Accounting and the Time Value of Money
After studying this chapter, you should be able to:
Describe the fundamental concepts related to the time value of money.
Solve future and present value of 1 problems.
Solve future value of ordinary and annuity due problems.
Solve present value of ordinary and annuity due problems.
Solve present value problems related to deferred annuities, bonds, and expected cash flows.
Statement of Financial Position and Statement of Cash Flowsreskino1
Statement of Financial Position and Statement of Cash Flows
After studying this chapter, you should be able to:
Explain the uses, limitations, and content of the statement of financial position.
Prepare a classified statement of financial position.
Explain the purpose, content, and preparation of the statement of cash flows.
Describe additional types of information provided.
This modelling guide looks at how to model key aspects of a loan – including a choice of debt repayment profiles (level debt service vs level principal).
The accompanying spreadsheet includes a presentation sheet that shows the main features of the loan.
Statement of Financial Position and Statement of Cash Flowsreskino1
Statement of Financial Position and Statement of Cash Flows
After studying this chapter, you should be able to:
Explain the uses, limitations, and content of the statement of financial position.
Prepare a classified statement of financial position.
Explain the purpose, content, and preparation of the statement of cash flows.
Describe additional types of information provided.
This modelling guide looks at how to model key aspects of a loan – including a choice of debt repayment profiles (level debt service vs level principal).
The accompanying spreadsheet includes a presentation sheet that shows the main features of the loan.
Chapter 14:
Describe the nature of bonds and indicate the accounting for bond issuances.
Explain the accounting for long-term notes payable.
Explain the accounting for the extinguishment of non-current liabilities.
Indicate how to present and analyze non-current liabilities.
Non-current liabilities (long-term debt) consist of an expected outflow of resources arising from present obligations that are not payable within a year or the operating cycle of the company, whichever is longer.
The presentation highlights some shortcut formulas that can speed up PV computations if a project have a particular set of cash flow patterns and the opportunity cost of capital is constant
Income Statement and Related Information
LEARNING OBJECTIVES
After studying this chapter, you should be able to:
Identify the uses and limitations of an income statement.
Describe the content and format of the income statement.
Discuss how to report various income items.
Explain the reporting of accounting changes and errors.
Describe related equity statements.
Chapter 14:
Describe the nature of bonds and indicate the accounting for bond issuances.
Explain the accounting for long-term notes payable.
Explain the accounting for the extinguishment of non-current liabilities.
Indicate how to present and analyze non-current liabilities.
Non-current liabilities (long-term debt) consist of an expected outflow of resources arising from present obligations that are not payable within a year or the operating cycle of the company, whichever is longer.
The presentation highlights some shortcut formulas that can speed up PV computations if a project have a particular set of cash flow patterns and the opportunity cost of capital is constant
Income Statement and Related Information
LEARNING OBJECTIVES
After studying this chapter, you should be able to:
Identify the uses and limitations of an income statement.
Describe the content and format of the income statement.
Discuss how to report various income items.
Explain the reporting of accounting changes and errors.
Describe related equity statements.
Learning Objectives
After studying this chapter, you should be able to:
[1] Indicate the benefits of budgeting.
[2] Distinguish between simple and compound interest.
[2] Identify the variables fundamental to solving present value problems.
[3] Solve for present value of a single amount.
[4] Solve for present value of an annuity.
[5] Compute the present value of notes and bonds.
Accounting for Pensions and Postretirement Benefitsreskino1
After studying this chapter, you should be able to:
Discuss the fundamentals of pension plan accounting.
Use a worksheet for employer’s pension plan entries.
Explain the accounting for past service costs.
Explain the accounting for remeasurements.
Describe the requirements for reporting pension plans in financial statements.
Explain the accounting for other postretirement benefits.
Current Liabilities, Provisions, and Contingenciesreskino1
Current Liabilities,
Provisions, and Contingencies
After studying this chapter, you should be able to:
1. Describe the nature, valuation, and reporting of current liabilities.
2. Explain the accounting for different types of provisions.
3. Explain the accounting for loss and gain contingencies.
4. Indicate how to present and analyze liability-related information
After studying this chapter, you should be able to:
1. Discuss the characteristics, valuation, and amortization of intangible assets.
2. Describe the accounting for various types of intangible assets.
3. Explain the accounting issues for recording goodwill.
4. Identify impairment procedures and presentation requirements for intangible assets.
5. Describe the accounting and presentation for research and development and similar costs.
Describe depreciation concepts and methods of depreciation.
Identify other depreciation issues.
Explain the accounting issues related to asset impairment.
Discuss the accounting procedures for depletion of mineral resources.
Apply the accounting for revaluations.
Demonstrate how to report and analyze property, plant, equipment, and mineral resources.
