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The ABCD model for writing objectives
Introduction
· Objectives include 4 distinct components: Audience (who),
Behavior (what), Condition (when and where) and Degree
(extent of change).
· Objectives must be both observable and measurable to be
effective.
· Using words like understand and learn in writing objectives is
generally not acceptable as they are difficult to measure.
· Written objectives are a vital part of program development and
implementation because they provide the roadmap for designing
and delivering health promotion programs.
Characteristics of objectives
· Specific – target a specific area for improvement.
· Measurable – quantify or at least suggest an indicator of
progress.
· Assignable – specify who will do it.
· Realistic – state what results can realistically be achieved,
given available resources.
· Time-related – specify when the result(s) can be achieved.
Samples
· Learning Objective
· After attending a 1-hour workshop on HIV, San Marcos high
school students will list five risk factors for HIV infection,
without error.
· Behavioral Objective
· Given access to free condoms in the nurse’s office, San
Marcos high school students will acquire a condom from the
nurse’s office, each time they have sex.
· Process
· HIV program coordinators will mail permission forms to all
high school students’ parents prior to implementing the HIV
program.
· Environmental
· Four prevention pamphlet stations will be available in each
San Marcos high school by August 2015.
· Program/Outcome
· Within the next five years, the rate of HIV infection in San
Marcos high school students will decrease by 10%.
Audience (who)
· Describe the intended target for the intervention
· Example: The high school student…
· Example: HIV program participants…
· Example: Employees of Google…
Behavior (what)
· Describes what a participant of a program will do
· Can also describe what will be done in an environmental of
outcome objective
· The “behavior” can include demonstration of knowledge or
skills in any of the domains of learning: cognitive,
psychomotor, affective, or interpersonal
· Example: … will write a report…
· Example: …will describe the steps…
· Example: …will list the steps…
· Cognitive domain
· Emphasizes remembering or reproducing something which has
presumably been learned
· Deal with what a learner should know, understand,
comprehend, solve, spell, critique, etc.
· Psychomotor domain
· Emphasizes some muscular motor skill, some manipulation of
material and objects, or some act that requires a neuromuscular
coordination
· Concerned with how a learner moves or controls his/her body
· Affective domain
· Composed of two different types of behaviors: reflexive
(attitudes) and voluntary reactions and actions (values)
· Stages: perception, decision, action and evaluation
· Interpersonal domain
· Emphasizes learner skills (not attitude or knowledge)
associated with interpersonal exchanges
· How a learner interacts with others in a variety of situations
Condition (when and/or where)
· Equipment or tools that may (or may not) be utilized in
completion of the behavior
· Environmental conditions may also be included
· Example: …given a pamphlet on HIV, participants will…
· Example: …after viewing an HIV video, participants will…
Degree (extent of change)
· States the standard for acceptable performance (time,
accuracy, proportion, quality, etc)
· Example: … without error.
· Example: … 50%.
· Example: …all.
Review of ABCD Objectives
· Who is to exhibit the performance?
· What observable performance will the participant exhibit?
· What conditions are provided for the participant at the time of
evaluation?
· What constitutes a minimum acceptable response?
Topic 2
Time Value of Money
Fundamentals of Finance
Fall 2017
Zhun Liu
Aug-17
1
1
Readings
Berk & DeMarzo, Chapters 3 and 4
Aug-17
2
Timeline of cash flows
Timelines
Constructing a Timeline
Identifying Dates on a Timeline
Date 0 is today, the beginning of the first year
Date 1 is the end of the first year
Aug-17
3
3
Inflows and Outflows
Timelines
Distinguishing Cash Inflows from Outflows
Representing Various Time Periods
Year? Month? Day? Hour/Second?
Just change the label, e.g.: from “Year” to “Month” if monthly
Aug-17
4
4
Combining Values
Rule 1: Comparing and Combining Values
It is only possible to compare or combine values at the same
point in time
Aug-17
5
5
Compounding
Rule 2: Compounding
To calculate a cash flow’s future value, you must compound it
Aug-17
6
6
Compounding
Rule 2: Compounding
Compound Interest
The effect of earning “interest on interest”
Aug-17
7
7
The Power of Compounding
Aug-17
8
8
Discounting
Rule 3: Discounting
To calculate the value of a future cash flow at an earlier point
in time, we must discount it.
