CHAPTER 5INTRODUCTION TO VALUATION THE TIME VALUE OF MONEY (C

CHAPTER 5
INTRODUCTION TO VALUATION: THE TIME VALUE OF
MONEY (CALCULATOR)
Copyright © 2019 McGraw-Hill Education. All rights reserved.
No reproduction or distribution without the prior written
consent of McGraw-Hill Education.
5C-‹#›
4.1
This version relies primarily on the financial calculator with a
brief presentation of formulas. The calculator discussed is the
TI BA-II+. The slides are easy to modify for whatever
calculator you prefer.
Determine the future value of an investment made today
Determine the present value of cash to be received at a future
date
Find the return on an investment

Calculate how long it takes for an investment to reach a desired
value
Key Concepts and Skills
5C-‹#›
Future Value and Compounding
Present Value and Discounting
More about Present and Future Values
Chapter Outline
5C-‹#›
Present Value – earlier money on a time line
Future Value – later money on a time line
Interest rate – “exchange rate” between earlier money and later

money
Discount rate
Cost of capital
Opportunity cost of capital
Required return
Basic Definitions
5C-‹#›
4.4
Section 5.1
It’s important to point out that there are many different ways to
refer to the interest rate that we use in time value of money
calculations. Students often get confused with the terminology,
especially since they tend to think of an “interest rate” only in
terms of loans and savings accounts.
Suppose you invest $1,000 for one year at 5% per year. What is
the future value in one year?
Interest = 1,000(.05) = 50
Value in one year = principal + interest = 1,000 + 50 = 1,050
Future Value (FV) = 1,000(1 + .05) = 1,050
Suppose you leave the money in for another year. How much
will you have two years from now?
FV = 1,000(1.05)(1.05) = 1,000(1.05)2 = 1,102.50

Future Value – Example 1
5C-‹#›
4.5
Section 5.1 (A)
Point out that we are just using algebra when deriving the FV
formula. We have 1,000(1) + 1,000(.05) = 1,000(1+.05)
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
Future Value: General Formula
5C-‹#›
Section 5.1 (A)

4.6
Simple interest vs. Compound interest
Consider the previous example
FV with simple interest = 1,000 + 50 + 50 = 1,100
FV with compound interest = 1,102.50
The extra 2.50 comes from the interest of .05(50) = 2.50 earned
on the first interest payment
Effects of Compounding
5C-‹#›
4.7
Section 5.1 (B)
Lecture Tip: Slide 5.7 distinguishes between simple interest and
compound interest and can be used to emphasize the effects of
compounding and earning interest on interest. It is important
that students understand the impact of compounding now, or
they will have more difficulty distinguishing when it is
appropriate to use the APR and when it is appropriate to use the
effective annual rate.
Texas Instruments BA-II Plus
FV = future value
PV = present value
I/Y = period interest rate

P/Y must equal 1 for the I/Y to be the period rate
Interest is entered as a percent, not a decimal
N = number of periods
Remember to clear the registers (CLR TVM) after each
problem.
Other calculators are similar in format.
Calculator Keys
5C-‹#›
4.8
Section 5.1 (B)
We are providing information on the Texas Instruments BA-II
Plus – other calculators are similar. If you recommend or
require a specific calculator other than this one, you may want
to make the appropriate changes.
Note: the more information students have to remember to enter,
the more likely they are to make a mistake. For this reason, I
normally tell my students to set P/Y = 1 and leave it that way.
Then I teach them to work on a period basis, which is consistent
with using the formulas. If you want them to use the P/Y
function, remind them that they will need to set it every time
they work a new problem and that CLR TVM does not affect
P/Y.
If students are having difficulty getting the correct answer,
make sure they have done the following:

Set decimal places to floating point (2nd Format, Dec = 9 enter)
or show 4 to 5 decimal places if using an HP
Double check and make sure P/Y = 1
Make sure to clear the TVM registers after finishing a problem
(or before starting a problem) It is important to point out that
CLR TVM clears the FV, PV, N, I/Y and PMT registers. C/CE
and CLR Work DO NOT affect the TVM keys
The remaining slides will work the problems using the notation
provided above for calculator keys. The formulas are presented
in the notes section.
Suppose you invest the $1,000 from the previous example for 5
years. How much would you have?
5 N; 5 I/Y; 1,000 PV
CPT FV = -1,276.28
The effect of compounding is small for a small number of
periods, but increases as the number of periods increases.
(Simple interest would have a future value of $1,250, for a
difference of $26.28.)
5C-‹#›
4.9
Section 5.1 (B)
It is important at this point to discuss the sign convention in the

calculator. The calculator is programmed so that cash outflows
are entered as negative and inflows are entered as positive. If
you enter the PV as positive, the calculator assumes that you
have received a loan that you will have to repay at some point.
The negative sign on the future value indicates that you would
have to repay $1,276.28 in 5 years. Show the students that if
they enter the 1,000 as negative, the FV will compute as a
positive number.
Also, you may want to point out the change sign key on the
calculator. There seems to be a few students each semester that
have never had to use it before.
Formula: FV = 1,000(1.05)5 = 1,000(1.27628) = 1,276.28
Suppose you had a relative deposit $10 at 5.5% interest 200
years ago. How much would the investment be worth today?
200 N; 5.5 I/Y; 10 PV
CPT FV = -447,189.84
What is the effect of compounding?
Simple interest = 10 + 200(10)(.055) = 120.00
Compounding added $447,069.84 to the value of the investment
5C-‹#›
4.10
Section 5.1 (B)

You might also want to point out that it doesn’t matter what
order you enter the information into the calculator.
Formula: FV = 10(1.055)200 = 10(44,718.9838) = 447,189.84
Suppose your company expects to increase unit sales of widgets
by 15% per year for the next 5 years. If you sell 3 million
widgets in the current year, how many widgets do you expect to
sell in the fifth year?
5 N;15 I/Y; 3,000,000 PV
CPT FV = -6,034,072 units (remember the sign convention)
Future Value as a General Growth Formula
5C-‹#›
4.11
Section 5.1 (C)
Formula: FV = 3,000,000(1.15)5 = 3,000,000(2.011357187) =
6,034,072
This example also presents a good illustration of the Rule of 72,
which approximates the number of years it will take to double
an initial amount at a given rate. In this example, 72/15 = 4.8,
or approximately 5 years.

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?
Quick Quiz – Part I
5C-‹#›
4.12
Section 5.1
N = 15; I/Y = 8; PV = 500; CPT FV = -1,586.08
Formula: 500(1.08)15 = 500(3.172169) = 1,586.08
500 + 15(500)(.08) = 1,100
Lecture Tip: You may wish to take this opportunity to remind
students that, since compound growth rates are found using only
the beginning and ending values of a series, they convey
nothing about the values in between. For example, a firm may
state that “EPS has grown at a 10% annually compounded rate
over the last decade” in an attempt to impress investors of the
quality of earnings. However, this just depends on EPS in year 1
and year 11. For example, if EPS in year 1 = $1, then a “10%

annually compounded rate” implies that EPS in year 11 is
(1.10)10 = 2.5937. So, the firm could have earned $1 per share
10 years ago, suffered a string of losses, and then earned $2.59
per share this year. Clearly, this is not what is implied by
management’s statement above.
How much do I have to invest today to have some amount in the
future?
FV = PV(1 + r)t
Rearrange to solve for PV = FV / (1 + r)t
When we talk about discounting, we mean finding the present
value of some future amount.
When we talk about the “value” of something, we are talking
about the present value unless we specifically indicate that we
want the future value.
Present Value
5C-‹#›
4.13
Section 5.2
Point out that the PV interest factor = 1 / (1 + r)t
Suppose you need $10,000 in one year for the down payment on
a new car. If you can earn 7% annually, how much do you need
to invest today?

PV = 10,000 / (1.07)1 = 9,345.79
Calculator
1 N
7 I/Y
10,000 FV
CPT PV = -9,345.79
Present Value –Example 1
5C-‹#›
4.14
Section 5.2 (A)
The remaining examples will just use the calculator keys.
Lecture Tip: It may be helpful to utilize the example of $100
compounded at 10 percent to emphasize the present value
concept. Start with the basic formula: FV = PV(1 + r)t and
rearrange to find PV = FV / (1 + r)t. Students should recognize
that the discount factor is the inverse of the compounding
factor. Ask the class to determine the present value of $110 and
$121 if the amounts are received in one year and two years,
respectively, and the interest rate is 10%. Then demonstrate the
mechanics:
$100 = $110 (1 / 1.1) = 110 (.9091)
$100 = $121 (1 / 1.12) = 121(.8264)
The students should recognize that it was an initial investment

of $100 invested at 10% that created these two future values.
You want to begin saving for your daughter’s college education
and you estimate that she will need $150,000 in 17 years. If you
feel confident that you can earn 8% per year, how much do you
need to invest today?
N = 17; I/Y = 8; FV = 150,000
CPT PV = -40,540.34 (remember the sign convention)
Present Value – Example 2
5C-‹#›
4.15
Section 5.2 (B)
Formula: 150,000 / (1.08)17 = 150,000(.270268951) =
40,540.34
Your parents set up a trust fund for you 10 years ago that is now
worth $19,671.51. If the fund earned 7% per year, how much
did your parents invest?
N = 10; I/Y = 7; FV = 19,671.51
CPT PV = -10,000