Acquisition and Disposition of Property, Plant, and Equipmentreskino1
Identify property, plant, and equipment and its related costs.
Discuss the accounting problems associated with interest capitalization.
Explain accounting issues related to acquiring and valuing plant assets.
Describe the accounting treatment for costs subsequent to acquisition.
Describe the accounting treatment for the disposal of property, plant, and equipment.
Describe and apply the lower-of-cost-or-net realizable value rule.
Identify other inventory valuation issues.
Determine ending inventory by applying the gross profit method.
Determine ending inventory by applying the retail inventory method.
Explain how to report and analyze inventory.
Valuation of Inventories: A Cost-Basis Approachreskino1
Describe inventory classifications and different inventory systems.
Identify the goods and costs included in inventory.
Compare the cost flow assumptions used to account for inventories.
Determine the effects of inventory errors on the financial statements.
This study aims to examine the tendency of fraud to the perception of
external auditors triggered by the five components of pentagon fraud:
pressure, opportunity, arrogance, rationalization,and competence. In
addition, the morality of the individual is placed as an intervention
variable for this relationship. This is a quantitative study with a survey
of external auditors at the BPK in Jakarta. The intervention model for
the research framework was developed to investigate the role of
individual morality interference. The findings suggest that the five
components of the pentagon's fraud theory are not fully proven to be
fraud triggers in the perception of external auditors. Arrogance,
rationalization, and competence have proven to have a positive effect
on the perception of fraud tendencies, while pressure and opportunity
have a negative impact on the perception of fraud tendencies. Then
pressure, rationalization, and competence are shown to negatively
impact individual morality, while opportunity and arrogance positively
impact individual morality. In addition, 5 (five) variables in fraud
pentagon theory, namely pressure, opportunity, arrogance,
rationalization, and competence, are proven to prevent the perception of
fraud tendency. This can be explained because this study is the first
study to examine pentagon fraud in the context of behavior in the
environment of government external auditors, so the results cannot be
compared with previous studies that used proxies in financial
statements as predictors of fraud.
The Accounting Information System
LEARNING OBJECTIVES
After studying this chapter, you should be able to:
Describe the basic accounting information system.
Record and summarize basic transactions.
Identify and prepare adjusting entries.
Prepare financial statements from the adjusted trial balance and prepare closing entries.
Prepare financial statements for a merchandising company.
Conceptual Framework for Financial Reportingreskino1
LEARNING OBJECTIVES
After studying this chapter, you should be able to:
Describe the usefulness of a conceptual framework and the objective of financial reporting.
Identify the qualitative characteristics of accounting information and the basic elements of financial statements.
Review the basic assumptions of accounting.
Explain the application of the basic principles of accounting.
Intermediate Accounting Chapter 1 about Financial Reporting
and Accounting Standards
After studying this chapter, you should be able to:
Describe the growing importance of global financial markets and its relation to financial reporting.
Explain the objective of financial reporting.
Identify the major policy-setting bodies and their role in the standard-setting process.
Discuss the challenges facing financial reporting.
PERAN PEMODERASI KUALITAS AUDIT ATAS PENGARUH PERENCANAAN PAJAK DAN PAJAK TAN...reskino1
The purpose of this study is to examine the impact of tax planning and deferred tax assets on earnings management in manufacturing companies listed on the Indonesia Stock Exchange from 2016 to 2018.
Pengaruh Organizational Justice Dan Religiosity Terhadap Employee Fraud Denga...reskino1
This study aims to examine the influence of organizational justice and religiosity on employee fraud mediated by whistleblowing intention. This study uses primary data by distributing questionnaires to employees who work in Islamic banks in the DKI Jakarta area. Sampling was done using the purposive sampling method. This study used sample of 71 respondents. The data analysis method that used as Partial Least Square (PLS)-SEM with the help of data analysis tool SmartPLS 3.0. The results of this study indicate that religiosity shows significant effect on whistleblowing intentions. Organizational justice unable to contribute significantly to whistleblowing intention. Whistleblowing intention have a significant effect on employee fraud. Organizational justice and religiosity unable to contribute significantly to the employee fraud. Furthermore, religiosity significantly influence on employee fraud through whistleblowing intentions. Organizational justice unable to contribute significantly to employee fraud through whistleblowing intentions.