Aug-17
9
9
Future Value
Rule 3: Discounting
If $826.45 is invested today for two years at 10% interest, the
future value will be $1000
Aug-17
10
10
Discounting Again
Rule 3: Discounting
If $1000 were three years away, the present value, if the interest
rate is 10%, will be $751.31
Aug-17
11
11
Using a Financial Calculator
Financial calculators and spreadsheets have the formulas pre-
programmed to quicken the process
There are five variables used most often:
N
PV
PMT
FV
I/Y
Aug-17
12
12
Example 1:
Present Value of a Single Future Cash Flow
Problem:
You are considering investing in a savings bond that will pay
$15,000 in 10 years.
If the competitive market interest rate is fixed at 6% per year,
what is the bond worth today?
Aug-17
13
13
Example 1:
Present Value of a Single Future Cash Flow
Aug-17
14
14
Using a financial calculator or Excel:
Given:106015,000Solve for:-8,375.92Excel Formula: =
PV(RATE,NPER, PMT, FV) = PV(0.06,10,0,15000)
Example 1:
Present Value of a Single Future Cash Flow
Aug-17
15
15
Problem:
XYZ Company expects to receive a cash flow of $2 million in
five years.
If the competitive market interest rate is fixed at 4% per year,
how much can they borrow today in order to be able to repay
the loan in its entirety with that cash flow?
Example 2:
Present Value of a Single Future Cash Flow
Aug-17
16
16
Example 2:
Present Value of a Single Future Cash Flow
Aug-17
17
17
Using a financial calculator or Excel:
Given:5402,000,000Solve for:-1,643,854.21Excel Formula: =
PV(RATE,NPER, PMT, FV) = PV(0.04,5,0,2000000)
Example 2:
Present Value of a Single Future Cash Flow
Aug-17
18
18
Problem:
You are considering investing in a savings bond that will pay
$20,000 in twenty years. If the competitive market interest rate
is fixed at 5% per year, what is the bond worth today?
Example 3:
Present Value of a Single Future Cash Flow
Aug-17
19
19
Example 3:
Present Value of a Single Future Cash Flow
Aug-17
20
20
Using a financial calculator or Excel:
Given:205020,000Solve for:-7,357.79Excel Formula: =
PV(RATE,NPER, PMT, FV) = PV(0.05,20,0,20000)
Example 3:
Present Value of a Single Future Cash Flow
Aug-17
21
21
The Three Rules of Valuing Cash Flows
Aug-17
22
22
FV of a Stream of Cash Flows
Suppose we plan to save $1,000 today, and $1,000 at the end of
each of the next two years
If we earn a fixed 10% interest rate on our savings, how much
will we have three years from today?
Aug-17
23
23
FV of a Stream of Cash Flows
We could solve the problem as follows:
Aug-17
24
24
FV of a Stream of Cash Flows
Another approach is to compute the future value in year 3 of
each cash flow separately
Once all amounts are in year 3 dollars, combine them
Aug-17
25
25
FV of a Stream of Cash Flows
Finally, the approach you should get used to in this course:
We first compute the present values of all cash flows:
We then compute the future value in year 3 of $2,735.54:
Aug-17
26
26
PV of a Stream of Cash Flows
Consider a stream of cash flows: C0 at date 0, C1 at date 1, and
so on, up to CN at date N
We compute the present value of this cash flow stream in two
steps
Aug-17
27
27
PV of a Stream of Cash Flows
First, compute the present value of each cash flow
Then combine the present values
Aug-17
28
28
Example 4:
Present Value of a Stream of Cash Flows
Problem:
You have just graduated and need money to buy a new car.
Your rich Uncle Henry will lend you the money so long as you
agree to pay him back within four years.
You offer to pay him the rate of interest that he would
otherwise get by putting his money in a savings account.
Based on your earnings and living expenses, you think you will
be able to pay him $5000 in one year, and then $8000 each year
for the next three years.
