Section 1: Module 3: Introduction To The Time Value Of Money

Front 1

The Importance of Time Value of Money

Back 1

Allows you to translate goals into $ amounts.

Allows you to know $ input required to achieve future results

Front 2

Five Basic Time Value of Money Factors

Back 2

PV -Present Value

FV - Future Value

PMT - Payment

I/YR - Interest

N- Number of periods

Front 3

Solving TVM problems

How to begin the problem - Set-Up Table

Back 3

N I/YR PV PMT FV
Number Interest Present Payment Future
Periods Rate Value Value
Per Year

Front 4

Set up the table for the following question...

A client wants to invest $10,000 for 5 years. If the investment grows @ 8% per year, how much will the investment be worth in 5 years?

Back 4

N I/YR PV PMT FV
5 8% $10,000 NA ???



Answer = $14,693.28

Front 5

Chapter 1: Fundamental Calculator Keystrokes

Common Calculator Mistakes

Back 5

Clearing display but not memory registers

Using default number of compounding periods

Using the wrong payment mode - Beginning vs End

Entering a rounded number

Front 6

Helpful hints with HP 10BII

Back 6

PV = Beginning Value (Lump Sum)

FV = Ending value

N = Number of compounding periods (not always years)

I/Yr = Interest rate per year with HP 10bII - NOT interest rate per compounding period

PMT = Payment - amount being put in repeatedly

Front 7

Using Negative Numbers in the calculator

Back 7

Whenever 2 dollar amounts entered into the calculator one of the numbers must be a negative.

Value representing an outflow would be negative number - Deposits, investments, payments.

Front 8

Capitalization of a number

Desired income $30,000 with 6% interest rate. What amount of capital would give you $30,000/year @ 6%.

Back 8

$30,000 / .06 = $500,000

A person with $500,000 earning 6% interest per year could withdrawal $30,000 / year indefinitely.

Front 9

Future Value of a Single Sum - Yearly Compounding

$1,000 deposited at 8% interest compounded annually for three years, What is the future value?

Back 9

Easiest of TVM calculations

n=3
I=8
PV= -1,000
pmt = NA
FV = Answer = 1,259.712

Front 10

Future Value of a Single Sum - Semiannually Compounded

$1,000 deposited at 8% annual interest compounded semiannually for 5 years, What is the future value?

Back 10

Ensure number of compounding periods per year is accurate. 2 periods per yer.

n=10 (Total number of compounding periods. 5 years * semiannual = 10)
I=8
PV=-1,000
PMT = NA
FV = Answer = 1,480.24

Front 11

Present Value of A Single Sum - Annual compounding

An individual will receive $1,000 in 3 years. How much is that worth today if the opportunity cost on investments is 8% annually?

Back 11

AKA discounting

3 known variables = Future value, discount rate, number of discounting periods

N=3
I=8
PV= answer = $793.83
PMT=NA
FV=1,000

Front 12

Present Value of Lump Sum - Frequent Compounding

An individual will receive $1,000 in 5 years and has an opportunity cost of 8% annual interest, compounded monthly. What is the value of the sum today?

Back 12

Ensure the discounting periods per year is set to 12

N = 60 = 5 years * 12 months
I=8
PV = Answer = $671.21
PMT=NA
FV=1,000

Front 13

Number of Compounding periods - Annual Compounding

An individual has $1,000 to invest. He wants to accumulate $3,760 . He can earn 8% annual interest on investments. How many years will it take to attain his goal?

Back 13

N=????
I=8%
PV=$1,000
PMT=NA
FV=$3,670

Answer N=16.89

Front 14

Number of Compounding Periods - More Frequent compounding

An individual has $1,000 to invest in an account earning an annual rate of 8% compounded semiannually. He wants to have a total fund balance of $3,670. How many years will it take to achieve his goal?

Back 14

N= ???
I=8
PV=1,000
PMT=NA
FV=3,670

Set P/YR=2

n=33.15

n= number of compounding periods not the number of years. Semiannual = 2 x's per year.

33.15 / 2 = 16.57 years

Front 15

Solve for interest rate

An individual has $1,000 to invest. He wants to accumulate $1,470 in five years. What annual interest rate must be earned for him to accomplish this goal?