Present Value – Example 3
5C-‹#›
4.16
Section 5.2 (B)
The actual number computes to –9999.998. This is a good place
to remind the students to pay attention to what the question
asked, and to be reasonable in their answers. A little common
sense should tell them that the original amount was 10,000 and
that the calculation doesn’t come out exactly because the future
value is rounded to the nearest cent.
Formula: 19,671.51 / (1.07)10 = 19,671.51(.508349292) =
9999.998 = 10,000
For a given interest rate – the longer the time period, the lower
the present value
What is the present value of $500 to be received in 5 years? 10
years? The discount rate is 10%
5 years: N = 5; I/Y = 10; FV = 500
CPT PV = -310.46
10 years: N = 10; I/Y = 10; FV = 500
CPT PV = -192.77
Present Value – Important Relationship I

5C-‹#›
4.17
Section 5.2 (B)
Remember the sign convention.
Formulas: PV = 500 / (1.1)5 = 500(.620921323) = 310.46
PV = 500 / (1.1)10 = 500(.385543289) = 192.77
For a given time period – the higher the interest rate, the
smaller the present value
What is the present value of $500 received in 5 years if the
interest rate is 10%? 15%?
Rate = 10%: N = 5; I/Y = 10; FV = 500
CPT PV = -310.46
Rate = 15%; N = 5; I/Y = 15; FV = 500
CPT PV = -248.59
Present Value – Important Relationship II

5C-‹#›
4.18
Section 5.2 (B)
Formulas: PV = 500 / (1.1)5 = 500(.620921323) = 310.46
PV = 500 / (1.15)5 = 500(.497176735) = 248.59
Since there is a reciprocal relationship between PVIFs and
FVIFs, you should also point out that future values increase as
the interest rate increases.
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?
Quick Quiz – Part II
5C-‹#›
4.19

Section 5.2
Relationship: The mathematical relationship is PV = FV / (1 +
r)t. One of the important things for them to take away from this
discussion is that the present value is always less than the
future value when we have positive rates of interest.
N = 3; I/Y = 6; FV = 15,000; CPT PV = -12,594.29
PV = 15,000 / (1.06)3 = 15,000(.839619283) = 12,594.29
N = 3; I/Y = 8; FV = 15,000; CPT PV = -11,907.48 (Difference
= 686.81)
PV = 15,000 / (1.08)3 = 15,000(.793832241) = 11,907.48
PV = FV / (1 + r)t
There are four parts to this equation:
PV, FV, r and t
If we know any three, we can solve for the fourth.
If you are using a financial calculator, be sure to remember the
sign convention or you will receive an error (or a nonsense
answer) when solving for r or t.
The Basic PV Equation - Refresher
5C-‹#›
4.20
Section 5.3

Lecture Tip: Students who fail to grasp the concept of time
value often do so because it is never really clear to them that
given a 10% opportunity rate, $110 to be received in one year is
equivalent to having $100 today (or $90.90 one year ago, or
$82.64 two years ago, etc.). At its most fundamental level,
compounding and discounting are nothing more than using a set
of formulas to find equivalent values at any two points in time.
In economic terms, one might stress that equivalence just means
that a rational person will be indifferent between $100 today
and $110 in one year, given a 10% opportunity. This is true
because she could (a) take the $100 today and invest it to have
$110 in one year or (b) she could borrow $100 today and repay
the loan with $110 in one year. A corollary to this concept is
that one can’t (or shouldn’t) add, subtract, multiply or divide
money values in different time periods unless those values are
expressed in equivalent terms, i.e., at a single point in time.
Often we will want to know what the implied interest rate is on
an investment
Rearrange the basic PV equation and solve for r
FV = PV(1 + r)t
r = (FV / PV)1/t – 1
If you are using formulas, you will want to make use of both the
yx and the 1/x keys
Discount Rate

5C-‹#›
Section 5.3 (B)
4.21
You are looking at an investment that will pay $1,200 in 5 years
if you invest $1,000 today. What is the implied rate of interest?
r = (1,200 / 1,000)1/5 – 1 = .03714 = 3.714%
Calculator – the sign convention matters!!!
N = 5
PV = -1,000 (you pay 1,000 today)
FV = 1,200 (you receive 1,200 in 5 years)
CPT I/Y = 3.714%
Discount Rate – Example 1
5C-‹#›
4.22
Section 5.3 (B)
It is very important at this point to make sure that the students
have more than 2 decimal places visible on their calculator.
Efficient key strokes for formula: 1,200 / 1,000 = yx 5 1/x = - 1
= .03714
If they receive an error when they try to use the financial keys,

they probably forgot to enter one of the numbers as a negative.
Suppose you are offered an investment that will allow you to
double your money in 6 years. You have $10,000 to invest.
What is the implied rate of interest?
N = 6
PV = -10,000
FV = 20,000
CPT I/Y = 12.25%
5C-‹#›
4.23
Section 5.3 (B)
Formula: r = (20,000 / 10,000)1/6 – 1 = .122462 = 12.25%
Suppose you have a 1-year old son and you want to provide
$75,000 in 17 years towards his college education.
You currently have $5,000 to invest.
What interest rate must you earn to have the $75,000 w hen you
need it?
N = 17; PV = -5,000; FV = 75,000
CPT I/Y = 17.27%

5C-‹#›
4.24
Section 5.3 (B)
Formula: r = (75,000 / 5,000)1/17 – 1 = .172686 = 17.27%
This is a great problem to illustrate how TVM can help you set
realistic financial goals and possibly adjust your expectations
based on what you can currently afford to save.
What are some situations in which you might want to know the
implied interest rate?
You are offered the following investments:
You can invest $500 today and receive $600 in 5 years. The
investment is considered low risk.
You can invest the $500 in a bank account paying 4%.
What is the implied interest rate for the first choice and which
investment should you choose?
Quick Quiz – Part III

5C-‹#›
4.25
Section 5.3
Implied rate: N = 5; PV = -500; FV = 600; CPT I/Y = 3.714%
r = (600 / 500)1/5 – 1 = 3.714%
Choose the bank account because it pays a higher rate of
interest (assuming tax rates and other issues are consistent
across both investments).
How would the decision be different if you were looking at
borrowing $500 today and either repaying at 4%, or repaying
$600? In this case, you would choose to repay $600 because you
would be paying a lower rate.
Start with the basic equation and solve for t (remember your
logs).
FV = PV(1 + r)t
t = ln(FV / PV) / ln(1 + r)
You can use the financial keys on the calculator as well; just
remember the sign convention.
Finding the Number of Periods

5C-‹#›
4.26
Section 5.3 (C)
Remind the students that ln is the natural logarithm and can be
found on the calculator.
The rule of 72 is a quick way to estimate how long it will take
to double your money: # years to double = 72 / r, where r is
number of percent.
You want to purchase a new car, and you are willing to pay
$20,000.
If you can invest at 10% per year and you currently have
$15,000, how long will it be before you have enough money to
pay cash for the car?
I/Y = 10; PV = -15,000; FV = 20,000
CPT N = 3.02 years
Number of Periods – Example 1
5C-‹#›
4.27
Section 5.3 (C)

Formula: t = ln(20,000 / 15,000) / ln(1.1) = 3.02 years
Suppose you want to buy a new house.
You currently have $15,000, and you figure you need to have a
10% down payment plus an additional 5% of the loan amount
for closing costs.
Assume the type of house you want will cost about $150,000
and you can earn 7.5% per year.
How long will it be before you have enough money for the down
payment and closing costs?
Number of Periods – Example 2
5C-‹#›
Section 5.3 (C)
4.28
How much do you need to have in the future?
Down payment = .1(150,000) = 15,000
Closing costs = .05(150,000 – 15,000) = 6,750
Total needed = 15,000 + 6,750 = 21,750
Compute the number of periods.
Using a financial calculator:
PV = -15,000; FV = 21,750; I/Y = 7.5
CPT N = 5.14 years

Using the formula:
t = ln(21,750 / 15,000) / ln(1.075) = 5.14 years
Number of Periods – Example 2 (ctd.)
5C-‹#›
4.29
Section 5.3 (C)
Loan amount = 150,000 – down payment = 150,000 – 15,000 =
135,000
When might you want to compute the number of periods?
Suppose you want to buy some new furniture for your family
room.
You currently have $500, and the furniture you want costs $600.
If you can earn 6%, how long will you have to wait if you don’t
add any additional money?
Quick Quiz – Part IV

5C-‹#›
4.30
Section 5.3
Calculator: PV = -500; FV = 600; I/Y = 6; CPT N = 3.13 years
Formula: t = ln(600/500) / ln(1.06) = 3.13 years
Use the following formulas for TVM calculations
FV(rate,nper,pmt,pv)
PV(rate,nper,pmt,fv)
RATE(nper,pmt,pv,fv)
NPER(rate,pmt,pv,fv)
The formula icon is very useful when you can’t remember the
exact formula.
Click on the Excel icon to open a spreadsheet containing four
different examples.
Spreadsheet Example
5C-‹#›
4.31
Section 5.4
Click on the tabs at the bottom of the worksheet to move

between examples.
Many financial calculators are available online.
Go to Investopedia’s website and work the following example:
You need $50,000 in 10 years. If you can earn 6% interest, how
much do you need to invest today?
You should get $27,919.74
Work the Web Example
5C-‹#›
Section 5.4
4.32
Table 5.4
5C-‹#›

You have $10,000 to invest for five years.
How much additional interest will you earn if the investment
provides a 5% annual return, when compared to a 4.5% annual
return?
How long will it take your $10,000 to double in value if it earns
5% annually?
What annual rate has been earned if $1,000 grows into $4,000
in 20 years?
Comprehensive Problem
5C-‹#›
4.34
Section 5.4
N = 5
PV = -10,000
At I/Y = 5, the FV = 12,762.82
At I/Y = 4.5, the FV = 12,461.82
The difference is attributable to interest. That difference is
12,762.82 – 12,461.82 = 301
To double the 10,000:
I/Y = 5