If Uncle Henry would otherwise earn 6% per year on his
savings, how much can you borrow from him?
Aug-17
29
29
Example 4:
Present Value of a Stream of Cash Flows
Aug-17
30
30
Example 4:
Present Value of a Stream of Cash Flows
Question:
Now, suppose that Uncle Henry gives you the money, and then
deposits your payments in the bank each year.
How much will he have four years from now?
If your uncle kept his $24,890.65 in the bank today earning 6%
interest, in four years he would have:
FV = $24,890.65×(1.06)4 = $31,423.87 in 4 years
Aug-17
31
31
Example 4:
Present Value of a Stream of Cash Flows
Cross Check:
If we want to compute the future value of the annual deposits,
we could compute the bank balance each year.
Crucial assumption – being able to reinvest at the same rate!!!
Aug-17
32
32
Example 5:
Present Value of a Stream of Cash Flows
Problem:
You have just graduated and need money to pay the deposit on
an apartment.
Your rich aunt will lend you the money so long as you agree to
pay her back within six months.
You offer to pay her the rate of interest that she would
otherwise get by putting her money in a savings account.
Based on your earnings and living expenses, you think you will
be able to pay her $70 next month, $85 in each of the next two
months, and then $90 each month for months 4 through 6.
If your aunt would otherwise earn 6% per year on her savings,
how much can you borrow from her?
Aug-17
33
33
Example 5:
Present Value of a Stream of Cash Flows
Aug-17
34
34
Example 5:
Present Value of a Stream of Cash Flows
Question:
Now, suppose that your aunt gives you the money, and then
deposits your payments in the bank each month.
How much will she have six months from now?
If your aunt kept her $500.90 in the bank today earning 6%
interest, in six months she would have:
FV = $500.90×(1.005)6 = $516.11 in 6 months
Aug-17
35
35
Example 5:
Present Value of a Stream of Cash Flows
Cross Check:
We could compute the future value of the monthly deposits.
One way is to compute the bank balance each month.
Aug-17
36
36
Perpetuities and Annuities
The formulas we have developed so far allow us to compute the
present or future value of any cash flow stream
Now we will consider two types of cash flow streams:
Perpetuities
Annuities
Aug-17
37
37
Perpetuities
Perpetuities
A perpetuity is a stream of equal cash flows that occur at
regular intervals and last forever
Here is the timeline for a perpetuity:
the first cash flow does not occur immediately; it arrives at the
end of the first period
Aug-17
38
38
Perpetuities
Aug-17
39
39
Perpetuities
Let’s derive a shortcut by creating our own perpetuity
Suppose you can invest $100 in a bank account paying 5%
interest per year forever
At the end of the year you’ll have $105 in the bank – your
original $100 plus $5 in interest
Suppose you withdraw the $5 and reinvest the $100 for another
year
By doing this year after year, you can withdraw $5 every year in
perpetuity:
Aug-17
40
40
Perpetuities
Aug-17
41
41
Example 6:
Endowing a Perpetuity (PV)
Problem:
You want to endow an annual graduation party at your alma
mater. You want the event to be a memorable one, so you
budget $30,000 per year forever for the party.
If the university earns 8% per year on its investments, and if the
first party is in one year’s time, how much will you need to
donate to endow the party?
Aug-17
42
42
Example 7:
Endowing a Perpetuity (PV)
Aug-17
43
43
Example 7:
Endowing a Perpetuity (cash flow)
Problem:
You just won the lottery, and you want to endow a professorship
at your alma mater.
You are willing to donate $4 million of your winnings for this
purpose.
If the university earns 5% per year on its investments, and the
professor will be receiving her first payment in one year, how
much will the endowment pay her each year?
Aug-17
44
44
Example 7:
Endowing a Perpetuity (cash flow)
Aug-17
45
45
Annuities
Annuities
An annuity is a stream of N equal cash flows paid at regular
intervals
The difference between an annuity and a perpetuity is that an
annuity ends after some fixed number of payments
Aug-17
46
46
Present Value of an Annuity
Aug-17
47
47
Example 8:
Present Value of a Lottery Prize Annuity
Problem:
You are the lucky winner of the $30 million state lottery.