STUDY OF FRAUD TENDENCY: THE ROLE OF UNETHICAL BEHAVIORS AS MEDIATIONreskino1
Islamic banking and Islamic insurance are institutions that are trusted by the public that play an important role in the economy that should uphold Islamic values. But in fact, there are still many cases of fraud that occur in Islamic banking and Islamic insurance. This study aims to examine the determinant factor fraud tendency with the role of unethical behavior as mediation. The sample used is the financial staff of Islamic banking and Islamic insurance in DKI Jakarta as many as 118 respondents. The data analysis method used in this research is Partial Least Square (PLS-SEM). The results of this study indicate that the implementation of good corporate governance (GCG) practice has a significant effect on unethical behavior, but conformity compensation does not have a significant effect on unethical behavior. Conformity compensation, implementation of GCG practice, and unethical behavior has a significant effect on the fraud tendency. Furthermore, the implementation of GCG practice has a significant effect on fraud tendency through unethical behavior, but conformity compensation has no significant effect on fraud tendency through unethical behavior.
MODEL PENDETEKSIAN KECURANGAN LAPORAN KEUANGAN DENGAN ANALISIS FRAUD TRIANGLEreskino1
The research purposes is to create a model to detect financial statement fraud. This research examines the variable of fraud triangle and auditor industry specialization with financial statement fraud.
Samples were 30 companies of fraud and 30 non-fraud companies that
were listed on the Indonesia Stock Exchange (IDX) and sanctioned by the Financial Services Authority (FSA). The result shows the financial targets can be detect financial statement fraud, while financial stability can’t be detect financial statement fraud.
ISLAMIC WORK ETHICS AND ORGANIZATIONAL JUSTICE IMPLEMENTATION IN REACHING ACC...reskino1
The topic of business ethics from Islamic perspective has become important for business currently. This paper investigates the influence of Islamic work ethics on organizational justice and its impact on accountants’ job satisfaction. A total of 202 accountants participated in this study from the Islamic finance industry in Indonesia. The analysis uses the AMOS 21 program as a tool to solve structural equation modeling problems. The results show that Islamic work ethics positively influence the two dimensions of organizational justice, which are procedural and interactive justice, but not on distributive justice. Moreover, all dimensions of organizational justice and Islamic work ethics were found to positively influence job satisfaction.
Currently pi network is not tradable on binance or any other exchange because we are still in the enclosed mainnet.
Right now the only way to sell pi coins is by trading with a verified merchant.
What is a pi merchant?
A pi merchant is someone verified by pi network team and allowed to barter pi coins for goods and services.
Since pi network is not doing any pre-sale The only way exchanges like binance/huobi or crypto whales can get pi is by buying from miners. And a merchant stands in between the exchanges and the miners.
I will leave the telegram contact of my personal pi merchant. I and my friends has traded more than 6000pi coins successfully
Tele-gram
@Pi_vendor_247
US Economic Outlook - Being Decided - M Capital Group August 2021.pdfpchutichetpong
The U.S. economy is continuing its impressive recovery from the COVID-19 pandemic and not slowing down despite re-occurring bumps. The U.S. savings rate reached its highest ever recorded level at 34% in April 2020 and Americans seem ready to spend. The sectors that had been hurt the most by the pandemic specifically reduced consumer spending, like retail, leisure, hospitality, and travel, are now experiencing massive growth in revenue and job openings.
Could this growth lead to a “Roaring Twenties”? As quickly as the U.S. economy contracted, experiencing a 9.1% drop in economic output relative to the business cycle in Q2 2020, the largest in recorded history, it has rebounded beyond expectations. This surprising growth seems to be fueled by the U.S. government’s aggressive fiscal and monetary policies, and an increase in consumer spending as mobility restrictions are lifted. Unemployment rates between June 2020 and June 2021 decreased by 5.2%, while the demand for labor is increasing, coupled with increasing wages to incentivize Americans to rejoin the labor force. Schools and businesses are expected to fully reopen soon. In parallel, vaccination rates across the country and the world continue to rise, with full vaccination rates of 50% and 14.8% respectively.
However, it is not completely smooth sailing from here. According to M Capital Group, the main risks that threaten the continued growth of the U.S. economy are inflation, unsettled trade relations, and another wave of Covid-19 mutations that could shut down the world again. Have we learned from the past year of COVID-19 and adapted our economy accordingly?
“In order for the U.S. economy to continue growing, whether there is another wave or not, the U.S. needs to focus on diversifying supply chains, supporting business investment, and maintaining consumer spending,” says Grace Feeley, a research analyst at M Capital Group.
While the economic indicators are positive, the risks are coming closer to manifesting and threatening such growth. The new variants spreading throughout the world, Delta, Lambda, and Gamma, are vaccine-resistant and muddy the predictions made about the economy and health of the country. These variants bring back the feeling of uncertainty that has wreaked havoc not only on the stock market but the mindset of people around the world. MCG provides unique insight on how to mitigate these risks to possibly ensure a bright economic future.