Back 15

N=5
I=???
PV=1,000
PMT=NA
FV=1,470

I=8.01%

Front 16

Interest Rate - More frequent compounding

An individual invests $1,000 and wants to accumulate $1,470 in five years. Earnings on this investment are compounded quarterly. What annual rate of earnings are required?

Back 16

N=5*4=20
P/YR = 4
I=???
PV=1,000
PMT=NA
FV=1,470

I=7.78%

Front 17

Rule of 72

An Individual invests $1,000 @ 8%, compounded annually. He wants to double his investment to $2,000. How long will it take?

An individual invests $1,000 for 10 years. Want interest rate will it take to double that investment?

Back 17

Provides guideline for determining how long it will take an investment to double in value.

or

Determine the rate of return required for an investment to double.

To calculate number of years required for an investment to double i value, 72 / annual interest rate.

72 / 8 = 9 years to double in value

To calculate interest rate required to double, divide 72 by number of years.

72 / 10 = 7.2%

Front 18

Rule of 116

Back 18

Just like Rule of 72 but instead of doubling 116 is how long it will take to triple.

Investment earning 8% will take 14.5 years to triple

116 / 8 = 14.5

Front 19

Present Value of an Annuity

Ordinary annuity vs annuity due

Back 19

A stream of equal periodic payments occurring at uniform intervals is known as an equity.

Ordinary Annuity (OA): Ordinary annuity payment made at the end of each period, in arrears.

On Calculator set BEG/END function to END

Ex: Mortgage payments, auto note payments, quarterly dividends, semiannual interest payments

Annuity Due (AD): Payments or receipts made at beginning of each period, in advance.

On Calculator set BEG/END function to BEG

Ex: Insurance policy premiums and lease payments.

Front 20

Present Value of an annuity

An individual expects to receive payment of $1,000 at the end of each of the next 3 years. If opportunity costs are 8% annually, what is the annuity worth today?

Stated differently

What amount would be required to be deposited today (PV) to insure payments of $1,000 at the end of each year for the next three years?

Answer will be present value of ordinary annuity PVOA

Back 20

n=3
I=8
P/YR=1
PV=???
PMT=1000
FV=NA

Ensure calculator programmed to calculate for ordinary annuity. Beginning/End function should be on End.

PV = 2,577.10

Front 21

Present Value of an annuity

An individual expects to receive payment of $1,000 at the end of each of the next 3 years. If opportunity costs are 8% annually, what is the annuity worth today?

Stated differently

What amount would be required to be deposited today (PV) to insure payments of $1,000 at the beginning of each year for the next three years?

Answer will be present value of annuity Due PVAD

Back 21

n=3
I=8
P/YR=1
PV=???
PMT=1000
FV=NA

Ensure calculator programmed to calculate for annuity Due. Beginning/End function should be on BEG

PV = 2,783.26

Front 22

Future Value of Annuity

An individual invests $1,000 at the beginning of each of the next three years (FVAD - FV annuity Due). He can earn 8% annual return on investments. What will be the value of the investment in three years?

Back 22

Used to determine how much money can be accumulated for a financial objective, such as retirement fund or college fund, if a fixed rate of return is assumed for uniform periodic payments.

N=3
I=8
PV=NA
PMT=1,000
FV=???

Set BEG/END function to BEG

FV = $3,506.11

Front 23

Annuities - More frequent compounding

Individual Invests $500 at end of each 6 month period over the next 3 years. He can earn annual rate of 8%, compounded semiannually. What will the the value be in three years?

Back 23

FVOA - Set BEG/END function to END

SET P/YR to 2

N=3*2=6
I=8
PV=NA
PMT=500

FV = $3,316.49
FV=???

Front 24

Periodic Payment or Receipt

An individual wants to purchase a car for $10,000 can finance the purchase at 12% compounded annually for four years.

Back 24

How to determine periodic payment or receipt when given, PV or FV, Interest rate, number of compounding periods.

Determine payment needed to attain a retirement or education goal.

N= 4
I= 12
PV=$10,000
PMT=???
FV= NA

PMT = - $3,292.34

Front 25

Periodic Payment - More frequent Compounding

#1) Individual borrows $10,000 to finance purchase of a car. Loan to be repaid over 4 years @ 12% annual interest compounded monthly. What will be the monthly payment?

