Present value: The current worth of a future sum of money or stream of cash flows, given a specified rate of return. Future cash flows are "discounted" at the discount rate; the higher the discount rate, the lower the present value of the future cash flows. Determining the appropriate discount rate is the key to valuing future cash flows properly, whether they be earnings or obligations.[2]
Present value of an annuity: An annuity is a series of equal payments or receipts that occur at evenly spaced intervals. Leases and rental payments are examples. The payments or receipts occur at the end of each period for an ordinary annuity while they occur at the beginning of each period for an annuity due.[3]
Present value of a perpetuity is an infinite and constant stream of identical cash flows.[4]
Compound interest (or compounding interest) is interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. Thought to have originated in 17th-century Italy, compound interest can be thought of as “interest on interest,” and will make a sum grow at a faster rate than simple interest, which is calculated only on the principal amount. The rate at which compound interest accrues depends on the frequency of compounding; the higher the number of compounding periods, the greater the compound interest. Thus, the amount of compound interest accrued on $100 compounded at 10% annually will be lower than that on $100 compounded at 5% semi-annually over the same time period.
Basic Time Value of Money Formula and Example
Depending on the exact situation in question, the TVM formula may change slightly. For example, in the case of annuity or perpetuity payments, the generalized formula has additional or less factors. But in general, the most fundamental TVM formula takes into account the following variables:
FV = Future value of money
PV = Present value of money
i = interest rate
n = number of compounding periods per year
t = number of years
Based on these variables, the formula for TVM is:
FV = PV x (1 + (i / n)) ^ (n x t)
For example, assume a sum of $10,000 is invested for one year at 10% interest. The future value of that money is:
FV = $10,000 x (1 + (10% / 1) ^ (1 x 1) = $11,000
The formula can also be rearranged to find the value of the future sum in present day dollars. For example, the value of $5,000 one year from today, compounded at 7% interest, is:
PV = $5,000 / (1 + (7% / 1) ^ (1 x 1) = $4,673
Time value of money is one of the key concept of finance. This presentation includes a basic idea about the time value of money, its significance with a practical problem
Time value of money is one of the key concept of finance. This presentation includes a basic idea about the time value of money, its significance with a practical problem
this is a lecture on time value of money which explains the topic time value of money in a very easy and simple way... it also explains some examples on the topic... plus definition of rate of return, real rate of return, inflation premium, nominal interest rate,market risk, maturity risk,liquidity risk,and default risk,
https://rb.gy/n89u77
Discuss the role of time value in finance, the use of computational tools, and the basic patterns of cash flow. Understand the concepts of future value and present value, their calculation for single amounts, and the relationship between them.
Drop Shipping in the Q-Commerce Era, A case study of Daraz. pk | Project by F...FaHaD .H. NooR
Drop Shipping in the Q-Commerce Era, A case study of Daraz. pk | Project by FAHAD HASSAN NOOR under observation by Mustafa Hannan Mehboob | UCP University Of Central PUNJAB
The research project considered dropshipping in the Q-commerce era in our national setting as
Pakistan's E-commerce industry is evolving, and the supply chain structure of Daraz.pk is
exactly the phenomenon to be studied. The article acknowledges that more entrepreneurs are
turning to dropship, which is market-driven and a way for entrepreneurs with little cash to set
into an e-commerce business. The importance of dropshipping as an instrument that dismantles
retailers from stock and warehouse concerns is emphasized here. The effort is shifted to
marketing and customer acquisition. This research will be about analyzing what Q-commerce –
assumed to be a non-conforming model that conforms to modern consumers’ demands of
instant service– has done to the economies and the dynamics in Pakistan.
Operations Management A-Z: Business Processes and Systems | Fahad Hassan NoorFaHaD .H. NooR
This certificate above verifies that Fahad Hassan Noor successfully completed the course Operations Management A-Z: Business Processes and Systems on 05/12/2022 as taught by Laurence Gartside, Rowtons Training on Udemy. The certificate indicates the entire course was completed as validated by the student. The course duration represents the total video hours of the course at time of most recent completion.
This certificate above verifies that Fahad Hassan Noor successfully completed the course Supply Chain Management A-Z: Operations & Logistics Basics on 01/16/2022 as taught by Laurence Gartside, Rowtons Training on Udemy. The certificate indicates the entire course was completed as validated by the student. The course duration represents the total video hours of the course at time of most recent completion.