The European Unemployment Puzzle: implications from population agingGRAPE
We study the link between the evolving age structure of the working population and unemployment. We build a large new Keynesian OLG model with a realistic age structure, labor market frictions, sticky prices, and aggregate shocks. Once calibrated to the European economy, we quantify the extent to which demographic changes over the last three decades have contributed to the decline of the unemployment rate. Our findings yield important implications for the future evolution of unemployment given the anticipated further aging of the working population in Europe. We also quantify the implications for optimal monetary policy: lowering inflation volatility becomes less costly in terms of GDP and unemployment volatility, which hints that optimal monetary policy may be more hawkish in an aging society. Finally, our results also propose a partial reversal of the European-US unemployment puzzle due to the fact that the share of young workers is expected to remain robust in the US.
how to swap pi coins to foreign currency withdrawable.DOT TECH
As of my last update, Pi is still in the testing phase and is not tradable on any exchanges.
However, Pi Network has announced plans to launch its Testnet and Mainnet in the future, which may include listing Pi on exchanges.
The current method for selling pi coins involves exchanging them with a pi vendor who purchases pi coins for investment reasons.
If you want to sell your pi coins, reach out to a pi vendor and sell them to anyone looking to sell pi coins from any country around the globe.
Below is the contact information for my personal pi vendor.
Telegram: @Pi_vendor_247
how can i use my minded pi coins I need some funds.DOT TECH
If you are interested in selling your pi coins, i have a verified pi merchant, who buys pi coins and resell them to exchanges looking forward to hold till mainnet launch.
Because the core team has announced that pi network will not be doing any pre-sale. The only way exchanges like huobi, bitmart and hotbit can get pi is by buying from miners.
Now a merchant stands in between these exchanges and the miners. As a link to make transactions smooth. Because right now in the enclosed mainnet you can't sell pi coins your self. You need the help of a merchant,
i will leave the telegram contact of my personal pi merchant below. 👇 I and my friends has traded more than 3000pi coins with him successfully.
@Pi_vendor_247
how can I sell pi coins after successfully completing KYCDOT TECH
Pi coins is not launched yet in any exchange 💱 this means it's not swappable, the current pi displaying on coin market cap is the iou version of pi. And you can learn all about that on my previous post.
RIGHT NOW THE ONLY WAY you can sell pi coins is through verified pi merchants. A pi merchant is someone who buys pi coins and resell them to exchanges and crypto whales. Looking forward to hold massive quantities of pi coins before the mainnet launch.
This is because pi network is not doing any pre-sale or ico offerings, the only way to get my coins is from buying from miners. So a merchant facilitates the transactions between the miners and these exchanges holding pi.
I and my friends has sold more than 6000 pi coins successfully with this method. I will be happy to share the contact of my personal pi merchant. The one i trade with, if you have your own merchant you can trade with them. For those who are new.
Message: @Pi_vendor_247 on telegram.
I wouldn't advise you selling all percentage of the pi coins. Leave at least a before so its a win win during open mainnet. Have a nice day pioneers ♥️
#kyc #mainnet #picoins #pi #sellpi #piwallet
#pinetwork
Turin Startup Ecosystem 2024 - Ricerca sulle Startup e il Sistema dell'Innov...Quotidiano Piemontese
Turin Startup Ecosystem 2024
Una ricerca de il Club degli Investitori, in collaborazione con ToTeM Torino Tech Map e con il supporto della ESCP Business School e di Growth Capital
how to sell pi coins in South Korea profitably.DOT TECH
Yes. You can sell your pi network coins in South Korea or any other country, by finding a verified pi merchant
What is a verified pi merchant?
Since pi network is not launched yet on any exchange, the only way you can sell pi coins is by selling to a verified pi merchant, and this is because pi network is not launched yet on any exchange and no pre-sale or ico offerings Is done on pi.
Since there is no pre-sale, the only way exchanges can get pi is by buying from miners. So a pi merchant facilitates these transactions by acting as a bridge for both transactions.
How can i find a pi vendor/merchant?
Well for those who haven't traded with a pi merchant or who don't already have one. I will leave the telegram id of my personal pi merchant who i trade pi with.
Tele gram: @Pi_vendor_247
#pi #sell #nigeria #pinetwork #picoins #sellpi #Nigerian #tradepi #pinetworkcoins #sellmypi
The secret way to sell pi coins effortlessly.DOT TECH
Well as we all know pi isn't launched yet. But you can still sell your pi coins effortlessly because some whales in China are interested in holding massive pi coins. And they are willing to pay good money for it. If you are interested in selling I will leave a contact for you. Just telegram this number below. I sold about 3000 pi coins to him and he paid me immediately.
Telegram: @Pi_vendor_247
BYD SWOT Analysis and In-Depth Insights 2024.pptxmikemetalprod
Indepth analysis of the BYD 2024
BYD (Build Your Dreams) is a Chinese automaker and battery manufacturer that has snowballed over the past two decades to become a significant player in electric vehicles and global clean energy technology.