You can take your prize money either as (a) 30 payments of $1
million per year (starting today), or (b) $12 million paid today.
If the interest rate is 8%, which option should you take?
What are the variables that matter?
r? Cash flow (PMT)? PV? N?
Aug-17
48
48
Solution
:
Option (a) provides $30 million in prize money but paid over
time. To evaluate it correctly, we must convert it to a present
value. Here is the timeline:
Because the first payment starts today, the last payment will
occur in 29 years (for a total of 30 payments).
The $1 million at date 0 is already stated in present value terms,
but we need to compute the present value of the remaining 29
payments.
Example 8:
Present Value of a Lottery Prize Annuity
Aug-17
49
49
Example 8:
Present Value of a Lottery Prize Annuity
Aug-17
50
50
Financial calculators or Excel can handle annuities easily—just
enter the cash flow in the annuity as the PMT:
Given:298.01,000,0000Solve for:-11,158,406Excel Formula:
=PV(RATE,NPER, PMT, FV) = PV(0.08,29,1000000,0)
Example 8:
Present Value of a Lottery Prize Annuity
Aug-17
51
51
Problem:
Ellen is 35 years old, and she has decided it is time to plan
seriously for her retirement.
At the end of each year until she is 65, she will save $10,000 in
a retirement account.
If the account earns 10% per year, how much will Ellen have
saved at age 65?
Example 9:
Future Value of a Savings Plan Annuity
Aug-17
52
52
Example 9:
Future Value of a Savings Plan Annuity
Aug-17
53
53
Alternatively, using Financial calculators or Excel:
Given:3010.00-10,000Solve for:-1,644,940Excel Formula:
=FV(RATE,NPER, PMT, PV) = FV(0.10,30,10000,0)
Example 9:
Future Value of a Savings Plan Annuity
Aug-17
54
54
Problem:
Adam is 25 years old, and he has decided it is time to plan
seriously for his retirement.
He will save $10,000 in a retirement account at the end of each
year until he is 45.
At that time, he will stop paying into the account, though he
does not plan to retire until he is 65.
If the account earns 10% per year, how much will Adam have
saved at age 65?
Example 10:
Future Value of a Savings Plan Annuity
Aug-17
55
55

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The ABCD model for writing objectivesIntroduction· Objectives .docx

  • 1. The ABCD model for writing objectives Introduction · Objectives include 4 distinct components: Audience (who), Behavior (what), Condition (when and where) and Degree (extent of change). · Objectives must be both observable and measurable to be effective. · Using words like understand and learn in writing objectives is generally not acceptable as they are difficult to measure. · Written objectives are a vital part of program development and implementation because they provide the roadmap for designing and delivering health promotion programs. Characteristics of objectives · Specific – target a specific area for improvement. · Measurable – quantify or at least suggest an indicator of progress. · Assignable – specify who will do it. · Realistic – state what results can realistically be achieved, given available resources. · Time-related – specify when the result(s) can be achieved. Samples · Learning Objective · After attending a 1-hour workshop on HIV, San Marcos high school students will list five risk factors for HIV infection, without error.
