TVOM LECTURE
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Arizona State University *
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Course
300
Subject
Finance
Date
Apr 25, 2024
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6
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FIN 300 TVOM: Time Value of Money The value of any asset (investment) is determined by: 1) Return –
the benefit from investing current income vs. capital gains income 2) Time –
how long you will have to wait to receive the return 3) Risk –
the chance that you will not receive the expected return Valuation areas: 1) Future Value of a Lump Sum (a single deposit) FVIF: Future Value Interest Factor Present Value ------------------> Future Value “compounding over time”
You invest $3000 into an account earning 5%. After 5 years, what has the account grown to? FV = PV (FVIF) = $3000 (FVIF 5%, 5 = 1.276) =$3828 If you leave the $3000 in the account for 10 years, what would the account grow to? FV = PV (FVIF) = $3000 (FVIF 5%, 10 = 1.629) = $4,887 The “Rule of 72” shows how long it would take to double your money 72 = Number of years needed to Int. Rate double your money 72 = Annual interest rate earned # of years
You invest $5000 at 8%, how long will it take to double your money? 72 = 9 years 8 If your investment doubled in 6 years, what annual interest rate were you earning? 72 = 12% 6 2) Future Value of an Annuity
an annuity is a series of equal payments (or benefits) made at equal time intervals
Annuity due-payment is made at the beginning of the period
Ordinary (or regular) annuity-
payment is made at the end of the period
FVIFA: Future Value Interest Factor of an Annuity You invest $5000 annually into your Roth IRA which is earning 8% annually. After 35 years, what is the balance of your IRA? FV = annuity (FVIFA) = 5000(FVIFA 8%, 35 = 172.31) = $861,550 What if you could earn 9% over the 40 years instead of 8%, what would your IRA balance be?
FV = annuity (FVIFA) = $5000(FVIFA 9%, 40 = 337.87) = $1,689,350 Any assumptions being made here? 3) Sinking Fund (FVIFA)
Deposits that are needed to accumulate a future amount
You are planning on retiring in 40 years and would like to save an additional $2,500,000 in addition to your retirement savings. How much will you need to save annually-
earning 8% interest-in order to reach your goal? FV = sinking fund annuity
FVIFA 2,500,000 = $9651 (FVIFA 8%,40=259.05)
If you could earn 10% interest (instead of 8%), how much would you need to save annually? 2,500,000
= $5649 (FVIFA 10%,40=442.58) In 30 years, you would like to establish a charitable foundation worth $1,000,000. If you plan to invest in the stock market-hopefully earning an average of 10% annually-how much would you have to deposit yearly in order to accumulate the $1,000,000? 1,000,000 = $6079
(FVIFA10%,30=164.49)
4) Present Value of a Lump Sum
What is a future benefit worth to you today?
PVIF: Present Value Interest Factor Present Value <--------------------Future Value Discounting over time You have just won a $2,000,000 court settlement which will be paid to you in 10 years. In other words, you won’t receive anything until the end of the tenth year. Assuming 7% interest, what is your settlement worth to you today? PV = FV (PVIF) = $2,000,000(PVIF 7%,10=.508) = $1,016,000 Assuming 9% interest instead of 7%, what is your settlement worth today? PV = FV (PVIF)
= 2,000,000(PVIF 9%,10=.422) = $844,000
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Related Questions
Match the terms to the description
Time Value of Money (TVM)
Discounting
Present Value (PV)
Future Value (FV)
Cash Flow (CF)
✓ [Choose ]
value of money at some later time
funds in a secure investment will increase to an equivalent future amount
the potential lost benefit when choosing one alternative over another
transferring money into our out of an account
calculating the present value of future cash flow stream
value of money right now
[Choose ]
[Choose ]
[Choose ]
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4. Present value
Finding a present value is the reverse of finding a future value.
A. is the process of calculating the present value of a cash flow or a series of cash flows to be received in the future.