This SWOT analysis examines BYD's strengths, weaknesses, opportunities, and threats as it competes in the fast-changing automotive and energy storage industries.
Founded in 1995 and headquartered in Shenzhen, BYD started as a battery company before expanding into automobiles in the early 2000s.
Initially manufacturing gasoline-powered vehicles, BYD focused on plug-in hybrid and fully electric vehicles, leveraging its expertise in battery technology.
Today, BYD is the world’s largest electric vehicle manufacturer, delivering over 1.2 million electric cars globally. The company also produces electric buses, trucks, forklifts, and rail transit.
On the energy side, BYD is a major supplier of rechargeable batteries for cell phones, laptops, electric vehicles, and energy storage systems.
how to sell pi coins effectively (from 50 - 100k pi)DOT TECH
Anywhere in the world, including Africa, America, and Europe, you can sell Pi Network Coins online and receive cash through online payment options.
Pi has not yet been launched on any exchange because we are currently using the confined Mainnet. The planned launch date for Pi is June 28, 2026.
Reselling to investors who want to hold until the mainnet launch in 2026 is currently the sole way to sell.
Consequently, right now. All you need to do is select the right pi network provider.
Who is a pi merchant?
An individual who buys coins from miners on the pi network and resells them to investors hoping to hang onto them until the mainnet is launched is known as a pi merchant.
debuts.
I'll provide you the Telegram username
@Pi_vendor_247
2. 6-2
1. Describe the fundamental
concepts related to the time
value of money.
2. Solve future and present value
of 1 problems.
3. Solve future value of ordinary
and annuity due problems.
4. Solve present value of
ordinary and annuity due
problems.
5. Solve present value
problems related to deferred
annuities, bonds, and
expected cash flows.
After studying this chapter, you should be able to:
Accounting and the
Time Value of Money
CHAPTER 6
LEARNING OBJECTIVES
4. 6-4
Basic Time
Value Concepts
A relationship between time and money.
A dollar received today is worth more than a dollar
promised at some time in the future.
Time Value of Money
When deciding among investment or borrowing
alternatives, it is essential to be able to compare
today’s dollar and tomorrow’s dollar on the same
footing—to “compare apples to apples.”
LO 1
LEARNING OBJECTIVE 1
Describe the fundamental
concepts r elated to the time
value of money.
5. 6-5
1. Notes
2. Leases
3. Pensions and Other
Postretirement
Benefits
4. Non-Current Assets
Applications of Time Value Concepts:
5. Shared-Based
Compensation
6. Business Combinations
7. Disclosures
8. Environmental Liabilities
Basic Time Value Concepts
LO 1
6. 6-6
Payment for the use of money.
Excess cash received or repaid over the amount lent or
borrowed (principal).
The Nature of Interest
LO 1
Basic Time Value Concepts
Variables in Interest Computation
1. Principal. The amount borrowed or invested.
2. Interest Rate. A percentage of the outstanding principal.
3. Time. The number of years or fractional portion of a year that the
principal is outstanding.
7. 6-7
Interest computed on the principal only.
Simple Interest
Illustration: Barstow Electric Inc. borrows $10,000 for 3 years at
a simple interest rate of 8% per year. Compute the total interest
to be paid for 1 year.
Interest = p x i x n
= $10,000 x .08 x 1
= $800
Annual
Interest
LO 1
Basic Time Value Concepts
8. 6-8
Interest computed on the principal only.
Simple Interest
Illustration: Barstow Electric Inc. borrows $10,000 for 3 years at
a simple interest rate of 8% per year. Compute the total interest
to be paid for 3 years.
Interest = p x i x n
= $10,000 x .08 x 3
= $2,400
Total
Interest
LO 1
Basic Time Value Concepts
9. 6-9
Simple Interest
Interest = p x i x n
= $10,000 x .08 x 3/12
= $200
Interest computed on the principal only.
Illustration: If Barstow borrows $10,000 for 3 months at a 8%
per year, the interest is computed as follows.
Partial
Year
LO 1
Basic Time Value Concepts
10. 6-10
Compound Interest
Computes interest on
► principal and
► interest earned that has not been paid or
withdrawn.
Typical interest computation applied in business
situations.
LO 1
Basic Time Value Concepts
11. 6-11
Illustration: Tomalczyk Company deposits $10,000 in the Last National
Bank, where it will earn simple interest of 9% per year. It deposits another
$10,000 in the First State Bank, where it will earn compound interest of 9%
per year compounded annually. In both cases, Tomalczyk will not
withdraw any interest until 3 years from the date of deposit.