PV = -10,000
FV = 20,000
CPT N = 14.2 years
Note, the rule of 72 indicates 72/5 = 14 years, approximately.
N = 20
PV = -1,000
FV = 4,000
CPT I/Y = 7.18%
End of Chapter
Chapter 5 - Calculator
5C-‹#›
5C-‹#›
4.35
Future ValueYou have $10,000 to invest. You will need the
money in 5 years and you expect to earn 8% per year. How
much will you have in 5 years.What are you looking for?PV
=10,000NPER =5Use the FV formula:RATE =8%(Same as

.08)FV(rate,nper,pmt,pv)ComputeFV =$14,693.28(Notice that
the spreadsheet has the same sign convention as the calculators
with positive inflows and negative outflows. A negative sign
was placed before the FV formula to make the result
positive.)Note that this problem does not include a payment, so
it was entered as 0.
Present ValueYou need $150,000 in 18 years for your daughter's
eductation. If you can earn 6% per year, how much do you need
to invest today?What are you looking for?FV =150,000NPER
=18Use the PV formula:RATE =6%(Same as
.06)PV(rate,nper,pmt,fv)ComputePV =$52,551.57
RateYou have $30,000 to invest and you need $45,000 for a
down payment and closing costs on a house. If you want to buy
the house in 2 years, what rate of interest do you need to
earn?What are you looking for?PV =30,000FV =45,000Use the
RATE formula: RATE(nper,pmt,pv,fv)NPER =2ComputeRATE
=22.47%(Note that the rate will display as a whole percent, you
need to format the cell to see the decimal places.)Note a
negative sign was entered before the cell reference for the FV to
maintain the sign convention.
Number of PeriodsYou have $15,000 to invest right now and
you figure you will need $25,000 to buy a new car. If you can
earn 9% per year, how long before you can buy the car?What
are you looking for?PV =15,000FV =25,000Use the NPER
formula:RATE =9%(Same as
.09)NPER(rate,pmt,pv,fv)ComputeNPER =5.9275850487years
Assessment Task 1:
Paper Review:1800 words
A review of a journal article based on a psychological
intervention
For example you could use one of these examples:

Hilton, L., Hempel, S., Ewing, B. A., Apaydin, E., Xenakis, L.,
Newberry, S., ... & Maglione, M. A. (2017). Mindfulness
meditation for chronic pain: systematic review and meta-
analysis. Annals of Behavioral Medicine, 51(2), 199-213.
Heron, K. E., & Smyth, J. M. (2010). Ecological momentary
interventions: incorporating mobile technology into
psychosocial and health behaviour treatments. British journal of
health psychology, 15(1), 1-39.
Tan, L., Wang, M. J., Modini, M., Joyce, S., Mykletun, A.,
Christensen, H., & Harvey, S. B. (2014). Preventing the
development of depression at work: a systematic review and
metaanalysis of universal interventions in the workplace. BMC
medicine, 12(1), 74
Suggested guidance for the paper review:
1. Write in the third person.
2. Give details of the paper, date, authors, where published
3. Present a summary of the key points along with a limited
number of examples. You can also briefly explain the author’s
purpose/intentions throughout the text and you may briefly
describe how the text is organised. The summary should only
make up about a third of the critical review.
4. The review should be a balanced discussion and evaluation of
the strengths in the form of a critique, weakness and notable
feature, and key arguments of the text. Remember to base your
discussion on specific criteria. Good reviews also include other
sources to support your evaluation (remember to reference).
5. Give a conclusion – drawing on the key issue raised
regarding the text, with recommendations for further work,
or/and application, impact, etc
6. Remember to cite any sources which you have used to

support/refute arguments etc (references)
Possible focus questions:
Significance and contribution to the field
* What is the author's aim?
* To what extent has this aim been achieved?
* What does this text add to the body of knowledge? (This
could be in terms of theory, data and/or practical application)
* What relationship does it bear to other works in the field?
* What is missing/not stated?
* Is this a problem?
Methodology or approach (this usually applies to more formal,
research-based texts)
* What approach was used for the research? (eg; quantitative
or qualitative, analysis/review of theory or current practice,
comparative, case study, personal reflection etc...)
* How objective/biased is the approach?
* Are the results valid and reliable?
* What analytical framework is used to discuss the results?
Argument and use of evidence
* Is there a clear problem, statement or hypothesis?
* What claims are made?
* Is the argument consistent?
Evidence/conclusions/assumptions
* What kinds of evidence does the text rely on?
* How valid and reliable is the evidence?
* How effective is the evidence in supporting the argument?
* What conclusions are drawn?
* Are these conclusions justified?
Writing style and text structure
* Does the writing style suit the intended audience? (eg;
expert/non-expert, academic/non-academic)
* What is the organising principle of the text? Could it be
better organised?

Suggested Reading:
Concise/Indicative Reading List
Books:
Davey, G.C. Psychopathology: Research, Assessment and
Treatment in Clinical Psychology. Oxford: John Wiley and
Sons.
Morrison, V. (2016). Introduction to Health Psychology (4th
Edition). Harlow: Pearson.
Wedding D and Corsini, R (2013). Current
Psychotherapies.(10th Edition) San Francisco: Wadsworth
Publishing
Journals:
British Journal of Clinical Psychology
British Journal of Health Psychology
Clinical Psychology Review
Health Psychology Review
Journal of Counselling Psychology
Learning Outcomes to be assessed: To critically appraise
research on psychological interventions to promote mental and
physical health and well being.
Grading Criteria:
CRITERIA
MARKS AWARDED
Introduction – 25%
· Give details of the paper, date, authors, where published.
· What was the authors aim, predictions/hypotheses?

· To what extent has this aim been achieved?
· What does this text add to the body of knowledge? (This could
be in terms of theory, data and/or practical application)
· What relationship does it bear to other works in the field?
/ 25
Main Body – 50%
· Present a summary of the key points along with a limited
number of examples.
· You can also briefly explain the author’s purpose/intentions
throughout the text and you may briefly describe how the text is
organised. The summary should only make up about a third of
the critical review.
· The review should be a balanced discussion and evaluation of
the strengths in the form of a critique, weakness and notable
feature, and key arguments of the text. E.g.
· What approach was used for the research? (eg; quantitative or
qualitative, analysis/review of theory or current practice,
comparative, case study, personal reflection etc...)
· How objective/biased is the approach?
· Are the results valid and reliable?
· What analytical framework is used to discuss the results?
Argument and use of evidence
· Is there a clear problem, statement or hypothesis?
· What claims are made?
· Is the argument consistent?
Evidence/conclusions/assumptions
· What kinds of evidence does the text rely on?

· How valid and reliable is the evidence?
· How effective is the evidence in supporting the argument?
· What conclusions are drawn?
· Are these conclusions justified?
/ 50
Conclusion– 25%
· A summary of your key points.
· Ability to draw main points of discussion together
· Linkage of conclusions to assignment title.
/ 25
Students should recognise that the marking criteria are weighted
to indicate its importance in relation to the information
required.
NB: these subsections should only be used as guidance towards
marking and content. This is an academic essay and subsections
should not be used within the main body of work.
Assessment Task 2:
Project Report. 4200 words.

Design a psychological based intervention in the form of an
informative leaflet to promote psychological health & well -
being
(700 words).
The proposed intervention should be accompanied by a report
(3500 words) focusing on all elements of the process
(formulation of the rationale for the intervention, proposed
delivery and subsequent method of evaluation).
Assignment Guidelines:
For the leaflet: Introduction (5%), main body and discussion
(10%) conclusion (5%).
Introduction (5%)
Should include: Definition, background and explanation of the
psychological based intervention of your choice supported by
research evidence.
Main body (10%)
Should include a detailed review and discussion of your
psychological based intervention and how similar interventions
in relation to your chosen area (e.g., managing stress or anxiety
in the workplace) have been found to promote psychological
health & well-being. A line of argument supporting the benefits
of your chosen intervention is also helpful. This should be
supported by research evidence.
Conclusion (5%)
A summary of your key points of your chosen intervention as to
how this promotes psychological health & well-being and
implications of such interventions for the future psychological
health & well-being.

For the report: Abstract (10%), Introduction (25%), Method
(20%), Discussion (15%) and Reference (10%):
Abstract (200-250 words)
An abstract is a brief summary of the research carried out. Its
length should be between 200 and 250 words. It must contain
brief details about:
1. Main background intervention
2. Aim of the intervention - the research question
3. The method used and the basic design of the intervention
4. Subsequent method of evaluation
Introduction (approx 1500-2000 words)
The Introduction should begin with a broad review of the area
leading towards a review of the specific question under study.
Its main purpose is to provide a rationale for the formulation of
the present intervention. Outline the key theories relevant to the
intervention, and mention any problems or controversies in the
area. The final paragraph should be clear statement/hypotheses
about the specific intervention under study of your choice.
Method: (Word count approx 500-700 words)
Here you should focus on the proposed delivery of your chosen
intervention. Details about design and method of proposed
delivery, e.g., weekly sessions? How many participants?
Confidentiality of participants? Etc.
Discussion (approx 400-550 words)
You should consider how you might evaluate your intervention:
Some focus questions to think about here: e.g., you should
appraise your own intervention critically (play devil’s advocate)
and evaluate it in the wider context and in its relation to
appropriate theories. Also its strengths/weaknesses; try to
support your arguments with theoretical/empirical findings
which have used similar interventions as a basis.