B. Which of the following investments that pay will $17,500 in 8 years will have a lower price today?
The security that earns an interest rate of 4.00%.
The security that earns an interest rate of 6.00%.
C. Eric wants to invest in government securities that promise to pay $1,000 at maturity. The opportunity cost (interest rate) of holding the security is 5.40%. Assuming that both investments have equal risk and Eric’s investment time horizon is flexible, which of the following investment options will exhibit the lower price?
An investment that matures in four years
An investment that matures in five years
D. Which of the following is true about present value calculations?
Other things remaining equal, the…
arrow_forward
4. Present value
Finding a present value is the reverse of finding a future value.
A. is the process of calculating the present value of a cash flow or a series of cash flows to be received in the future.
B. Which of the following investments that pay will $17,500 in 8 years will have a lower price today?
The security that earns an interest rate of 4.00%.
The security that earns an interest rate of 6.00%.
C. Eric wants to invest in government securities that promise to pay $1,000 at maturity. The opportunity cost (interest rate) of holding the security is 5.40%. Assuming that both investments have equal risk and Eric’s investment time horizon is flexible, which of the following investment options will exhibit the lower price?
An investment that matures in four years
An investment that matures in five years
D. Which of the following is true about present value calculations?
Other things remaining equal, the…
arrow_forward
3. Future value
The principal of the time value of money is probably the single most important concept in financial management. One of the most frequently
encountered applications involves the calculation of a future value.
The process for converting present values into future values is called
four time-value-of-money variables. Which of the following is not one of these variables?
The trend between the present and future values of an investment
The duration of the deposit (N)
The interest rate (t) that could be earned by deposited funds
The present value (PV) of the amount deposited
This process requires knowledge of the values of three of
4
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Value UI T IUF WHich PW(1)c
PW (1)p?
10.
Investments A and B have the net cash flows given.
End of year
1
4.
$ 75
$ 75
$150
А
-$250
-$250
$175
$ 75
$150
$ 75
В
$150
Compare the present worth of A with the present worth of B for an in-
terest rate of 5%. Which has the higher value? Answer: A
If the interest rate is 15%, which has the higher value? Answer: B
а.
b.
On the same axis, graph the present worth of each investment as a func-
tion of the interest rate.
с.
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What do you understand by the present value of money?
Group of answer choices
A. Amount borrowed or deposited
B. Maximum that can be deposited
C. Sum of deposit and interest
D. Another name for the future
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Asset M
Asset N
j
P??
Return, ??
P??
Return, ??
1
0.25
10%
0.15
10%
2
0.25
-6%
0.30
8%
3
0.15
2%
0.20
15%
4
0.20
5%
0.05
0%
5
0.15
20%
0.30
-2%
Calculate the expected value of return, ?̅, for each of the two assets. Which provides the largest expected return?
Calculate the standard deviation, ?? , for each of the two assets’ returns. Which appears to have the greatest risk?
Calculate the portfolio expected return if you invest 27% of your wealth in M and 73% inN, of your total wealth of $40,000.
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Tasks/ calculation these questions are :-
by 6 functions are :
1. Accumulative (future) money value 1/ Simple interest FV=PV*(1+* ? *N) 2/ Aggregate interest FV=PV (1+ ? )N
2. Present money value PV = FV * ^note N- total times of getting income^ R= ?????? ??? / N n- frequency of income generation per year
3. Present payment value PV = PMT *
4. Future payment value (PMT) FV = PMT *
5. Amortization payment PMT = PV *
6. Solatium fond factor (SFF) PMT = FV *
Q1/ The investor wants to invest in the purchase of an office building. He suggests he can rent it out for 10 years at an annual rent of 1,850,000. At the end of the tenth year it is expected to sell the company for 18 million d.e. Income rate 20% What is the current value of the building?