Year 1 $10,000.00 x 9% $ 900.00 $ 10,900.00
Year 2 $10,900.00 x 9% $ 981.00 $ 11,881.00
Year 3 $11,881.00 x 9% $1,069.29 $ 12,950.29
ILLUSTRATION 6.1
Simple vs. Compound Interest
Compound Interest
LO 1
12. 6-12
Table 6.1 - Future Value of 1
Table 6.2 - Present Value of 1
Table 6.3 - Future Value of an Ordinary Annuity of 1
Table 6.4 - Present Value of an Ordinary Annuity of 1
Table 6.5 - Present Value of an Annuity Due of 1
Compound Interest Tables
Number of Periods = number of years x the number of compounding
periods per year.
Compounding Period Interest Rate = annual rate divided by the number
of compounding periods per year.
LO 1
Basic Time Value Concepts
13. 6-13
How much principal plus interest a dollar accumulates to at the end of
each of five periods, at three different rates of compound interest.
ILLUSTRATION 6.2
Excerpt from Table 6.1
Compound Interest Tables
LO 1
Basic Time Value Concepts
14. 6-14
Formula to determine the future value factor (FVF) for 1:
Where:
Compound Interest Tables
FVFn,i = future value factor for n periods at i interest
n = number of periods
i = rate of interest for a single period
LO 1
Basic Time Value Concepts
15. 6-15
To illustrate the use of interest tables to calculate compound
amounts, Illustration 6.3 shows the future value to which 1
accumulates assuming an interest rate of 9%.
ILLUSTRATION 6.3
Accumulation of Compound Amounts
Compound Interest Tables
LO 1
Basic Time Value Concepts
*Note that these amounts appear in Table 6.1 in the 5% column.
16. 6-16
Number of years X number of compounding periods per year =
Number of periods
ILLUSTRATION 6.4
Frequency of Compounding
Compound Interest Tables
LO 1
Basic Time Value Concepts
17. 6-17
A 9% annual interest compounded daily provides a 9.42% yield.
Effective Yield for a $10,000 investment.
ILLUSTRATION 6.5
Comparison of Different Compounding Periods
Compound Interest Tables
LO 1
Basic Time Value Concepts
18. 6-18
Rate of Interest
Number of Time Periods
Fundamental Variables
ILLUSTRATION 6.6
Basic Time Diagram
Future Value
Present Value
LO 1
Basic Time Value Concepts
19. 6-19
Single-Sum Problems
Unknown Future Value
Two Categories
Unknown Present Value
LO 2
LEARNING OBJECTIVE 2
Solve future and present value
of 1 problems.
ILLUSTRATION 6.6
Basic Time Diagram
20. 6-20
Value at a future date of a given amount invested, assuming
compound interest.
FV = future value
PV = present value (principal or single sum)
= future value factor for n periods at i interest
FVFn,i
Where:
Future Value of a Single Sum
LO 2
Single-Sum Problems
21. 6-21
Future Value of a Single Sum
Illustration: Bruegger AG wants to determine the future value
of €50,000 invested for 5 years compounded annually at an
interest rate of 6%.
= €66,912
ILLUSTRATION 6.7
Future Value Time
Diagram (n = 5, i = 6%)
LO 2
22. 6-22
What table do
we use?
Alternate
Calculation
ILLUSTRATION 6.7
Future Value Time
Diagram (n = 5, i = 11%)
LO 2
Future Value of a Single Sum
Illustration: Bruegger AG wants to determine the future value
of €50,000 invested for 5 years compounded annually at an
interest rate of 6%.
23. 6-23
What factor do we use?
€50,000
Present Value Factor Future Value
x 1.33823 = €66,912
Future Value of a Single Sum Alternate
Calculation
LO 2
TABLE 6.1 FUTURE VALUE OF 1 (FUTURE VALUE OF A SINGLE SUM) i=6%
n=5
24. 6-24
Illustration: Shanghai Electric Power (CHN) deposited
¥250 million in an escrow account with Industrial and Commercial
Bank of China (CHN) at the beginning of 2019 as a commitment
toward a power plant to be completed December 31, 2022. How
much will the company have on deposit at the end of 4 years if
interest is 10%, compounded semiannually?
What table do we use?
Future Value of a Single Sum
ILLUSTRATION 6.8
Future Value Time
Diagram (n = 8, i = 5%)
LO 2
25. 6-25
Present Value Factor Future Value
¥250,000,000 x 1.47746 = ¥369,365,000
Future Value of a Single Sum
LO 2
TABLE 6.1 FUTURE VALUE OF 1 (FUTURE VALUE OF A SINGLE SUM) i=5%
n=8
26. 6-26
Present Value of a Single Sum
Single-Sum Problems
Amount needed to invest now, to produce a known future value.
Formula to determine the present value factor for 1:
Where:
PVFn,i = present value factor for n periods at i interest
n = number of periods
i = rate of interest for a single period
LO 2
27. 6-27
Assuming an interest rate of 9%, the present value of 1
discounted for three different periods is as shown in Illustration
6.10.