  • 2. · Behavioral Objective · Given access to free condoms in the nurse’s office, San Marcos high school students will acquire a condom from the nurse’s office, each time they have sex. · Process · HIV program coordinators will mail permission forms to all high school students’ parents prior to implementing the HIV program. · Environmental · Four prevention pamphlet stations will be available in each San Marcos high school by August 2015. · Program/Outcome · Within the next five years, the rate of HIV infection in San Marcos high school students will decrease by 10%. Audience (who) · Describe the intended target for the intervention · Example: The high school student… · Example: HIV program participants… · Example: Employees of Google… Behavior (what) · Describes what a participant of a program will do · Can also describe what will be done in an environmental of outcome objective · The “behavior” can include demonstration of knowledge or skills in any of the domains of learning: cognitive, psychomotor, affective, or interpersonal · Example: … will write a report…
  • 3. · Example: …will describe the steps… · Example: …will list the steps… · Cognitive domain · Emphasizes remembering or reproducing something which has presumably been learned · Deal with what a learner should know, understand, comprehend, solve, spell, critique, etc. · Psychomotor domain · Emphasizes some muscular motor skill, some manipulation of material and objects, or some act that requires a neuromuscular coordination · Concerned with how a learner moves or controls his/her body · Affective domain · Composed of two different types of behaviors: reflexive (attitudes) and voluntary reactions and actions (values) · Stages: perception, decision, action and evaluation · Interpersonal domain · Emphasizes learner skills (not attitude or knowledge) associated with interpersonal exchanges · How a learner interacts with others in a variety of situations Condition (when and/or where) · Equipment or tools that may (or may not) be utilized in completion of the behavior · Environmental conditions may also be included
  • 4. · Example: …given a pamphlet on HIV, participants will… · Example: …after viewing an HIV video, participants will… Degree (extent of change) · States the standard for acceptable performance (time, accuracy, proportion, quality, etc) · Example: … without error. · Example: … 50%. · Example: …all. Review of ABCD Objectives · Who is to exhibit the performance? · What observable performance will the participant exhibit? · What conditions are provided for the participant at the time of evaluation? · What constitutes a minimum acceptable response? Topic 2 Time Value of Money Fundamentals of Finance Fall 2017 Zhun Liu Aug-17 1
  • 5. 1 Readings Berk & DeMarzo, Chapters 3 and 4 Aug-17 2 Timeline of cash flows Timelines Constructing a Timeline Identifying Dates on a Timeline Date 0 is today, the beginning of the first year Date 1 is the end of the first year Aug-17 3 3 Inflows and Outflows Timelines
  • 6. Distinguishing Cash Inflows from Outflows Representing Various Time Periods Year? Month? Day? Hour/Second? Just change the label, e.g.: from “Year” to “Month” if monthly Aug-17 4 4 Combining Values Rule 1: Comparing and Combining Values It is only possible to compare or combine values at the same point in time Aug-17 5 5
  • 7. Compounding Rule 2: Compounding To calculate a cash flow’s future value, you must compound it Aug-17 6 6 Compounding Rule 2: Compounding Compound Interest The effect of earning “interest on interest” Aug-17 7 7 The Power of Compounding Aug-17
  • 8. 8 8 Discounting Rule 3: Discounting To calculate the value of a future cash flow at an earlier point in time, we must discount it. Aug-17 9 9 Future Value Rule 3: Discounting If $826.45 is invested today for two years at 10% interest, the future value will be $1000
  • 9. Aug-17 10 10 Discounting Again Rule 3: Discounting If $1000 were three years away, the present value, if the interest rate is 10%, will be $751.31 Aug-17 11 11 Using a Financial Calculator Financial calculators and spreadsheets have the formulas pre- programmed to quicken the process There are five variables used most often: N PV PMT FV I/Y Aug-17 12
  • 10. 12 Example 1: Present Value of a Single Future Cash Flow Problem: You are considering investing in a savings bond that will pay $15,000 in 10 years. If the competitive market interest rate is fixed at 6% per year, what is the bond worth today? Aug-17 13 13 Example 1: Present Value of a Single Future Cash Flow Aug-17 14
