similar investments.
What is the most you should pay for this one?
Find the PV of each cash flow and add them:
Year 1 CF: $200 / (1.12)1 = $ 178.57
Year 2 CF: $400 / (1.12)2 = $ 318.88
Year 3 CF: $600 / (1.12)3 = $ 427.07
Year 4 CF: $800 / (1.12)4 = $ 508.41
Total PV
= $1,432.93
22
Present Value of a Multiple Series of Cash Flows
Timeline
0
1
2
3
4
Time
(years)
178.57
200
318.88 = 1/(1.12)2 x
427.07 = 1/(1.12)3 x
508.41 = 1/(1.12)4 x
1,432.93
400
600
800
23
Multiple Uneven Cash Flows
• Press the CF button
• CF0 is displayed as 0.00
• Enter the Period 0 cash flow
▫ If an outflow, press +/- to change the
sign
• To enter the figure in the cash flow register,
press ENTER.
• Arrow down to C01.
Enter a value, arrow
F01
• down
Repeat forto
all cash
flows, and
in order.enter
how many times C01
• To
find NPV: (default is
occurs
▫ Press NPV button and I appears on the screen
1).
▫ Enter the interest rate (in %), press ENTER and arrow
down to display NPV.
▫ Press CPT
24
Example: Multiple Uneven Cash Flows
CF Function on the Calculator
• Suppose you are looking at the following possible cash flows:
▫ Year 1 CF = $100;
▫ Years 2 and 3 CFs = $200;
▫ Years 4 and 5 CFs = $300.
Display
You Enter
▫ The required discount rate is 7%
• What is the value of the CFs at year 5?
Press CF
• What is the value of the CFs today?
C00
0,
ENTER,
C01
F01
C02
F02
C03
F03
100,
1,
200,
2,
300,
2,
Press NPV
I
7
Press CPT
NPV = 1432.93
ENTER,
ENTER,
ENTER,
ENTER,
ENTER,
ENTER,
ENTER,
25
Example continued
Using Excel
26
Example: PV and FV of CFS
Using the Timeline
$
$
$
$
$
$
874.12
213.90
228.87
163.26
174.69
93.46
PV
7%
Period
0
1
2
3
4
5
CFs
0
100
200
200
300
300
FV =
300.00
$
321.00
$
228.98
$
245.01
$
131.08
$
$ 1,226.07
27
Annuities and Perpetuities
• Annuity – finite series of equal payments that occur at
regular intervals
▫ If the first payment occurs at the end of the period, it is
called an ordinary annuity
▫ If the first payment occurs at the beginning of the period, it
is called an annuity due
• Perpetuity – infinite series of equal payments.
• Perpetuity: PV = PMT / r
1
1
• Annuities:
t
PV PMT
(1 r )
r
(1 r ) t 1
FV PMT
r
28
Setting Annuity and Time Value Parameters
• The PMT key on the calculator is used for the equal payment
• The sign convention still holds
• Ordinary annuity versus Annuity due
▫ Switch your calculator between the two types (see below)
▫ If you see “BGN” in the display of your calculator, you have it set
for an annuity due
▫ Most problems are ordinary annuities (END mode).
• Set END for an ordinary annuity or BGN for an annuity due
▫ Press 2nd and then BGN
▫ This is a toggle switch. The default is END.
▫ To change to BEGIN, press 2nd and ENTER to go back and
forth.
▫ Press 2nd and QUIT to exit.
29
Important Points to Remember
• Interest rate and time period must match!
▫ Annual periods annual rate
▫ Monthly periods monthly rate
• The Sign Convention
▫ Cash inflows are positive
▫ Cash outflows are negative
• You want to receive $5,000 per month for the next 5 years.
How much would you need to deposit today if you can earn
.75% per month?
Calculator
60, N
0.75, I/Y
5000, PMT
0, FV
CPT PV = -
Excel
=PV(0.0075,60,5000,0)
30
PV and FV of Multiple CFs Recap
31
Interest Rates
• Effective Annual Rate (EAR)
▫ The interest rate expressed as if it were compounded once per
year.