You must include a full and accurate APA reference list. You
can refer to the APA website for guidance on this
http://www.apastyle.org/index.aspx Alternatively,
Purdue Online Writing Lab is a useful and practical resource
https://owl.english.purdue.edu/owl/section/2/10/
Further Guidance for this assessment
The question is very broad so your challenge is to decide how to
focus your answer.
The key issue in this Project Report:
Design a psychological based intervention in the form of an
informative leaflet to promote psychological health & well -
being (700 words).
You are required to consider one psychological based
intervention for e.g., stress management, anxiety, depression,
resilience. These are just examples. You need to do some
reading around the topic before deciding upon the type of
intervention to be considered.
Psychological stress, as an example can take many forms in
terms of it being a major stressor, minor hassles or the
transaction between stress and your appraisal. This may take
into account coping strategies, social support, personality
factors etc.
Your proposed intervention should focus on all elements of the
process: e.g., formulation of the rationale for the intervention,
proposed delivery and subsequent method of evaluation.
There is not a SINGLE answer that is appropriate; you may
choose to answer the question in a number of ways. DO NOT
TRY TO INCLUDE EVERYTHING that might be relevant or
important. Instead, you should select and justify the approach
you have decided to take and select research evidence around
this topic.

The title gives you a lot of scope for researching an area which
you find interesting. One important consideration is the balance
between breadth (how many different ideas/arguments you
present) and depth (how much attention you pay to each
idea/argument in your work). It is generally better to focus on
fewer ideas/arguments in greater detail than to make brief and
superficial reference to multiple ideas, without discussing or
evaluating any of the evidence. You should avoid composing
paragraphs containing only the conclusions from multiple
studies, without any sense of what was done in key studies and
the quality of this research.
You must include a full and accurate APA reference list. You
can refer to the APA website for guidance on this
http://www.apastyle.org/index.aspx Alternatively,
Purdue Online Writing Lab is a useful and practical resource
https://owl.english.purdue.edu/owl/section/2/10/
To make your choice more straightforward, look for appropriate
articles in Health Psychology journals (e.g., British Journal of
Health Psychology, Health Psychology, European Journal of
Health Psychology) and Clinical Journals such as the British
Journal of Clinical Psychology.
Text books or specialist topic books are useful for getting an
introduction to the area of interest and review articles,
especially systematic review and meta-analysis articles, are also
helpful in providing an overview of recent research findings.
You can always chase up the references in a review article if
you need more information about the individual studies
presented in the review.
Suggested Reading
Learning Outcomes to be assessed: To engage in sophisticated
critical appraisal of the efficacy of different psychological
interventions to promote health and mental health.

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CHAPTER 6
DISCOUNTED CASH FLOW VALUATION (CALCULATOR)
6C-‹#›
5.1
This version relies primarily on the financial calculator with a
brief presentation of formulas. The calculator discussed is the
TI-BA-II+. The slides are easy to modify for whatever

calculator you prefer.
Determine the future and present value of investments with
multiple cash flows
Explain how loan payments are calculated and how to find the
interest rate on a loan
Describe how loans are amortized or paid off
Show how interest rates are quoted (and misquoted)
6C-‹#›
Future and Present Values of Multiple Cash Flows
Valuing Level Cash Flows: Annuities and Perpetuities
Comparing Rates: The Effect of Compounding
Loan Types and Loan Amortization
Chapter Outline

6C-‹#›
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 three years?
How much will you have in four years?
Multiple Cash Flows – FV (Example 6.1)
6C-‹#›
Section 6.1 (A)
5.4
Find the value at year 3 of each cash flow and add them
together.
Today’s (year 0) CF: 3 N; 8 I/Y; -7,000 PV; CPT FV = 8817.98
Year 1 CF: 2 N; 8 I/Y; -4,000 PV; CPT FV = 4,665.60
Year 2 CF: 1 N; 8 I/Y; -4,000 PV; CPT FV = 4,320
Year 3 CF: value = 4,000
Total value in 3 years = 8,817.98 + 4,665.60 + 4,320 + 4,000 =
21,803.58
Value at year 4: 1 N; 8 I/Y; -21,803.58 PV; CPT FV =
23,547.87
Multiple Cash Flows – FV (Example 6.1, CTD.)

6C-‹#›
5.5
Section 6.1 (A)
The students can read the example in the book. It is also
provided here.
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 three years? In four years?
Point out that there are several ways that this can be worked.
The book works this example by rolling the value forward each
year. The presentation will show the second way to work the
problem, finding the future value at the end for each cash flow
and then adding. Point out that you can find the value of a set of
cash flows at any point in time, all you have to do is get the
value of each cash flow at that point in time and then add them
together.
I entered the PV as negative for two reasons. (1) It is a cash
outflow since it is an investment. (2) The FV is computed as
positive, and the students can then just store each calcul ation
and then add from the memory registers, instead of writing
down all of the numbers and taking the risk of keying something
back into the calculator incorrectly.
Formula:
Today (year 0): FV = 7000(1.08)3 = 8,817.98

Year 1: FV = 4,000(1.08)2 = 4,665.60
Year 2: FV = 4,000(1.08) = 4,320
Year 3: value = 4,000
Total value in 3 years = 8817.98 + 4665.60 + 4320 + 4000 =
21,803.58
Value at year 4 = 21,803.58(1.08) = 23,547.87
Suppose you invest $500 in a mutual fund today and $600 in
one year.
If the fund pays 9% annually, how much will you have in two
years?
Year 0 CF: 2 N; -500 PV; 9 I/Y; CPT FV = 594.05
Total FV = 594.05 + 654.00 = 1,248.05
Multiple Cash Flows – FV Example 2
6C-‹#›
5.6
Section 6.1 (A)
Formula: FV = 500(1.09)2 + 600(1.09) = 1,248.05
How much will you have in 5 years if you make no further
deposits?

First way:
Total FV = 769.31 + 846.95 = 1,616.26
Second way – use value at year 2:
3 N; -1,248.05 PV; 9 I/Y; CPT FV = 1,616.26
Multiple Cash Flows – FV Example 2 (ctd.)
6C-‹#›
5.7
Section 6.1 (A)
Formula:
First way: FV = 500(1.09)5 + 600(1.09)4 = 1,616.26
Second way: FV = 1248.05(1.09)3 = 1,616.26
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%?
Total FV = 136.05 + 349.92 = 485.97
Multiple Cash Flows – FV Example 3

6C-‹#›
5.8
Section 6.1 (A)
Formula:
FV = 100(1.08)4 + 300(1.08)2 = 136.05 + 349.92 = 485.97
Find the PV of each cash flow and add them
Year 1 CF: N = 1; I/Y = 12; FV = 200; CPT PV = -178.57
Total PV = 178.57 + 318.88 + 427.07 + 508.41 = 1,432.93
Multiple Cash Flows – pv (Example 6.3)
6C-‹#›

5.9
Section 6.1 (B)
The students can read the example in the book.
You are offered an investment that will pay you $200 in one
year, $400 the next year, $600 the next year and $800 at the end
of the fourth year. You can earn 12 percent on very similar
investments. What is the most you should pay for this one?
Point out that the question could also be phrased as “How much
is this investment worth?”
Remember the sign convention. The negative numbers imply
that we would have to pay 1,432.93 today to receive the cash
flows in the future.
Formula:
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
Example 6.3 Timeline
0
1
2
3
4

200
400
600
800
178.57
318.88
427.07
508.41
1,432.93
6C-‹#›
Section 6.1 (B)
5.10
You can use the PV or FV functions in Excel to find the present
value or future value of a set of cash flows.
Setting the data up is half the battle – if it is set up properly,
then you can just copy the formulas.

Click on the Excel icon for an example.
Multiple Cash Flows Using a Spreadsheet
6C-‹#›
5.11
Section 6.1 (B)
Click on the tabs at the bottom of the worksheet to move from a
future value example to a present value example.
Lecture Tip: The present value of a series of cash flows depends
heavily on the choice of discount rate. You can easily illustrate
this dependence in the spreadsheet on Slide 6.10 by changing
the cell that contains the discount rate. A separate worksheet on
the slide provides a graph of the relationship between PV and
the discount rate.
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?
N = 1; I/Y = 10; FV = 1,000; CPT PV = -909.09
N = 2; I/Y = 10; FV = 2,000; CPT PV = -1,652.89
N = 3; I/Y = 10; FV = 3,000; CPT PV = -2,253.94
PV = 909.09 + 1,652.89 + 2,253.94 = 4,815.93

Multiple Cash Flows – PV Another Example
6C-‹#›
5.12
Section 6.1 (B)
Formula:
PV = 1000 / (1.1)1 = 909.09
PV = 2000 / (1.1)2 = 1,652.89
PV = 3000 / (1.1)3 = 2,253.94
PV = 909.09 + 1,652.89 + 2,253.94 = 4,815.92
Another way to use the financial calculator for uneven cash
flows is to use the cash flow keys.
Press CF and enter the cash flows beginning with year 0.
You have to press the “Enter” key for each cash flow.
Use the down arrow key to move to the next cash flow.
The “F” is the number of times a given cash flow occurs in
consecutive periods.
Use the NPV key to compute the present value by entering the
interest rate for I, pressing the down arrow, and then computing
the answer.
Clear the cash flow worksheet by pressing CF and then 2nd
CLR Work.
Multiple Uneven Cash Flows – Using the Calculator

6C-‹#›
5.13
Section 6.1 (B)
The next example will be worked using the cash flow keys.
Note that with the BA-II Plus, the students can double check the
numbers they have entered by pressing the up and down arrows.
It is similar to entering the cash flows into spreadsheet cells.
Other calculators also have cash flow keys. You enter the
information by putting in the cash flow and then pressing CF.
You have to always start with the year 0 cash flow, even if it is
zero.
Remind the students that the cash flows have to occur at even
intervals, so if you skip a year, you still have to enter a 0 cash
flow for that year.
Your broker calls you and tells you that he has this great
investment opportunity.
If you invest $100 today, you will receive $40 in one year and
$75 in two years.
If you require a 15% return on investments of this risk, should
you take the investment?
Use the CF keys to compute the value of the investment.
CF; CF0 = 0; C01 = 40; F01 = 1; C02 = 75; F02 = 1