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Question 12
Which of the following methods does not adjust for the time value of money:
A internal rate of return
B net present value
C profitability index
D payback period
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A. Assume that the variables I, N, and PV represent the interest rate, investment or deposit period, and present value of the amount deposited or invested, respectively. Which equation best represents the calculation of a future value (FV) using:
Compound interest?
FV = (1 + I)NN / PV
FV = PV / (1 + I)NN
FV = PV x (1 + I)NN
B. Simple interest?
FV = PV + (PV x I x N)
FV = PV - (PV x I x N)
FV = PV / (PV x I x N)
C. Identify whether the following statements about the simple and compound interest methods are true or false.
Statement
True
False
After the end of the second year and all other factors remaining equal, a future value based on compound interest will never exceed the future value based on simple interest.
All other variables held constant, investments paying simple interest have to pay significantly higher interest rates to earn the same amount of interest as an account earning compound…
arrow_forward
Which figure of merit provides an interest rate at which the present value of the future cash flows equals the amount invested?
a) NPV
b) IRR
c) Cap Rate
d) DCF
Please ensure accuracy and explain your choice
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Rate of interest = 10%
Present its feasibility using 1. Rate or Return Method 2. Annual Worth Method 3. Present Worth Method 4. Future Worth Method 5. Payback Method All method should be presented with the cash flow diagram
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Question # 4
A Report a Problem
GRevisit
Choose the best option
Indicates the current value of future cash flow over a fixed period of time at a
O Present value
specified rate of return.
O Future value
O Compounded value
O Cash value
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+918047190917 I
metti •
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2. Future value
The principal of the time value of money is probably the single most important concept in financial management. One of the most frequently encountered applications involves the calculation of a future value.
The process for converting present values into future values is called . This process requires knowledge of the values of three of four time-value-of-money variables. Which of the following is not one of these variables?
The interest rate (I) that could be earned by deposited funds
The trend between the present and future values of an investment
The duration of the deposit (N)
The present value (PV) of the amount deposited
All other things being equal, the numerical difference between a present and a future value corresponds to the amount of interest earned during the deposit or investment period. Each line on the following graph corresponds to an interest rate: 0%, 9%, or 17%. Identify the interest rate that corresponds…
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Determine the ERR (External rate of return) of the cash flows if external rate (e) is given as %12.
Cash
Flow
Year
0
1
2
3
4
5
6
7
Select one:
a.0.228861
b.0.204146
c.0.245007
d.0.274516
e.0.181262
f.0.168017
g.0.19667
h.0.264278
-5000
2000
4000
-1500
3000
4000
-6000
9000
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Single Cash Flow
Future Value
Inputs
Single Cash Flow
Discount Rate/Period
747.25
6.00%
Number of Periods
Future Value using a Time Line
Period
2
3
4
Cash Flows
Future Value of Each Cash Flow
Future Value
Future Value using the Formula
Future Value
Future Value using the FV Function
Future Value
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Q2: Uneven Cash Flow Stream:
Year
Cash Stream A
Cash Stream B
1
100
400
300
2
400
3
400
400
4
300
400
300
100
a) Find the PV of the following cash flow streams. The interest rate is 8 percent. (Hint:
use multiple steps method as done in class)
b. What is the present value of each cash flow stream (A and B) at a 0 per cent interest
rate?
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Consider the following timeline:
Date
0
i +
$500
2
OA. $666.
B. $605.
C. $500.
OD. $650.
3
Cash
flow
If the current market rate of interest is 10%, then the future value of the cash flows on this timeline is closest to:
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2. Present value
Aa Aa
Finding a present value is the reverse of finding a future value.
Which of the following is true about finding the present value of cash flows?
O Finding the present value of cash flows tells you what a cash flow will be worth in future years at a specified
rate of return.
O Finding the present value of cash flows tells you how much you need to invest today so that it grows to a
given future amount at a specified rate of return.
Which of the following investments that pay will $13,500 in 13 years will have a higher price today?
The security that earns an interest rate of 7.00%.
The security that earns an interest rate of 10.50%.