▫ Used to compare two alternative investments with different
compounding periods
APR
EAR 1
m
m
1
m = number of compounds per year
• Annual Percentage Rate (APR) “Nominal”
▫ The annual rate quoted by law
▫ APR = periodic rate X number of periods per year
▫ Periodic rate = APR / periods per year
32
Example: Effective Annual Rate (EAR)
• Which savings accounts should you choose:
▫ 5.25% with daily compounding.
▫ 5.30% with semiannual compounding.
• First account:
EAR = (1 + .0525/365)365 – 1 = 5.39%
• Second account:
EAR = (1 + .053/2)2 – 1 = 5.37%
33
Questions for Reflection & Study
• What is the difference between simple interest and compound
interest?
• Suppose you have $500 to invest and you believe that you can earn
8% per year over the next 15 years.
• How much would you have at the end of 15 years using compound
interest?
▫ How much would you have using simple interest?
• What is the relationship between present value and future value?
• Suppose you need $15,000 in 3 years. If you can earn 6%
annually, how much do you need to invest today?)
• If you could invest the money at 8%, would you have to invest
more or less than at 6%? How much?
34
Questions for Reflection & Study cont.
• What is the relationship between present value and future value?
• Suppose you need $15,000 in 3 years. If you can earn 6% annually,
how much do you need to invest today?
• If you could invest the money at 8%, would you have to invest more
or less than at 6%? How much?
• You are considering an investment that will pay you $1,000 in one
year, $2,000 in two years and $3,000 in three years.
• If you want to earn 10% on your money, how much would you be
willing to pay?
• You want to receive $5,000 per month in retirement. If you can
earn .75% per month and you expect to need the income for 25
years, how much do you need to have in your account at retirement?
• What is the difference between APR and EAR?
35
What next?
•
•
•
•
Take the Hall Quiz
Complete your detailed reading
Answer the discussion questions
Complete the writing assignments
36
References
• Financial Statements and some additional information was
provided by slides from Essentials of Corporate Finance, 7th
edition (2011), by Ross, Westerfield and Jordon.
37
This concludes Hall 7 Part 1
1
Human Resource Management
MSL660/MPA606
Hall 7 Part 2
I Have Rights Too!
2
Format for Hall session
•
•
•
•
Introduction of the Hall
Hall Topics
Christian worldview applications
Major points for the week’s learning
3
Topics we’ll cover
•
•
•
•
•
•
•
•
•
•
•
Employer & Employee Rights & Responsibilities
Rights Affecting the Employment Relationship
Managing Individual Employee & Employer Rights Issues
Balancing Employer Security & Employee Rights
HR Policies, Procedures, & Rules
Employee Absenteeism
Employee Discipline
Unions & Their History in the U.S.
U.S. Labor Laws
The Unionization Process
Collective Bargaining
4
Biblical Foundation: 1 John 2:1
5
Hall Objectives
• What rights do employees & employers have
• What are the rights that affect the employment
relationship
• How do organizations manage their rights & their
employees’ rights
• To get a good understanding of what HR policies,
procedures, and rules are
• To understand how employee absenteeism affects the
organization
• To understand how employers administer discipline
• To understand unions, the different labor laws, and the
unionization process
6
Questions or Topics for Reflection &
Study
• What is the difference between wrongful
discharge & constructive discharge?
• What are the steps in the progressive discipline
approach?
• What U.S. Labor Law established the National
Labor Relations Board (NLRB)?
• What is involved in the unionization process?
7
Employee & Employer Rights
• Rights – Powers, privileges, or interests that
belong by law, nature, or tradition.
• Statutory rights – Rights based on laws or
statutes passed by federal, state, or local
governments.
• Responsibilities – Obligations to perform
certain tasks & duties.
• Contractual rights – Rights based on a
specific contract between an employer & an
employee.
8
Employee & Employer Rights
• Employer rights include:
▫ The right to keep trade secrets confidential
▫ The right to have employees bring business
opportunities to the employer first before
pursuing them elsewhere
▫ A common-law copyright for works & other
documents prepared by employees for their
employers
9
Rights Affecting the Employment
Relationship
• Employment-at-will (EAW) – Common-law
doctrine stating that employers have the right to
hire, fire, demote, or promote whomever they
choose, unless there is a contract to the contrary.
• Wrongful discharge – Termination of an
individual’s employment for reasons that are
illegal or improper.