NPV; I = 15; CPT NPV = 91.49
No – the broker is charging more than you would be willing to
pay.
Decisions, Decisions
6C-‹#›
5.14
Section 6.1 (B)
You can also use this as an introduction to NPV by having the
students put –100 in for CF0. When they compute the NPV, they
will get –8.51. You can then discuss the NPV rule and point out
that a negative NPV means that you do not earn your required
return. You should also remind them that the sign convention on
the regular TVM keys is NOT the same as getting a negative
NPV.
You are offered the opportunity to put some money away for
retirement.
You will receive five annual payments of $25,000 each
beginning in 40 years.
How much would you be willing to invest today if you desire an
interest rate of 12%?
Use cash flow keys:
CF; CF0 = 0; C01 = 0; F01 = 39; C02 = 25,000; F02 = 5; NPV; I
= 12; CPT NPV = 1,084.71
Saving For Retirement

6C-‹#›
Section 6.1 (B)
5.15
Saving For Retirement Timeline
0 1 2 … 39 40 41 42 43 44
0 0 0 … 0 25K 25K 25K 25K 25K
Notice that the year 0 cash flow = 0 (CF0 = 0)
The cash flows in years 1 – 39 are 0 (C01 = 0; F01 = 39)
The cash flows in years 40 – 44 are 25,000 (C02 = 25,000; F02
= 5)

6C-‹#›
Section 6.1 (B)
5.16
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.
The required discount rate is 7%.
What is the value of the cash flows at year 5?
What is the value of the cash flows today?
What is the value of the cash flows at year 3?
Quick Quiz – Part I
6C-‹#›
5.17
Section 6.1
The easiest way to work this problem is to use the uneven cash
flow keys and find the present value first and then compute the
others based on that.
CF0 = 0; C01 = 100; F01 = 1; C02 = 200; F02 = 2; C03 = 300;
F03 = 2; I = 7; CPT NPV = 874.17

Value in year 5: PV = 874.17; N = 5; I/Y = 7; CPT FV =
1,226.07
Value in year 3: PV = 874.17; N = 3; I/Y = 7; CPT FV =
1,070.90
Using formulas and one CF at a time:
Year 1 CF: FV5 = 100(1.07)4 = 131.08; PV0 = 100 / 1.07 =
93.46; FV3 = 100(1.07)2 = 114.49
Year 2 CF: FV5 = 200(1.07)3 = 245.01; PV0 = 200 / (1.07)2 =
174.69; FV3 = 200(1.07) = 214
Year 3 CF: FV5 = 200(1.07)2 = 228.98; PV0 = 200 / (1.07)3 =
163.26; FV3 = 200
Year 4 CF: FV5 = 300(1.07) = 321; PV0 = 300 / (1.07)4 =
228.87; PV3 = 300 / 1.07 = 280.37
Year 5 CF: FV5 = 300; PV0 = 300 / (1.07)5 = 213.90; PV3 =
300 / (1.07)2 = 262.03
Value at year 5 = 131.08 + 245.01 + 228.98 + 321 + 300 =
1,226.07
Present value today = 93.46 + 174.69 + 163.26 + 228.87 +
213.90 = 874.18 (difference due to rounding)
Value at year 3 = 114.49 + 214 + 200 + 280.37 + 262.03 =
1,070.89 (difference due to rounding)
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
Annuities and Perpetuities Defined

6C-‹#›
Section 6.2
5.18
Perpetuity: PV = C / r
Annuities:
Annuities and Perpetuities – Basic Formulas
6C-‹#›
5.19
Section 6.2
Lecture Tip: The annuity factor approach is a short-cut
approach in the process of calculating the present value of
multiple cash flows and it is only applicable to a finite series of
level cash flows. Financial calculators have reduced the need
for annuity factors, but it may still be useful from a conceptual
standpoint to show that the PVIFA is just the sum of the PVIFs
across the same time period.

You can use the PMT key on the calculator for the equal
payment.
The sign convention still holds.
Ordinary annuity versus annuity due
You can switch your calculator between the two types by using
the 2nd BGN 2nd Set on the TI BA-II Plus.
If you see “BGN” or “Begin” in the display of your calculator,
you have it set for an annuity due.
Most problems are ordinary annuities.
Annuities and the Calculator
6C-‹#›
5.20
Section 6.2
Other calculators also have a key that allows you to switch
between Beg/End.
After carefully going over your budget, you have determined
you can afford to pay $632 per month toward a new sports car.
You call up your local bank and find out that the going rate is 1
percent per month for 48 months.
How much can you borrow?
To determine how much you can borrow, we need to calculate
the present value of $632 per month for 48 months at 1 percent
per month.

Annuity – Example 6.5
6C-‹#›
Section 6.2 (A)
5.21
You borrow money TODAY so you need to compute the present
value.
48 N; 1 I/Y; -632 PMT; CPT PV = 23,999.54 ($24,000)
Formula:
Annuity – Example 6.5 (ctd.)
6C-‹#›
5.22
Section 6.2 (A)
The students can read the example in the book.

After carefully going over your budget, you have determined
you can afford to pay $632 per month towards a new sports car.
You call up your local bank and find out that the going rate is 1
percent per month for 48 months. How much can you borrow?
Note that the difference between the answer here and the one in
the book is due to the rounding of the Annuity PV factor in the
book.
Suppose you win the Publishers Clearinghouse $10 million
sweepstakes.
The money is paid in equal annual end-of-year installments of
$333,333.33 over 30 years.
If the appropriate discount rate is 5%, how much is the
sweepstakes actually worth today?
30 N; 5 I/Y; 333,333.33 PMT;
CPT PV = 5,124,150.29
Annuity – Sweepstakes Example
6C-‹#›
5.23
Section 6.2 (A)
Formula:
PV = 333,333.33[1 – 1/1.0530] / .05 = 5,124,150.29
You are ready to buy a house, and you have $20,000 for a down

payment and closing costs.
Closing costs are estimated to be 4% of the loan value.
You have an annual salary of $36,000, and the bank is willing
to allow your monthly mortgage payment to be equal to 28% of
your monthly income.
The interest rate on the loan is 6% per year with monthly
compounding (.5% per month) for a 30-year fixed rate loan.
How much money will the bank loan you?
How much can you offer for the house?
Buying a House
6C-‹#›
5.24
Section 6.2 (A)
It might be good to note that the outstanding balance on the
loan at any point in time is simply the present value of the
remaining payments.
Bank loan
Monthly income = 36,000 / 12 = 3,000
Maximum payment = .28(3,000) = 840
30×12 = 360 N
.5 I/Y
-840 PMT
CPT PV = 140,105
Total Price
Closing costs = .04(140,105) = 5,604

Down payment = 20,000 – 5,604 = 14,396
Total Price = 140,105 + 14,396 = 154,501
Buying a House (ctd.)
6C-‹#›
5.25
Section 6.2 (A)
You might point out that you would probably not offer 154,501.
The more likely scenario would be 154,500 , or less if you
assumed negotiations would occur.
Formula
PV = 840[1 – 1/1.005360] / .005 = 140,105
The present value and future value formulas in a spreadsheet
include a place for annuity payments.
Click on the Excel icon to see an example.
Annuities on the Spreadsheet – Example

6C-‹#›
Section 6.2 (A)
5.26
You know the payment amount for a loan, and you want to know
how much was borrowed. Do you compute a present value or a
future value?
You want to receive 5,000 per month in retirement.
If you can earn 0.75% per month and you expect to need the
income for 25 years, how much do you need to have in your
account at retirement?
Quick Quiz – Part II
6C-‹#›
5.27
Section 6.2 (A)
Calculator
PMT = 5,000; N = 25×12 = 300; I/Y = .75; CPT PV = 595,808
Formula
PV = 5000[1 – 1 / 1.0075300] / .0075 = 595,808
Suppose you want to borrow $20,000 for a new car.
You can borrow at 8% per year, compounded monthly (8/12 =
.66667% per month).

If you take a 4-year loan, what is your monthly payment?
4(12) = 48 N; 20,000 PV; .66667 I/Y; CPT PMT = 488.26
Finding the Payment
6C-‹#›
5.28
Section 6.2 (A)
Formula
20,000 = PMT[1 – 1 / 1.006666748] / .0066667
PMT = 488.26
Another TVM formula that can be found in a spreadsheet is the
payment formula.
PMT(rate, nper, pv, fv)
The same sign convention holds as for the PV and FV formulas.
Click on the Excel icon for an example.
Finding the Payment on a Spreadsheet

6C-‹#›
Section 6.2 (A)
5.29
You ran a little short on your spring break vacation, so you put
$1,000 on your credit card.
You can afford only the minimum payment of $20 per month.
The interest rate on the credit card is 1.5 percent per month.
How long will you need to pay off the $1,000?
Finding the Number of Payments – Example 6.6
6C-‹#›
Section 6.2 (A)
5.30
The sign convention matters!
1.5 I/Y
1,000 PV
-20 PMT
CPT N = 93.111 months = 7.75 years
And this is only if you don’t charge anything more on the card!
Finding the Number of Payments – Example 6.6 (ctd.)