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This certificate above verifies that Fahad Hassan Noor successfully completed the course Supply Chain Management A-Z: Operations & Logistics Basics on 01/16/2022 as taught by Laurence Gartside MEng Cantab on Udemy. The certificate indicates the entire course was completed as validated by the student. The course duration represents the total video hours of the course at time of most recent completion.
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While many firms are part of supply chain not all are managed in any truly coordinated fashion.
Many firms within supply chain wants to work independently.
Firms with large system inventories, many suppliers, complex product assemblies and highly valued customers benefit most from the practice of supply chain management.
For these firms, even moderate supply chain management success can mean lower purchasing and inventory carrying costs, better product quality and higher levels of customer service—all leading to more sales.
Creating and Managing Supplier RelationshipsFaHaD .H. NooR
Companies require their suppliers to deliver innovative and quality products not only in just-in-time (JIT) fashion, but also at a competitive price.
Good supplier relations can provide many benefits such as flexibility in terms of delivery, better quality, better information, and better material flows between buyers and suppliers.
Selecting the right supply partners and successfully managing these relationships over time is thus strategically important; it is often stated that “a firm is only as good as its suppliers.”
Purchasing departments contributes in product design, quality, cost of goods sold, manufacturing cycle time.
Ethical and Sustainable sourcing practices have become area of concern over the past five to ten years.
Global population growth, increasing environmental awareness, consumers desires for better corporate responsibility, and declining worldwide levels of natural resources has pressured companies to effectively implement these practices.
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Accomplish this as economically as possible, within acceptable standards of quality and service.
“Purchasing profession can be defined as the act of obtaining merchandise; equipment; raw materials; services; or maintenance, repair and operating (MRO) supplies in exchange for money or its equivalent”.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
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This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
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Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
2. Types of Annuities
• An Annuity represents a series of equal payments
(or receipts) occurring over a specified number of
periods.
• Ordinary Annuity: Payments or receipts occur at
the end of each period.
• For example, straight bonds usually pay coupon payments at the end
of every six months until the bond's maturity date.
• Annuity Due: Payments or receipts occur at the
beginning of each period.
• Rent is an example of annuity due. You are usually required to
pay rent when you first move in at the beginning of the month,
and then on the first of each month thereafter.
4. Parts of an Annuity
• (Ordinary Annuity)
• End of Period 1 End of period 2 End of period 3
0 1 2 3
0 100 100 100
Today
Equal cash flow. each 1
period apart
5. Parts of an Annuity
• (Annuity Due)
• Start of Period 1 Start of period 2 Start of period3
0 1 2 3
100 100 100
Today
Equal cashflow each 1
period apart
6. FVAn = R(1+i)n-1 + R(1+i)n-2 + =R[(1+i)n -1]/i
... + R(1+i)1 + R(1+i)0
Overview of an
Ordinary Annuity -- FVA
R R R
0 1 2 n n+1
FVAn
R = Periodic
Cash Flow
Cash flows occur at the end of the period
i% . . .
7. Example Ordinary Annuity =FVA
• If you are receiving $1000 a year for three years. Lets
further assume that you deposit each annual receipt in
saving account earning 7% interest rate. How much money
you have at the end of 3 years?
8. FVA3 = $1,000(1.07)2 +
$1,000(1.07)1 + $1,000(1.07)0
= $1,145 + $1,070 + $1,000
= $3,215
Example of an
Ordinary Annuity -- FVA
$1,000 $1,000 $1,000
0 1 2 3 4
$3,215 = FVA3
7%
$1,070
$1,145
Cash flows occur at the end of the period
9. Example
• Explanation
• Money received at the end of year 1 can further be
invested for two more years @ the rate of 7% which will
be $1145.
• Money received at the end of year 2 can further be
invested for one more year @ the rate of 7% which will be
$1070.
• And at the end of year 3, $1000 will be received which
cant invested further because that’s the last year and
maturity period is over.
10. PVAn = R/(1+i)1 + R/(1+i)2
+ ... + R/(1+i)n
Overview of an
Ordinary Annuity -- PVA
R R R
0 1 2 n n+1
PVAn
R = Periodic
Cash Flow
i% . . .
Cash flows occur at the end of the period
11. PVA3 = $1,000/(1.07)1 +
$1,000/(1.07)2 +
$1,000/(1.07)3
= $934.58 + $873.44 + $816.30
= $2,624.32
Example of an
Ordinary Annuity -- PVA
$1,000 $1,000 $1,000
0 1 2 3 4
$2,624.32 = PVA3
7%
$ 934.58
$ 873.44
$ 816.30
Cash flows occur at the end of the period
12. Hint
• The future value of an ordinary annuity can be
viewed as occurring at the end of the last cash flow.