  • 11. 14 Using a financial calculator or Excel: Given:106015,000Solve for:-8,375.92Excel Formula: = PV(RATE,NPER, PMT, FV) = PV(0.06,10,0,15000) Example 1: Present Value of a Single Future Cash Flow Aug-17 15 15 Problem: XYZ Company expects to receive a cash flow of $2 million in five years. If the competitive market interest rate is fixed at 4% per year, how much can they borrow today in order to be able to repay the loan in its entirety with that cash flow? Example 2: Present Value of a Single Future Cash Flow Aug-17 16
  • 12. 16 Example 2: Present Value of a Single Future Cash Flow Aug-17 17 17 Using a financial calculator or Excel: Given:5402,000,000Solve for:-1,643,854.21Excel Formula: = PV(RATE,NPER, PMT, FV) = PV(0.04,5,0,2000000) Example 2: Present Value of a Single Future Cash Flow Aug-17 18 18
  • 13. Problem: You are considering investing in a savings bond that will pay $20,000 in twenty years. If the competitive market interest rate is fixed at 5% per year, what is the bond worth today? Example 3: Present Value of a Single Future Cash Flow Aug-17 19 19 Example 3: Present Value of a Single Future Cash Flow Aug-17 20 20 Using a financial calculator or Excel: Given:205020,000Solve for:-7,357.79Excel Formula: =
  • 14. PV(RATE,NPER, PMT, FV) = PV(0.05,20,0,20000) Example 3: Present Value of a Single Future Cash Flow Aug-17 21 21 The Three Rules of Valuing Cash Flows Aug-17 22 22 FV of a Stream of Cash Flows Suppose we plan to save $1,000 today, and $1,000 at the end of each of the next two years If we earn a fixed 10% interest rate on our savings, how much will we have three years from today? Aug-17 23
  • 15. 23 FV of a Stream of Cash Flows We could solve the problem as follows: Aug-17 24 24 FV of a Stream of Cash Flows Another approach is to compute the future value in year 3 of each cash flow separately Once all amounts are in year 3 dollars, combine them Aug-17 25 25 FV of a Stream of Cash Flows Finally, the approach you should get used to in this course: We first compute the present values of all cash flows:
  • 16. We then compute the future value in year 3 of $2,735.54: Aug-17 26 26 PV of a Stream of Cash Flows Consider a stream of cash flows: C0 at date 0, C1 at date 1, and so on, up to CN at date N We compute the present value of this cash flow stream in two steps Aug-17
  • 17. 27 27 PV of a Stream of Cash Flows First, compute the present value of each cash flow Then combine the present values Aug-17 28 28 Example 4: Present Value of a Stream of Cash Flows Problem: You have just graduated and need money to buy a new car. Your rich Uncle Henry will lend you the money so long as you agree to pay him back within four years. You offer to pay him the rate of interest that he would otherwise get by putting his money in a savings account. Based on your earnings and living expenses, you think you will
  • 18. be able to pay him $5000 in one year, and then $8000 each year for the next three years. If Uncle Henry would otherwise earn 6% per year on his savings, how much can you borrow from him? Aug-17 29 29 Example 4: Present Value of a Stream of Cash Flows Aug-17 30 30 Example 4: Present Value of a Stream of Cash Flows Question: Now, suppose that Uncle Henry gives you the money, and then deposits your payments in the bank each year. How much will he have four years from now?
  • 19. If your uncle kept his $24,890.65 in the bank today earning 6% interest, in four years he would have: FV = $24,890.65×(1.06)4 = $31,423.87 in 4 years Aug-17 31 31 Example 4: Present Value of a Stream of Cash Flows Cross Check: If we want to compute the future value of the annual deposits, we could compute the bank balance each year. Crucial assumption – being able to reinvest at the same rate!!! Aug-17 32
  • 20. 32 Example 5: Present Value of a Stream of Cash Flows Problem: You have just graduated and need money to pay the deposit on an apartment. Your rich aunt will lend you the money so long as you agree to pay her back within six months. You offer to pay her the rate of interest that she would otherwise get by putting her money in a savings account. Based on your earnings and living expenses, you think you will be able to pay her $70 next month, $85 in each of the next two months, and then $90 each month for months 4 through 6. If your aunt would otherwise earn 6% per year on her savings, how much can you borrow from her? Aug-17 33 33 Example 5: Present Value of a Stream of Cash Flows
  • 21. Aug-17 34 34 Example 5: Present Value of a Stream of Cash Flows Question: Now, suppose that your aunt gives you the money, and then deposits your payments in the bank each month. How much will she have six months from now? If your aunt kept her $500.90 in the bank today earning 6% interest, in six months she would have: FV = $500.90×(1.005)6 = $516.11 in 6 months Aug-17 35 35 Example 5: Present Value of a Stream of Cash Flows Cross Check: We could compute the future value of the monthly deposits.