• Constructive discharge – Process of
deliberately making conditions intolerable to get
an employee to quit.
10
Rights Affecting the Employment
Relationship
• Just cause – Reasonable justification for
taking employment-related action.
• Due process – Requirement that the employer
use a process to determine employee
wrongdoing & that the employee have an
opportunity to explain & defend his or her
actions.
11
Managing Individual Employee &
Employer Rights Issues
• Right to privacy – An individual’s freedom
from unauthorized & unreasonable intrusion
into personal affairs.
• Employee Medical Records
▫ Must be kept separate from general personnel
files
• Employees’ Free Speech
• Monitoring Electronic Communications
12
Recommended
Employer Actions
Regarding
Electronic
Communications
• Fig. 15-5
Source: Mathis & Jackson (2011), Human Resource
Management (13th ed.),
Mason, OH, Cengage Southwestern.
13
HR Policies, Procedures, & Rules
• Policies – General guidelines that focus
organizational actions.
• Procedures – Customary methods of handling
activities.
• Rules – Specific guidelines that regulate & restrict
the behavior of individuals.
• Employee handbooks
14
Employee Absenteeism
• Absenteeism – Any failure by an employee to
report for work as scheduled or to stay at work when
scheduled.
▫ Involuntary, voluntary
• Ways to Control:
▫
▫
▫
▫
▫
Disciplinary approach
Positive reinforcement
Combination approach
“No-fault” policy
Paid-time-off (PTO) programs
15
Measuring Employee Absenteeism
• Widely used formula for calculating
absenteeism:
# of person-days lost thru job absence during period
-------------------------------------------------------------- x 100
(avg # of employees) X (# of workdays)
16
Employee Discipline
• Discipline – Form of training that enforces
organizational rules.
▫ Positive Discipline Approach
▫ Progressive Discipline Approach
• Discharge – When an employee is removed from a job
at an employer.
17
Progressive Discipline Approach
• Fig. 15-9
Source: Mathis & Jackson (2011), Human Resource Management (13th ed.),
Mason, OH, Cengage Southwestern.
18
Unions & Why Employees Unionize
• Union – Formal association of workers that promotes
the interests of its members through collective action.
• Fig. 16-1
Source: Mathis & Jackson (2011), Human Resource Management (13th ed.),
Mason, OH, Cengage Southwestern.
19
History of Unions in the U.S.
• From 1945-1960, 30% of workforce
• 2009 – 12.4% (7.9 million) of civilian
workers, 7.4% private-sector
• As early as 1794, shoemakers organized a
union, picketed, & conducted strikes
• Reasons for decline in membership
▫ Geographic changes
▫ Industrial changes
▫ Workforce changes
20
U.S. Labor Laws
• Wagner Act (National Labor Relations Act)
▫ (Pro-union) Established the right of workers to
organize unhampered by management through
unfair labor practices (ULP, NLRB)
• Taft-Hartley Act (Labor Management Relations
Act)
▫ (Pro-management) Balanced the power between
unions & management (National emergency
strikes, right-to-work laws)
• Landrum-Griffin Act (Labor Management
Reporting & Disclosure Act)
▫ Monitors union conduct
21
The Unionization
Process
Fig. 16-6
Source: Mathis & Jackson (2011), Human Resource Management (13th ed.),
Mason, OH, Cengage Southwestern.
22
Collective Bargaining Process
• Preparation & Initial Demands
• Continuing Negotiations
▫ Good Faith
• Settlement & Contract Agreement
▫ Ratification (union members vote on agreement)
• Bargaining Impasse
▫ Conciliation/mediation/arbitration
• Strikes
▫ Work stoppage by employees
• Lockouts
▫ Work stoppage by management
23
Questions or Topics for Review
• What is the difference between wrongful
discharge & constructive discharge?
• What are the steps in the progressive discipline
approach?
• What U.S. Labor Law established the National
Labor Relations Board (NLRB)?
• What is involved in the unionization process?
24
What next?
•
•
•
•
Take the Hall Quiz
Complete your detailed reading
Answer the discussion questions
Complete the writing assignments
25
References
• Mathis, Robert & Jackson, John. (2011) Human
Resource Management (13th ed.) Mason, OH:
Cengage Southwestern.
26
This concludes Hall 7 Part 2
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