6C-‹#›
5.31
Section 6.2 (A)
You ran a little short on your spring break vacation, so you put
$1,000 on your credit card. You can only afford to make the
minimum payment of $20 per month. The interest rate on the
credit card is 1.5 percent per month. How long will you need to
pay off the $1,000?
This is an excellent opportunity to talk about credit card debt
and the problems that can develop if it is not handled properly.
Many students don’t understand how it works, and it is rarely
discussed. This is something that students can take away from
the class, even if they aren’t finance majors.
1000 = 20(1 – 1/1.015t) / .015
.75 = 1 – 1 / 1.015t
1 / 1.015t = .25
1 / .25 = 1.015t
t = ln(1/.25) / ln(1.015) = 93.111 months = 7.75 years
Suppose you borrow $2,000 at 5%, and you are going to make
annual payments of $734.42.
How long before you pay off the loan?
Sign convention matters!!!
5 I/Y
2,000 PV
-734.42 PMT
CPT N = 3 years

Finding the Number of Payments – Another Example
6C-‹#›
5.32
Section 6.2 (A)
2000 = 734.42(1 – 1/1.05t) / .05
.136161869 = 1 – 1/1.05t
1/1.05t = .863838131
1.157624287 = 1.05t
t = ln(1.157624287) / ln(1.05) = 3 years
Suppose you borrow $10,000 from your parents to buy a car.
You agree to pay $207.58 per month for 60 months.
What is the monthly interest rate?
Sign convention matters!!!
60 N
10,000 PV
-207.58 PMT
CPT I/Y = .75%
Finding the Rate

6C-‹#›
Section 6.2 (A)
5.33
Trial and Error Process
Choose an interest rate and compute the PV of the payments
based on this rate.
Compare the computed PV with the actual loan amount.
If the computed PV > loan amount, then the interest rate is too
low.
If the computed PV < loan amount, then the interest rate is too
high.
Adjust the rate and repeat the process until the computed PV
and the loan amount are equal.
Annuity – Finding the Rate Without a Financial Calculator
6C-‹#›
Section 6.2 (A)
5.34
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
0.75% per month?
What monthly rate would you need to earn if you only have
$200,000 to deposit?

Suppose you have $200,000 to deposit and can earn 0.75% per
month.
How many months could you receive the $5,000 payment?
How much could you receive every month for 5 years?
Quick Quiz – Part III
6C-‹#›
5.35
Section 6.2 (A)
Q1: 5(12) = 60 N; .75 I/Y; 5000 PMT; CPT PV = -240,867
PV = 5000(1 – 1 / 1.007560) / .0075 = 240,867
Q2: -200,000 PV; 60 N; 5000 PMT; CPT I/Y = 1.439%
Trial and error without calculator
Q3: -200,000 PV; .75 I/Y; 5000 PMT; CPT N = 47.73 (47
months plus partial payment in month 48)
200,000 = 5000(1 – 1 / 1.0075t) / .0075
.3 = 1 – 1/1.0075t
1.0075t = 1.428571429
t = ln(1.428571429) / ln(1.0075) = 47.73 months
Q4: -200,000 PV; 60 N; .75 I/Y; CPT PMT = 4,151.67
200,000 = C(1 – 1/1.007560) / .0075
C = 4,151.67
Suppose you begin saving for your retirement by depositing
$2,000 per year in an IRA.

If the interest rate is 7.5%, how much will you have in 40
years?
Remember the sign convention!
40 N
7.5 I/Y
-2,000 PMT
CPT FV = 454,513.04
Future Values for Annuities
6C-‹#›
5.36
Section 6.2 (B)
FV = 2000(1.07540 – 1)/.075 = 454,513.04
Lecture Tip: It should be emphasized that annuity factor tables
(and the annuity factors in the formulas) assumes that the first
payment occurs one period from the present, with the final
payment at the end of the annuity’s life. If the first payment
occurs at the beginning of the period, then FV’s have one
additional period for compounding and PV’s have one less
period to be discounted. Consequently, you can multiply both
the future value and the present value by (1 + r) to account for
the change in timing.
You are saving for a new house and you put $10,000 per year in
an account paying 8%. The first payment is made today.
How much will you have at the end of 3 years?

2nd BGN 2nd Set (you should see BGN in the display)
3 N
-10,000 PMT
8 I/Y
CPT FV = 35,061.12
2nd BGN 2nd Set (be sure to change it back to an ordinary
annuity)
Annuity Due
6C-‹#›
5.37
Section 6.2 (C)
Note that the procedure for changing the calculator to an
annuity due is similar on other calculators.
Formula:
FV = 10,000[(1.083 – 1) / .08](1.08) = 35,061.12
What if it were an ordinary annuity? FV = 32,464 (so you
receive an additional 2,597.12 by starting to save today.)
Annuity Due Timeline

0 1 2 3
10000 10000 10000
32,464
35,016.12
6C-‹#›
5.38
Section 6.2 (C)
If you use the regular annuity formula, the FV will occur at the
same time as the last payment. To get the value at the end of the
third period, you have to take it forward one more period.
Suppose the Fellini Co. wants to sell preferred stock at $100 per
share.
A similar issue of preferred stock already outstanding has a
price of $40 per share and offers a dividend of $1 every quarter.
What dividend will Fellini have to offer if the preferred stock is
going to sell?
Perpetuity – Example 6.7

6C-‹#›
Section 6.2 (D)
5.39
Perpetuity formula: PV = C / r
Current required return:
40 = 1 / r
r = .025 or 2.5% per quarter
Dividend for new preferred:
100 = C / .025
C = 2.50 per quarter
Perpetuity – Example 6.7 (ctd.)
6C-‹#›
5.40
Section 6.2 (D)
This is a good preview to the valuation issues discussed in
future chapters. The price of an investment is just the present
value of expected future cash flows.
Example statement:

Suppose the Fellini Co. wants to sell preferred stock at $100 per
share. A very similar issue of preferred stock already
outstanding has a price of $40 per share and offers a dividend of
$1 every quarter. What dividend will Fellini have to offer if the
preferred stock is going to sell?
You want to have $1 million to use for retirement in 35 years.
If you can earn 1% per month, how much do you need to deposit
on a monthly basis if the first payment is made in one month?
What if the first payment is made today?
You are considering preferred stock that pays a quarterly
dividend of $1.50.
If your desired return is 3% per quarter, how much would you
be willing to pay?
Quick Quiz – Part IV
6C-‹#›
5.41
Section 6.2 (D)
Q1: 35(12) = 420 N; 1,000,000 FV; 1 I/Y; CPT PMT = 155.50
1,000,000 = C (1.01420 – 1) / .01
C = 155.50
Q2:Set calculator to annuity due and use the same inputs as
above. CPT PMT = 153.96

The payments would be smaller by one period’s interest. Divide
the above result by 1.01.
1,000,000 = C[(1.01420 – 1) / .01] ( 1.01)
C = 153.96
Q3: PV = 1.50 / .03 = $50
Another online financial calculator can be found at
MoneyChimp.
Go to the website and work the following example.
Choose calculator and then annuity
You just inherited $5 million. If you can earn 6% on your
money, how much can you withdraw each year for the next 40
years?
MoneyChimp assumes annuity due!
Payment = $313,497.81
Work the Web Example
6C-‹#›
Section 6.2 (D)
5.42
Table 6.2

6C-‹#›
Section 6.2 (D)
5.43
A growing stream of cash flows with a fixed maturity
Growing Annuity
6C-‹#›
Section 6.2 (E)
5.44
A defined-benefit retirement plan offers to pay $20,000 per year
for 40 years and increase the annual payment by three-percent
each year. What is the present value at retirement if the
discount rate is 10 percent?
Growing Annuity: Example

6C-‹#›
Section 6.2 (E)
5.45
A growing stream of cash flows that lasts forever
Growing Perpetuity
6C-‹#›
5.46
Section 6.2 (E)
Lecture Tip: To prepare students for the chapter on stock
valuation, it may be helpful to include a discussion of equity as

a growing perpetuity.
The expected dividend next year is $1.30, and dividends are
expected to grow at 5% forever.
If the discount rate is 10%, what is the value of this promised
dividend stream?
Growing Perpetuity: Example
6C-‹#›
5.47
Section 6.2 (E)
It is important to note to students that in this example the year 1
cash flow was given. If the current dividend were $1.30, then
we would need to multiply it by one plus the growth rate to
estimate the year 1 cash flow.
This is the actual rate paid (or received) after accounting for
compounding that occurs during the year
If you want to compare two alternative investments with
different compounding periods, you need to compute the EAR
and use that for comparison.
Effective Annual Rate (EAR)

6C-‹#›
5.48
Section 6.3 (A)
This is the annual rate that is quoted by law
By definition APR = period rate times the number of periods per
year.
Consequently, to get the period rate we rearrange the APR
equation:
Period rate = APR / number of periods per year
You should NEVER divide the effective rate by the number of
periods per year – it will NOT give you the period rate.
Annual Percentage Rate
6C-‹#›
Section 6.3 (A)
5.49
What is the APR if the monthly rate is .5%?

.5(12) = 6%
What is the APR if the semiannual rate is .5%?
.5(2) = 1%
What is the monthly rate if the APR is 12% with monthly
compounding?
12 / 12 = 1%
Computing APRs
6C-‹#›
Section 6.3 (A)
5.50
You ALWAYS need to make sure that the interest rate and the
time period match.
If you are looking at annual periods, you need an annual rate.
If you are looking at monthly periods, you need a monthly rate.
If you have an APR based on monthly compounding, you have
to use monthly periods for lump sums, or adjust the interest rate
appropriately if you have payments other than monthly.
Things to Remember

6C-‹#›
Section 6.3 (A)
5.51
Suppose you can earn 1% per month on $1 invested today.
What is the APR? 1(12) = 12%
How much are you effectively earning?
FV = 1(1.01)12 = 1.1268
Rate = (1.1268 – 1) / 1 = .1268 = 12.68%
Suppose you put it in another account and earn 3% per quarter.
What is the APR? 3(4) = 12%
How much are you effectively earning?
FV = 1(1.03)4 = 1.1255
Rate = (1.1255 – 1) / 1 = .1255 = 12.55%
Computing EARs – Example
6C-‹#›
5.52
Section 6.3 (B)
Point out that the APR is the same in either case, but your
effective rate is different. Ask them which account they should
use.