  • 22. One way is to compute the bank balance each month. Aug-17 36 36 Perpetuities and Annuities The formulas we have developed so far allow us to compute the present or future value of any cash flow stream Now we will consider two types of cash flow streams: Perpetuities Annuities Aug-17 37 37 Perpetuities Perpetuities A perpetuity is a stream of equal cash flows that occur at regular intervals and last forever Here is the timeline for a perpetuity:
  • 23. the first cash flow does not occur immediately; it arrives at the end of the first period Aug-17 38 38 Perpetuities Aug-17 39 39 Perpetuities Let’s derive a shortcut by creating our own perpetuity Suppose you can invest $100 in a bank account paying 5% interest per year forever At the end of the year you’ll have $105 in the bank – your original $100 plus $5 in interest Suppose you withdraw the $5 and reinvest the $100 for another year By doing this year after year, you can withdraw $5 every year in perpetuity:
  • 24. Aug-17 40 40 Perpetuities Aug-17 41 41 Example 6: Endowing a Perpetuity (PV) Problem: You want to endow an annual graduation party at your alma mater. You want the event to be a memorable one, so you budget $30,000 per year forever for the party. If the university earns 8% per year on its investments, and if the first party is in one year’s time, how much will you need to donate to endow the party? Aug-17 42
  • 25. 42 Example 7: Endowing a Perpetuity (PV) Aug-17 43 43 Example 7: Endowing a Perpetuity (cash flow) Problem: You just won the lottery, and you want to endow a professorship at your alma mater. You are willing to donate $4 million of your winnings for this purpose. If the university earns 5% per year on its investments, and the professor will be receiving her first payment in one year, how much will the endowment pay her each year? Aug-17 44
  • 26. 44 Example 7: Endowing a Perpetuity (cash flow) Aug-17 45 45 Annuities Annuities An annuity is a stream of N equal cash flows paid at regular intervals The difference between an annuity and a perpetuity is that an annuity ends after some fixed number of payments Aug-17 46 46 Present Value of an Annuity
  • 27. Aug-17 47 47 Example 8: Present Value of a Lottery Prize Annuity Problem: You are the lucky winner of the $30 million state lottery. You can take your prize money either as (a) 30 payments of $1 million per year (starting today), or (b) $12 million paid today. If the interest rate is 8%, which option should you take? What are the variables that matter? r? Cash flow (PMT)? PV? N? Aug-17 48 48 Solution
  • 28. : Option (a) provides $30 million in prize money but paid over time. To evaluate it correctly, we must convert it to a present value. Here is the timeline: Because the first payment starts today, the last payment will occur in 29 years (for a total of 30 payments). The $1 million at date 0 is already stated in present value terms, but we need to compute the present value of the remaining 29 payments. Example 8: Present Value of a Lottery Prize Annuity Aug-17 49 49
  • 29. Example 8: Present Value of a Lottery Prize Annuity Aug-17 50 50 Financial calculators or Excel can handle annuities easily—just enter the cash flow in the annuity as the PMT: Given:298.01,000,0000Solve for:-11,158,406Excel Formula: =PV(RATE,NPER, PMT, FV) = PV(0.08,29,1000000,0) Example 8: Present Value of a Lottery Prize Annuity Aug-17 51
  • 30. 51 Problem: Ellen is 35 years old, and she has decided it is time to plan seriously for her retirement. At the end of each year until she is 65, she will save $10,000 in a retirement account. If the account earns 10% per year, how much will Ellen have saved at age 65? Example 9: Future Value of a Savings Plan Annuity Aug-17 52 52
  • 31. Example 9: Future Value of a Savings Plan Annuity Aug-17 53 53 Alternatively, using Financial calculators or Excel: Given:3010.00-10,000Solve for:-1,644,940Excel Formula: =FV(RATE,NPER, PMT, PV) = FV(0.10,30,10000,0) Example 9: Future Value of a Savings Plan Annuity Aug-17 54
  • 32. 54 Problem: Adam is 25 years old, and he has decided it is time to plan seriously for his retirement. He will save $10,000 in a retirement account at the end of each year until he is 45. At that time, he will stop paying into the account, though he does not plan to retire until he is 65. If the account earns 10% per year, how much will Adam have saved at age 65? Example 10: Future Value of a Savings Plan Annuity Aug-17 55
  • 33. 55