Eric wants to invest in government securities that promise to pay $1,000 at maturity. The opportunity cost (interest
rate) of holding the security is 12.40%. Assuming that both investments have equal risk and Eric's investment time
horizon is flexible, which of the following investment options will exhibit the lower price?
O An investment…
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1. 1: Time Value of Money: Introduction
A dollar in hand today is worth -Select- ✓a dollar to be received in the future because if you had it now you could invest that dollar and Select-
interest. Of all the techniques used in finance, none is more important than the concept of time value of money (TVM), also called
-Select-
analysis. Time value analysis has many applications including retirement planning, stock and bond valuation, loan amortization
and capital budgeting analysis. Time value of money uses the concept of compound interest rather than simple interest.
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Classify the type of financial formula for the information given.
Lump-Sum Problems
P
A
known
unknown
O future value
O present value
O ordinary annuity
O amortization
O sinking fund
Need Help?
Read It
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Chapter 10 Homework Questions
1. Explain why money has a time value.
2. What is the difference between simple interest and compound interest?
3. Explain the Rule of 72.
4. What is the meaning of present value (PV)?
5. What do we mean by internal rate of return (IRR)
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Consider the following cash flows and interest rates:
0
r = 2.5%
1
r = 1.5%
5,000
2
r = 1.9%
5,000
3
r = 2.4%
5,000
a. Calculate the present value of these cash flows (at time 0).
b. Calculate the future value of these cash flows (at time 4).
4
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Select all of the time value of money factors that are known in a NPV assessment.
O Present value of single-sums
O Present value of annuities
O Interest rate
Number of periods
O Future value of single-sums
O Future value of annuities
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Consider the following timeline:
Date
Cash
flow
0
?
1
OA. $472
B. $944
C. $600
D. $614
$100
2
$200
3
$300
If the current market rate of interest is 11%, then the present value (PV) of this timeline as of year 0 is
closest to:
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,Match the following terms with the appropriate definition.Effective yield or interest rateMonetary liabilityCompound interestPresent ValueFuture value of a single amountA.Fixed obligation to pay an amount in cash.B.The rate at which money will actually grow.C.Interest accumulates on interest.D.Current worth of future cash flows.E.The money to which an amount invested will grow over time.
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Related Questions
- Match the terms to the description Time Value of Money (TVM) Discounting Present Value (PV) Future Value (FV) Cash Flow (CF) ✓ [Choose ] value of money at some later time funds in a secure investment will increase to an equivalent future amount the potential lost benefit when choosing one alternative over another transferring money into our out of an account calculating the present value of future cash flow stream value of money right now [Choose ] [Choose ] [Choose ]arrow_forward4. Present value Finding a present value is the reverse of finding a future value. A. is the process of calculating the present value of a cash flow or a series of cash flows to be received in the future. B. Which of the following investments that pay will $17,500 in 8 years will have a lower price today? The security that earns an interest rate of 4.00%. The security that earns an interest rate of 6.00%. C. Eric wants to invest in government securities that promise to pay $1,000 at maturity. The opportunity cost (interest rate) of holding the security is 5.40%. Assuming that both investments have equal risk and Eric’s investment time horizon is flexible, which of the following investment options will exhibit the lower price? An investment that matures in four years An investment that matures in five years D. Which of the following is true about present value calculations? Other things remaining equal, the…arrow_forward4. Present value Finding a present value is the reverse of finding a future value. A. is the process of calculating the present value of a cash flow or a series of cash flows to be received in the future. B. Which of the following investments that pay will $17,500 in 8 years will have a lower price today? The security that earns an interest rate of 4.00%. The security that earns an interest rate of 6.00%. C. Eric wants to invest in government securities that promise to pay $1,000 at maturity. The opportunity cost (interest rate) of holding the security is 5.40%. Assuming that both investments have equal risk and Eric’s investment time horizon is flexible, which of the following investment options will exhibit the lower price? An investment that matures in four years An investment that matures in five years D. Which of the following is true about present value calculations? Other things remaining equal, the…arrow_forward