ILLUSTRATION 6.10
Present Value of 1 Discounted at 5% for Three Periods
Present Value of a Single Sum
LO 2
*Note that these amounts appear in Table 6.2 in the 5% column.
28. 6-28
ILLUSTRATION 6.9
Excerpt from Table 6.2
Illustration 6.9 shows the “present value of 1 table” for five
different periods at three different rates of interest.
Present Value of a Single Sum
LO 2
29. 6-29
Amount needed to invest now, to produce a known future value.
Where:
FV = future value
PV = present value
= present value factor for n periods at i interest
PVF n,i
LO 2
Present Value of a Single Sum
30. 6-30
Illustration: What is the present value of €73,466 to be
received or paid in 5 years discounted at 8% compounded
annually?
Present Value of a Single Sum
= €50,000
(rounded by €.51)
ILLUSTRATION 6.11
Present Value Time
Diagram (n = 5, i = 8%)
LO 2
31. 6-31
Illustration: What is the present value of €73,466 to be
received or paid in 5 years discounted at 8% compounded
annually?
Present Value of a Single Sum
ILLUSTRATION 6.11
Present Value Time
Diagram (n = 5, i = 8%)
LO 2
What table do we use?
32. 6-32
€73,466
Future Value Factor Present Value
x .68058 = €50,000
What factor?
i=8%
n=5
Present Value of a Single Sum
LO 2
TABLE 6.2 PRESENT VALUE OF 1
33. 6-33
Illustration: Assume that your rich uncle decides to give you $2,000
for a vacation when you graduate from college 3 years from now.
He proposes to finance the trip by investing a sum of money now at
8% compound interest that will provide you with $2,000 upon your
graduation. The only conditions are that you graduate and that you
tell him how much to invest now.
What table do we use?
ILLUSTRATION 6.12
Present Value Time
Diagram (n = 3, i = 8%)
Present Value of a Single Sum
LO 2
34. 6-34
$2,000
Future Value Factor Present Value
x .79383 = $1,587.66
What factor?
i=8%
n=3
Present Value of a Single Sum
LO 2
TABLE 6.2 PRESENT VALUE OF 1
35. 6-35
Solving for Other Unknowns
Example—Computation of the Number of Periods
The Village of Somonauk wants to accumulate $70,000 for the
construction of a veterans monument in the town square. At the
beginning of the current year, the Village deposited $47,811 in a
memorial fund that earns 10% interest compounded annually. How
many years will it take to accumulate $70,000 in the memorial
fund?
ILLUSTRATION 6.13
Single-Sum Problems
LO 2
36. 6-36
Example—Computation of the Number of Periods
ILLUSTRATION 6.14
Using the future value factor of
1.46410, refer to Table 6.1 and read
down the 10% column to find that
factor in the 4-period row.
Solving for Other Unknowns
LO 2
TABLE 6.1 FUTURE VALUE OF 1
37. 6-37
Example—Computation of the Number of Periods
ILLUSTRATION 6.14
Using the present value factor of
.68301, refer to Table 6.2 and read
down the 10% column to find that
factor in the 4-period row.
Solving for Other Unknowns
LO 2
TABLE 6.2 PRESENT VALUE OF 1
38. 6-38
ILLUSTRATION 6.15
Advanced Design, SA needs €1,070,584 for basic research five
years from now. The company currently has €800,000 to invest
for that purpose. At what rate of interest must it invest the
€800,000 to fund basic research projects of €1,070,584, five
years from now?
Example—Computation of the Interest Rate
Solving for Other Unknowns
LO 2
39. 6-39
ILLUSTRATION 6.16
Using the future value factor of
1.33823, refer to Table 6.1 and
read across the 5-period row to
find the factor.
Example—Computation of the Interest Rate
Solving for Other Unknowns
LO 2
TABLE 6.1 FUTURE VALUE OF 1 (FUTURE VALUE OF A SINGLE SUM)
40. 6-40
Using the present value factor of
.74726, refer to Table 6.2 and
read across the 5-period row to
find the factor.
Example—Computation of the Interest Rate
Solving for Other Unknowns
ILLUSTRATION 6.16
LO 2
TABLE 6.2 PRESENT VALUE OF 1
41. 6-41
(1) Periodic payments or receipts (called rents) of the
same amount,
(2) Same-length interval between such rents, and
(3) Compounding of interest once each interval.
Annuity requires:
Ordinary Annuity - rents occur at the end of each period.
Annuity Due - rents occur at the beginning of each period.
Two
Types
Annuities
LO 3
LEARNING OBJECTIVE 3
Solve future value of ordinary
and annuity due problems.
42. 6-42
Future Value of an Ordinary Annuity
Rents occur at the end of each period.