Back 25

1) Set P/YR = 12 ,

Set to calculate ordinary annuity - Set to END

N=48
I=12
PV= 10,000
PMT=???
FV=NA

PMT = - $263.34 / month

Front 26

Periodic Payment / Receipt - More Frequent Compounding

# 2

An individual wants to accumulate $10,000 in 4 years for child's education. He can earn 12% annual interest compounded monthly. Individual wants to invest a periodic amount at the beginning of each month over the next four years to attain his goal. What is required payment each month?

Back 26

2)

Set P/YR = 12
Set to calculate annuity due = BEG

N=48
I=12
PV=NA
PMT=???
FV=10,000

PMT = -$161.72 / month

Front 27

Keeping some of the money at the END of the Annuitization period

Barb has $250,000 and wants to receive monthly payments over 20 years. She can earn 6% on investments and wants to have $25,000 remaining at the end of the 20 years. Monthly Compounding

Back 27

Set P/YR = 12

N=20*12= 240
I=6
PV= - 250,000
PMT=???
FV=25,000

Be sure to use PV as negative.

PMT = $1,736.97

Front 28

Chapter 3: Intermediate Time Value of Money Calculations

Serial Payments

Back 28

As apposed to fixed annuity which payment is constant. Serial payments increase over time. Helps annuitant maintain purchasing power.

Front 29

Present Value of a Serial Payment

Client wants to receive equivalent of $10,000 in today's dollars at the beginning of each year for the next 4 years. Inflation will average 5% and he can earn 8% compound annual return. Wants to invest a lump sum today and dissipate the fund entirely at the beginning of the fourth year, when last payment is received.

Back 29

Present value of serial payment computed by compounding the periodic payment at the inflation rate and then discounting the payment for the return on investments.

Exhibit 1 page 41.

1) Find $10,000 adjusted for inflation in each year.

2) Discount each year's inflated number to the present value.

Front 30

Inflation-adjusted Interest Rate

Expected Inflation Rate: 5%

Expected Rate of Return: 8%

Back 30

Cannot use the difference in inflation and Interest rate, must use inflation adjust rate of return calculation.

[(1+Interest/1+inflation)-1]*100= inflation adjusted interest rate

[(1.08/1.05)-1]*100= 2.8571%

Front 31

Using Inflation adjusted Interest Rate
Client wants to receive equivalent of $10,000 in today's dollars at the beginning of each year for the next 4 years. Inflation will average 5% and he can earn 8% compound annual return. Wants to invest a lump sum today and dissipate the fund entirely at the beginning of the fourth year, when last payment is received.

Back 31

Inflation-adjusted interest rate = 2.8571%

Set to annuity Due = BEG

n=4
i= 2.8571% Be careful with rounding this number
PV=????
PMT=10,000
FV=Na

PV = 38,363.98

Front 32

College Funding Example

One years college tuition is $10,000 today; inflation is 6%, and rate of return is 8%. Mary is three years old and will begin four-year college program at age 18. Calculate the present value of what is needed to fund her college.

Back 32

page: 44

Front 33

Calculations with Unequal Cash Flows

Rules for using Calculator

Back 33

1 - Cash Flows to investor = positive number
Cash Outflows from investor = negative number

2 - 1st start by finding compounding period, period of time between two consecutive cash flows.

3 - Cash Flow or zero must be entered for every compounding period

4 - IRR calculated may me average compound return for one period N, which is same length of time between two consecutive cash flows. If period N not a year then IRR must be adjusted to annual basis.

5 - Equal consecutive cash flows can be input together

6 - First cash outflow, usually a purchase, called Cash Flow 0 (CF0) Occurs at N = 0

7 - If PV being calculated CF0 must be zero

Front 34

Calculating Internal Rate of Return

What is the average compound rate of return that has been earned from investing in a antique chair that was purchased 6 years ago for $300, repaired at end of 2nd year, and just sold for $850?

Back 34

-300 CFi
0 CFi
-150 CFi
0 CFi
0 CFi
0 CFi
850 CFi
Gold, IRR/YR

IRR or Compound rate of return = 12.54%

Front 35

Calculating IRR

- using calculator "short hand" for cash flows

What is the average compound rate of return that has been earned from investing in a antique chair that was purchased 6 years ago for $300, repaired at end of 2nd year, and just sold for $850?