- 3. Future value The principal of the time value of money is probably the single most important concept in financial management. One of the most frequently encountered applications involves the calculation of a future value. The process for converting present values into future values is called four time-value-of-money variables. Which of the following is not one of these variables? The trend between the present and future values of an investment The duration of the deposit (N) The interest rate (t) that could be earned by deposited funds The present value (PV) of the amount deposited This process requires knowledge of the values of three of 4arrow_forwardValue UI T IUF WHich PW(1)c PW (1)p? 10. Investments A and B have the net cash flows given. End of year 1 4. $ 75 $ 75 $150 А -$250 -$250 $175 $ 75 $150 $ 75 В $150 Compare the present worth of A with the present worth of B for an in- terest rate of 5%. Which has the higher value? Answer: A If the interest rate is 15%, which has the higher value? Answer: B а. b. On the same axis, graph the present worth of each investment as a func- tion of the interest rate. с.arrow_forwardWhat do you understand by the present value of money? Group of answer choices A. Amount borrowed or deposited B. Maximum that can be deposited C. Sum of deposit and interest D. Another name for the futurearrow_forward
- Asset M Asset N j P?? Return, ?? P?? Return, ?? 1 0.25 10% 0.15 10% 2 0.25 -6% 0.30 8% 3 0.15 2% 0.20 15% 4 0.20 5% 0.05 0% 5 0.15 20% 0.30 -2% Calculate the expected value of return, ?̅, for each of the two assets. Which provides the largest expected return? Calculate the standard deviation, ?? , for each of the two assets’ returns. Which appears to have the greatest risk? Calculate the portfolio expected return if you invest 27% of your wealth in M and 73% inN, of your total wealth of $40,000.arrow_forwardTasks/ calculation these questions are :- by 6 functions are : 1. Accumulative (future) money value 1/ Simple interest FV=PV*(1+* ? *N) 2/ Aggregate interest FV=PV (1+ ? )N 2. Present money value PV = FV * ^note N- total times of getting income^ R= ?????? ??? / N n- frequency of income generation per year 3. Present payment value PV = PMT * 4. Future payment value (PMT) FV = PMT * 5. Amortization payment PMT = PV * 6. Solatium fond factor (SFF) PMT = FV * Q1/ The investor wants to invest in the purchase of an office building. He suggests he can rent it out for 10 years at an annual rent of 1,850,000. At the end of the tenth year it is expected to sell the company for 18 million d.e. Income rate 20% What is the current value of the building?arrow_forwardQuestion 12 Which of the following methods does not adjust for the time value of money: A internal rate of return B net present value C profitability index D payback periodarrow_forward
- A. Assume that the variables I, N, and PV represent the interest rate, investment or deposit period, and present value of the amount deposited or invested, respectively. Which equation best represents the calculation of a future value (FV) using: Compound interest? FV = (1 + I)NN / PV FV = PV / (1 + I)NN FV = PV x (1 + I)NN B. Simple interest? FV = PV + (PV x I x N) FV = PV - (PV x I x N) FV = PV / (PV x I x N) C. Identify whether the following statements about the simple and compound interest methods are true or false. Statement True False After the end of the second year and all other factors remaining equal, a future value based on compound interest will never exceed the future value based on simple interest. All other variables held constant, investments paying simple interest have to pay significantly higher interest rates to earn the same amount of interest as an account earning compound…arrow_forwardWhich figure of merit provides an interest rate at which the present value of the future cash flows equals the amount invested? a) NPV b) IRR c) Cap Rate d) DCF Please ensure accuracy and explain your choicearrow_forwardRate of interest = 10% Present its feasibility using 1. Rate or Return Method 2. Annual Worth Method 3. Present Worth Method 4. Future Worth Method 5. Payback Method All method should be presented with the cash flow diagramarrow_forward
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