• The present value of an ordinary annuity can be
viewed as occurring at the beginning of the first cash
flow period.
13. FVADn = R(1+i)n + R(1+i)n-1 +
... + R(1+i)2 + R(1+i)1
= FVAn (1+i)
Overview View of an
Annuity Due -- FVAD
R R R R R
0 1 2 3 n-1 n
FVADn
i% . . .
Cash flows occur at the beginning of the period
14. FVAD3 = $1,000(1.07)3 +
$1,000(1.07)2 + $1,000(1.07)1
= $1,225 + $1,145 + $1,070
= $3,440
Example of an
Annuity Due -- FVAD
$1,000 $1,000 $1,000 $1,070
0 1 2 3 4
$3,440 = FVAD3
7%
$1,225
$1,145
Cash flows occur at the beginning of the period
15. PVAn = R/(1+i)1 + R/(1+i)2
+ ... + R/(1+i)n
Overview of an
Ordinary Annuity -- PVAD
R R R
0 1 2 n n+1
PVAn
R = Periodic
Cash Flow
i% . . .
Cash flows occur at the end of the period
16. PVADn = $1,000/(1.07)0 + $1,000/(1.07)1 +
$1,000/(1.07)2 = $2,808.02
Example of an
Annuity Due -- PVAD
$1,000.00 $1,000 $1,000
0 1 2 3 4
$2,808.02 = PVADn
7%
$ 934.58
$ 873.44
Cash flows occur at the beginning of the period
17. HINT
• future value of an annuity due can be viewed as occurring
at the beginning of the last cash flow period.
• the present value of an annuity due can be viewed as
occurring at the end of the first cash flow period.
18. 1. Read problem thoroughly
2. Determine if it is a PV or FV problem
3. Create a time line
4. Put cash flows and arrows on time line
5. Determine if solution involves a single
CF, annuity stream(s), or mixed flow
6. Solve the problem
Steps to Solve Time Value of
Money Problems
19. Julie Miller will receive the set of cash flows
below. What is the Present Value at a
discount rate of 10%?
Mixed Flows Example
0 1 2 3 4 5
$600 $600 $400 $400 $100
PV0
10%
20. 1. Solve a “piece-at-a-time” by
discounting each piece back to t=0.
2. Solve a “group-at-a-time” by first
breaking problem into groups of annuity
streams and any single cash flow group.
Then discount each group back to t=0.
How to Solve?
22. Frequency of Compounding
General Formula:
FVn = PV0(1 + [i/m])mn
n: Number of Years
m: Compounding Periods per Year
i: Annual Interest Rate
FVn,m: FV at the end of Year n
PV0: PV of the Cash Flow today
23. Impact of Frequency
Julie Miller has $1,000 to invest for 2 years at an
annual interest rate of 12%.
Annual FV2 = 1,000(1+ [.12/1])(1)(2)
= 1,254.40
Semi FV2 = 1,000(1+ [.12/2])(2)(2)
= 1,262.48
Qrtly FV2 = 1,000(1+ [.12/4])(4)(2)
= 1,266.77
Monthly FV2 = 1,000(1+ [.12/12])(12)(2)
= 1,269.73
Daily FV2 = 1,000(1+[.12/365])(365)(2)
= 1,271.20
24. PV of compounding periods
• PV0 = FVn /(1 + [i/m])mn
Qrtly PV4 = 1266.77/(1+ [.12/4])(4)(2)
=1000
25. Effective Annual
Interest Rate
Effective Annual Interest Rate
The actual rate of interest earned (paid) after
adjusting the stated (nominal) for factors such as
the number of compounding periods per year.
• EAR is the rate compounded annually that provides
the same annual interest rate as nominal rate if it is
compounded annually.
1+EAR= =(1 + [ i / m ] )m (n)
• EAR=(1 + [ i / m ] )m(n) - 1
26. Example
Basket Wonders (BW) has a $1,000 at the bank. The
interest rate is 6% compounded quarterly for 1 year.
What is the Effective Annual Interest Rate (EAR)?
EAR = ( 1 + 6% / 4 )4(1) - 1
= 1.0614 - 1 = .0614 or 6.14%!