EAR – Formula
Remember that the APR is the quoted rate, and
m is the number of compounding periods per year
6C-‹#›
5.53
Section 6.3 (B)
Using the calculator:
The TI BA-II Plus has an I conversion key that allows for easy
conversion between quoted rates and effective rates.
2nd I Conv NOM is the quoted rate; down arrow EFF is the
effective rate; down arrow C/Y is compounding periods per
year. You can compute either the NOM or the EFF by entering
the other two pieces of information, then going to the one you
wish to compute and pressing CPT.
You are looking at two savings accounts. One pays 5.25%, with
daily compounding. The other pays 5.3% with semiannual
compounding. Which account should you use?
First account:
EAR = (1 + .0525/365)365 – 1 = 5.39%

Second account:
EAR = (1 + .053/2)2 – 1 = 5.37%
Which account should you choose and why?
Decisions, Decisions II
6C-‹#›
5.54
Section 6.3 (B)
Remind students that rates are quoted on an annual basis. The
given numbers are APRs, not daily or semiannual rates.
Calculator:
2nd I conv 5.25 NOM Enter up arrow 365 C/Y Enter up arrow
CPT EFF = 5.39%
5.3 NOM Enter up arrow 2 C/Y Enter up arrow CPT EFF =
5.37%
Let’s verify the choice. Suppose you invest $100 in each
account. How much will you have in each account in one year?
First Account:
365 N; 5.25 / 365 = .014383562 I/Y; 100 PV; CPT FV = 105.39
Second Account:
2 N; 5.3 / 2 = 2.65 I/Y; 100 PV; CPT FV = 105.37
You have more money in the first account.
Decisions, Decisions II (ctd.)

6C-‹#›
5.55
Section 6.3 (B)
It is important to point out that the daily rate is NOT .014, it is
.014383562
Lecture Tip: Here is a way to drive the point of this section
home. Ask how many students have taken out a car loan. Now
ask one of them what annual interest rate s/he is paying on the
loan. Students will typically quote the loan in terms of the APR.
Point out that, since payments are made monthly, the effective
rate is actually more than the rate s/he just quoted, and
demonstrate the calculation of the EAR.
If you have an effective rate, how can you compute the APR?
Rearrange the EAR equation and you get:
Computing APRs from EARs

6C-‹#›
Section 6.3 (C)
5.56
Suppose you want to earn an effective rate of 12% and you are
looking at an account that compounds on a monthly basis. What
APR must they pay?
APR – Example
6C-‹#›
5.57
Section 6.3 (C)
On the calculator: 2nd I conv down arrow 12 EFF Enter down
arrow 12 C/Y Enter down arrow CPT NOM
Suppose you want to buy a new computer system and the store
is willing to allow you to make monthly payments. The entire
computer system costs $3,500.
The loan period is for 2 years, and the interest rate is 16.9%
with monthly compounding.
What is your monthly payment?
2(12) = 24 N; 16.9 / 12 = 1.408333333 I/Y; 3,500 PV; CPT

PMT = -172.88
Computing Payments with APRs
6C-‹#›
5.58
Section 6.3 (C)
Monthly rate = .169 / 12 = .01408333333
Number of months = 2(12) = 24
3,500 = C[1 – (1 / 1.01408333333)24] / .01408333333
C = 172.88
Suppose you deposit $50 a month into an account that has an
APR of 9%, based on monthly compounding.
How much will you have in the account in 35 years?
35(12) = 420 N
9 / 12 = .75 I/Y
50 PMT
CPT FV = 147,089.22
Future Values with Monthly Compounding

6C-‹#›
5.59
Section 6.3 (D)
FV = 50[1.0075420 – 1] / .0075 = 147,089.22
You need $15,000 in 3 years for a new car.
If you can deposit money into an account that pays an APR of
5.5% based on daily compounding, how much would you need
to deposit?
3(365) = 1,095 N
5.5 / 365 = .015068493 I/Y
15,000 FV
CPT PV = -12,718.56
Present Value with Daily Compounding
No reproduction or distribution without the prior w ritten
6C-‹#›
5.60
Section 6.3 (D)
FV = 15,000 / (1.00015068493)1095 = 12,718.56
Sometimes investments or loans are figured based on continuous
compounding.
EAR = eq – 1
The e is a special function on the calculator normally denoted
by ex.

Example: What is the effective annual rate of 7% compounded
continuously?
EAR = e.07 – 1 = .0725 or 7.25%
Continuous Compounding
6C-‹#›
Section 6.3 (D)
5.61
What is the definition of an APR?
What is the effective annual rate?
Which rate should you use to compare alternative investments
or loans?
Which rate do you need to use in the time value of money
calculations?
Quick Quiz – Part V
6C-‹#›

5.62
Section 6.3 (D)
APR = period rate × # of compounding periods per year
EAR is the rate we earn (or pay) after we account for
compounding.
We should use the EAR to compare alternatives.
We need the period rate, and we have to use the APR to get it.
Treasury bills are excellent examples of pure discount loans.
The principal amount is repaid at some future date, without any
periodic interest payments.
If a T-bill promises to repay $10,000 in 12 months and the
market interest rate is 7 percent, how much will the bill sell for
in the market?
1 N; 10,000 FV; 7 I/Y; CPT PV = -9,345.79
Pure Discount Loans – Example 6.12
6C-‹#›
5.63
Section 6.4 (A)
PV = 10,000 / 1.07 = 9345.79
Remind students that the value of an investment is the present
value of expected future cash flows.

Consider a 5-year, interest-only loan with a 7% interest rate.
The principal amount is $10,000. Interest is paid annually.
What would the stream of cash flows be?
Years 1 – 4: Interest payments of .07(10,000) = 700
Year 5: Interest + principal = 10,700
This cash flow stream is similar to the cash flows on corporate
bonds, and we will talk about them in greater detail later.
Interest-Only Loan – Example
6C-‹#›
Section 6.4 (B)
5.64
Consider a $50,000, 10 year loan at 8% interest. The loan
agreement requires the firm to pay $5,000 in principal each year
plus interest for that year.
Click on the Excel icon to see the amortization table.
Amortized Loan with Fixed Principal Payment – Example

6C-‹#›
Section 6.4 (C)
5.65
Each payment covers the interest expense plus reduces
principal.
Consider a 4 year loan with annual payments. The interest rate
is 8%, and the principal amount is $5,000.
What is the annual payment?
4 N
8 I/Y
5,000 PV
CPT PMT = -1,509.60
Click on the Excel icon to see the amortization table.
Amortized Loan with Fixed Payment – Example
6C-‹#›
5.66
Section 6.4 (C)
Lecture Tip: Consider a $200,000, 30-year loan with monthly
payments of $1330.60 (7% APR with monthly compounding).
You would pay a total of $279,016 in interest over the life of
the loan. Suppose instead, you cut the payment in half and pay
$665.30 every two weeks (note that this entails paying an extra
$1330.60 per year because there are 26 two week periods). You

will cut your loan term to just under 24 years and save almost
$70,000 in interest over the life of the loan.
Calculations on TI-BAII plus
First: PV = 200,000; N=360; I=7; P/Y=C/Y=12; CPT PMT =
1330.60 (interest = 1330.60×360 – 200,000)
Second: PV = 200,000; PMT = -665.30; I = 7; P/Y = 26; C/Y =
12; CPT N = 614 payments / 26 = 23.65 years (interest =
665.30×614 – 200,000)
There are websites available that can easily prepare
amortization tables.
Check out the Bankrate website and work the following
example.
You have a loan of $25,000 and will repay the loan over 5 years
at 8% interest.
What is your loan payment?
What does the amortization schedule look like?
Work the Web Example-2
6C-‹#›
5.67
Section 6.4 (C)
The monthly payment is $506.91.

What is a pure discount loan?
What is a good example of a pure discount loan?
What is an interest-only loan?
What is a good example of an interest-only loan?
What is an amortized loan?
What is a good example of an amortized loan?
Quick Quiz – Part VI
6C-‹#›
Section 6.4
5.68
Suppose you are in a hurry to get your income tax refund.
If you mail your tax return, you will receive your refund in 3
weeks.
If you file the return electronically through a tax service, you
can get the estimated refund tomorrow.
The service subtracts a $50 fee and pays you the remaining
expected refund. The actual refund is then mailed to the
preparation service.
Assume you expect to get a refund of $978.
What is the APR with weekly compounding?
What is the EAR?
How large does the refund have to be for the APR to be 15%?
What is your opinion of this practice?

Ethics Issues
6C-‹#›
5.69
Using a financial calculator to find the APR: PV = 978 – 50 =
928; FV = -978; N = 3 weeks; CPT I/Y = 1.765% per week;
APR = 1.765 (52 weeks per year) = 91.76%!!!
Compute the EAR = (1.01765)52 – 1 = 148.34%!!!!
You would be better off taking a cash advance on your credit
card and paying it off when the refund check comes, even if you
have the most expensive card available.
Refund needed for a 15% APR:
PV + 50 = PV(1 + (.15/52))3
PV = $5,761.14
An investment will provide you with $100 at the end of each
year for the next 10 years. What is the present value of that
annuity if the discount rate is 8% annually?
What is the present value of the above if the payments are
received at the beginning of each year?
If you deposit those payments into an account earning 8%, what
will the future value be in 10 years?