Back 35

Do have to enter equal consecutive cash flows individually.

- 300 CFi
0 CFi
-150 CFi
0 CFi
3 Gold Ni
850 CFi
Gold, IRR/YR

IRR = 12.54

Front 36

IRR problem #2

What is the IRR earned on a 3 year investment in a mutual fund that pays the following quarterly distributions: 4 distributions @ $50, 4 @ $57, 4 @ $60. Distributions were not reinvested back into the fund. Initial investment into fund was $12,000, final value of the mutual fund at time of last quarterly distribution $16,500.

Back 36

(4, gold, P/YR)
-12,000 CFi
50 CFi
4 gold, Ni
57 CFi
4 gold, Ni
60 CFI
3 gold, Ni
$16,560 CFi
gold, IRR/YR

IRR = 12.36%

Front 37

Calculating Present value and Net Present Value of Unequal cash flows.

Back 37

Capital projects and long-term investments can be evaluated by discounting future cash flows at a given discount rate to determine their total present value.

Difference between total present value of cash flows and amount of initial outlay or cost = Net present value, NPV.

Present value of cash flows - Cost = NPV

Positive NPV = investment earns return greater than discount rate (required rate of return).

Negative NPV = earn less than the discount rate

Front 38

Net Present Value problem 1

Real estate property being offered for $100,000 expected to have cash flows of $6,000, $7,000, $8,000 over each year over three years. At end of 3 years expected to have value of $115,000.

If investor has Required rate of return of 10%, what is present value and net present value of the property?

Back 38

0 CFi
6,000CFi
7,000CFi
123,000CFi
10 I/YR
gold, NPV

PV = $103,651

103,651 - 100,000 = $3,651 NPV

Since NPV is positive, IRR is higher than the discount rate.

IRR calculation

-100,000 CFi
6,000 CFi
7,000 CFi
123,000 CFi
Gold, IRR/YR

IRR = 11.40% vs. Discount rate of 10%

Front 39

NPV problem #2

What is the present value of an investment for which the following cash flows are expected, client's required rate of return is 10.5%?

end of Year 1, +10
end of Year 2, -50
end of Year 3, -50
end of Year 4, -50
end of Year 5, 0
end of Year 6, +30

Back 39

0 CFi
100 CFi
-50 CFi
3 gold, Ni
0 CFi
300 CFi
10.5 I/Yr
gold, NPV

Present Value that will allow a 10.5% return on the investment is $143.75.

If you invested $143.75 today and received the cash flows as indicated you would achieve a 10.5% return.

If you invest more than $143.75 you will receive return less than 10.5%.

Invest less than $143.75, return will be more than 10.5%.

Front 40

Squares, Square Roots, and Nth Roots

What is product of 4.5 squared? 4.5^2?

What is square root of 20.25?

What is the Fifth root of 100?

Back 40

Set your calculator to 4 decimals.

4.50, gold, x^2 = 20.25

20.25, gold, √x = 4.5

5√100 = 100^1/5 = 100^0.2

- express the problem with fractional exponent (1/5)

- change the exponent into a decimal (1/5) = .2

- use y^x key

100, gold, y^x, 0.2 = 2.5119

Front 41

Amortization

Back 41

Process of liquidating a debt by making installment payments. Divides payments into the amount that applies to interest and principal.

2 calculations -

1 - Calculate periodic payment
2 - interest and principal amounts

Front 42

Amortization problem

Ted and Mary Bigelow planning to purchase $300,000 home, by making 20% down payment, and financing remainder with 30-year, 7.25% fixed-rate mortgage.

What will monthly payment be?

How much principal and interest will be paid by end of 1st year. (12 months)

Back 42

Step 1 - Calculate monthly payments

gold, P/YR = 12

PV = 240,000 (300,000-20%)
N=360 (30 years*12 annual payments)
I = 7.25%
PMT = ???

Payment = $1,637.22

Step 2 - Determine interest and principal payments

1, INPUT, 12, gold AMORT, Equals, ( = cycles through interest, principal, balance)

Principle = 2,322.86
Interest = 17,323.82
Balance = 237,677.14