What will the future value be if you open the account with
$1,000 today, and then make the $100 deposits at the end of
each year?
Comprehensive Problem
6C-‹#›
5.70
Section 6.5
Present value problems:
End of the year: 10 N; 8 I/Y; 100 PMT; CPT PV = -671.01
Beginning of the year: PV = $671.00 × 1.08 = $724.69
Future value problems:
10 N; 8 I/Y; -100 PMT; CPT FV = 1,448.66
10N; 8 I/Y; -1,000 PV; -100 PMT; CPT FV = 3,607.58
End of Chapter
Chapter 6 - calculator

6C-‹#›
6C-‹#›
Future ValueConsider the cash flows presented in the table
below. What is the value of the cash flows in year
5?Rate15%(Same as .15)YearNPERCash FlowFuture
ValueFormula141000$1,749.01=-
FV($B$3,B6,0,C6)233000$4,562.63=-
FV($B$3,B7,0,C7)325000$6,612.50=-
FV($B$3,B8,0,C8)417000$8,050.00=-
FV($B$3,B9,0,C9)509000$9,000.00=-
FV($B$3,B10,0,C10)Total
PV$29,974.13=SUM(D6:D10)Comments:The negative sign
before the FV formula makes the result positive.The dollar
signs around B3 make the rate an absolute reference so that the
formula may be entered once and then copied down.The formua
asks for a payment between number of periods and present
value, hence the 0.
Present ValueConsider the cash flows presented in the table
below. What is the present value?Rate15%(Same as
.15)YearCash FlowPresent ValueFormula11000$869.5 7=-
PV($B$3,A6,0,B6)23000$2,268.43=-
PV($B$3,A7,0,B7)35000$3,287.58=-
PV($B$3,A8,0,B8)47000$4,002.27=-
PV($B$3,A9,0,B9)59000$4,474.59=-PV($B$3,A10,0,B10)Total
PV$14,902.44=SUM(C6:C10)Comments:The negative sign
before the PV formula makes the result positive.The dollar
signs around B3 make the rate an absolute reference so that the
formula may be entered once and then copied down.The formua
asks for a payment between number of periods and future value,
hence the 0.

r
r
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t
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Present ValueWhat is the present value of $50,000 per year for
15 years if the interest rate is 7%?PMT =50,000RATE
=7%(Same as .07)NPER =15Present Value
=$455,395.70Formula:=-PV(B4,B5,B3)Note: The negative sign
in the formula makes the result positive. You could also put a
negative sign before the PMT inside the parentheses.
Future ValueWhat is the future value of $50,000 per year for 15
years if the interest rate is 7%?PMT =50,000RATE =7%(Same
as .07)NPER =15Present Value =$1,256,451.10Formula:=-
FV(B4,B5,B3)Note: The negative sign in the formula makes the
result positive. You could also put a negative sign before the
PMT inside the parentheses.
Sheet1You are going to borrow $250,000 to buy a house. What

will your monthly payment be if the interest rate is .58% per
month and you borrow the money for 30 years?PV
=250,000NPER =360(30 years * 12 months per year)RATE
=0.58%(Same as .0058)Monthly Payment
=($1,656.55)Formula=PMT(B5,B4,B3)The payment was left as
negative to indicate that it is a cash outflow.
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12/1
Sheet1YearBeginning BalanceInterest PaymentPrincipal
PaymentTotal PaymentEnding
Balance150,0004,0005,0009,00045,000245,0003,6005,0008,600
40,000340,0003,2005,0008,20035,000435,0002,8005,0007,8003
0,000530,0002,4005,0007,40025,000625,0002,0005,0007,00020
,000720,0001,6005,0006,60015,000815,0001,2005,0006,20010,
000910,0008005,0005,8005,000105,0004005,0005,4000
Sheet1YearBeginning BalanceTotal PaymentInterest
PaidPrincipal PaidEnding
Balance15,000.001,509.60400.001,109.603,890.4023,8 90.401,5
09.60311.231,198.372,692.0332,692.031,509.60215.361,294.24
1,397.7941,397.791,509.60111.821,397.780.01Totals6,038.401,
038.414,999.99Note: The ending balance of .01 is due to
rounding. The last payment would actually be 1,509.61.
CHAPTER 9
NET PRESENT VALUE AND
OTHER INVESTMENT CRITERIA

9-‹#›
Show the reasons why the net present value criterion is the best
way to evaluate proposed investments
Discuss the payback rule and some of its shortcomings
Discuss the discounted payback rule and some of its
shortcomings
Explain accounting rates of return and some of the problems
with them
Present the internal rate of return criterion and its strengths and
weaknesses
Calculate the modified internal rate of return
Illustrate the profitability index and its relation to net present
value

9-‹#›
Net Present Value
The Payback Rule
The Discounted Payback
The Average Accounting Return
The Internal Rate of Return
The Profitability Index
The Practice of Capital Budgeting
Chapter Outline
9-‹#›
8.3
Lecture Tip: A logical prerequisite to the analysis of investment
opportunities is the creation of investment opportunities. Unlike
the field of investments, where the analyst more or less takes
the investment opportunity set as a given, the field of capital
budgeting relies on the work of people in the areas of

engineering, research and development, information technology
and others for the creation of investment opportunities. As such,
it is important to remind students of the importance of creativity
in this area, as well as the importance of analytical techniques.
We need to ask ourselves the following questions when
evaluating capital budgeting decision rules:
Does the decision rule adjust for the time value of money?
Does the decision rule adjust for risk?
Does the decision rule provide information on whether we are
creating value for the firm?
Good Decision Criteria
9-‹#›
8.4
Section 9.1
Economics students will recognize that the practice of capital
budgeting defines the firm’s investment opportunity schedule.
The difference between the market value of a project and its
cost
How much value is created from undertaking an investment?

The first step is to estimate the expected future cash flows.
The second step is to estimate the required return for projects of
this risk level.
The third step is to find the present value of the cash flows and
subtract the initial investment.
Net Present Value
9-‹#›
8.5
Section 9.1 (A)
We learn how to estimate the cash flows and the required return
in subsequent chapters.
The NPV measures the increase in firm value, which is also the
increase in the value of what the shareholders own. Thus,
making decisions with the NPV rule facilitates the achievement
of our goal in Chapter 1 – making decisions that will maximize
shareholder wealth.
Lecture Tip: Although this point may seem obvious, it is often
helpful to stress the word “net” in net present value. It is not
uncommon for some students to carelessly calculate the PV of a
project’s future cash flows and fail to subtract out its cost (after
all, this is what the programmers of Lotus and Excel did when
they programmed the NPV function). The PV of future cash

flows is not NPV; rather, NPV is the amount remaining after
offsetting the PV of future cash flows with the initial cost.
Thus, the NPV amount determines the incremental value created
by undertaking the investment.
You are reviewing a new project and have estimated the
following cash flows:
Year 0: CF = -165,000
Year 1: CF = 63,120; NI = 13,620
Year 2: CF = 70,800; NI = 3,300
Year 3: CF = 91,080; NI = 29,100
Average Book Value = 72,000
Your required return for assets of this risk level is 12%.
Project Example Information
9-‹#›
8.6
Section 9.1 (B)
This example will be used for each of the decision rules so that
the students can compare the different rules and see that
conflicts can arise. This illustrates the importance of
recognizing which decision rules provide the best information
for making decisions that will increase owner wealth.
If the NPV is positive, accept the project.

A positive NPV means that the project is expected to add value
to the firm and will therefore increase the wealth of the owners.
Since our goal is to increase owner wealth, NPV is a direct
measure of how well this project will meet our goal.
NPV – Decision Rule
9-‹#›
8.7
Section 9.1 (B)
Lecture Tip: Here’s another perspective on the meaning of NPV.
If we accept a project with a negative NPV of -$2,422, this is
financially equivalent to investing $2,422 today and receiving
nothing in return. Therefore, the total value of the firm would
decrease by $2,422. This assumes that the various components
(cash flow estimates, discount rate, etc.) used in the
computation are correct.
Lecture Tip: In practice, financial managers are rarely presented
with zero NPV projects for at least two reasons. First, in an
abstract sense, zero is just another of the infinite number of
values the NPV can take; as such, the likelihood of obtaining
any particular number is small. Second, and more pragmatically,
in most large firms, capital investment proposals are submitted
to the finance group from other areas for analysis. Those
submitting proposals recognize the ambivalence associated with
zero NPVs and are less likely to send them to the finance group

in the first place.
Using the formulas:
NPV = -165,000 + 63,120/(1.12) + 70,800/(1.12)2 +
91,080/(1.12)3 = 12,627.41
Using the calculator:
CF0 = -165,000; C01 = 63,120; F01 = 1; C02 = 70,800; F02 = 1;
C03 = 91,080; F03 = 1; NPV; I = 12; CPT NPV = 12,627.41
Do we accept or reject the project?
Computing NPV for the Project
9-‹#›
8.8
Section 9.1 (B)
Again, the calculator used for the illustration is the TI BA-II
plus. The basic procedure is the same; you start with the year 0
cash flow and then enter the cash flows in order. F01, F02, etc.
are used to set the frequency of a cash flow occurrence. Many
calculators only require you to use this function if the frequency
is something other than 1.
Since we have a positive NPV, we should accept the project.
Does the NPV rule account for the time value of money?

CHAPTER 5INTRODUCTION TO VALUATION THE TIME VALUE OF MONEY (C

CHAPTER 5INTRODUCTION TO VALUATION THE TIME VALUE OF MONEY (C

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