No interest during 1st period.
0 1
Present Value
2 3 4 5 6 7 8
$20,000 20,000 20,000 20,000 20,000 20,000 20,000 20,000
Future Value
Annuities (Future Value)
LO 3
43. 6-43
Illustration: Assume that $1 is deposited at the end of each of
five years (an ordinary annuity) and earns 12% interest
compounded annually. Illustration 6.17 shows the
computation of the future value, using the “future value of 1”
table (Table 6.1) for each of the five $1 rents.
ILLUSTRATION 6.17
Future Value of an Ordinary Annuity
LO 3
44. 6-44
Illustration 6.18 provides an excerpt from the “future value of an
ordinary annuity of 1” table.
ILLUSTRATION 6.18
Future Value of an Ordinary Annuity
LO 3
*Note that this annuity table factor is the same as the sum
of the future values of 1 factors shown in Illustration 6.17.
45. 6-45
R = periodic rent
FVF-OA = future value factor of an ordinary annuity
factor for n periods at i interest
A formula provides a more efficient way of expressing the
future value of an ordinary annuity of 1.
Where:
n,i
Future Value of an Ordinary Annuity
LO 3
46. 6-46
Illustration: What is the future value of five $5,000 deposits
made at the end of each of the next five years, earning interest
of 6%?
= $28,185.45
ILLUSTRATION 6.19
Time Diagram for Future Value of Ordinary Annuity (n = 5, i = 6%)
Future Value of an Ordinary Annuity
LO 3
47. 6-47
What table do we use?
Future Value of an Ordinary Annuity
Alternate
Calculation
ILLUSTRATION 6.19
LO 3
Illustration: What is the future value of five $5,000 deposits
made at the end of each of the next five years, earning interest
of 6%?
48. 6-48
$5,000
Deposits Factor Future Value
x 5.63709 = $28,185.45
What factor?
Future Value of an Ordinary Annuity
LO 3
TABLE 6.3 FUTURE VALUE OF AN ORDINARY ANNUITY OF 1 i=6%
n=5
49. 6-49
Illustration: Hightown Electronics deposits $75,000 at the end of
each six-month period for the next three years, to accumulate
enough money to meet debts that mature in three years. What is
the future value that the company will have on deposit at the end
of three years if the annual interest rate is 10%?
What table do we use?
Future Value of an Ordinary Annuity
LO 3
50. 6-50
Deposit Factor Future Value
$75,000 x 6.80191 = $510,143.25
Future Value of an Ordinary Annuity
LO 3
i=5%
n=6
TABLE 6.3 FUTURE VALUE OF AN ORDINARY ANNUITY OF 1
51. 6-51
Future Value of an Annuity Due
Rents occur at the beginning of each period.
Interest will accumulate during 1st period.
Annuity due has one more interest period than ordinary
annuity.
Factor = multiply future value of an ordinary annuity factor by
1 plus the interest rate.
0 1 2 3 4 5 6 7 8
20,000 20,000 20,000 20,000 20,000 20,000 20,000
$20,000
Future Value
Annuities
LO 3
52. 6-52 LO 3
ILLUSTRATION 6.21
Comparison of Ordinary Annuity with an Annuity Due
Future Value of an Annuity Due
53. 6-53
Illustration: Assume that you plan to accumulate CHF14,000 for a
down payment on a condominium apartment 5 years from now. For
the next 5 years, you earn an annual return of 8% compounded
semiannually. How much should you deposit at the end of each 6-
month period?
R = CHF1,166.07
ILLUSTRATION 6.24
Computation of Rent
Future Value of Annuity Problems
LO 3
54. 6-54
Computation of Rent
ILLUSTRATION 6.24
CHF14,000
= CHF1,166.07
12.00611
Alternate
Calculation
LO 3
Future Value of Annuity Problems
TABLE 6.3 FUTURE VALUE OF AN ORDINARY ANNUITY OF 1
55. 6-55
Illustration: Suppose that a company’s goal is to accumulate
$117,332 by making periodic deposits of $20,000 at the end of each
year, which will earn 8% compounded annually while accumulating.
How many deposits must it make?
ILLUSTRATION 6.25
Computation of Number of Periodic Rents
5.86660
LO 3
Future Value of Annuity Problems
56. 6-56
Illustration: Walter Goodwrench deposits $2,500 today in a savings
account that earns 9% interest. He plans to deposit $2,500 every
year for a total of 30 years. How much cash will Mr. Goodwrench
accumulate in his retirement savings account, when he retires in 30
years?
ILLUSTRATION 6.27
Computation of Future Value
LO 3
Future Value of Annuity Problems
57. 6-57
Present Value of an Ordinary Annuity
Present value of a series of equal amounts to be
withdrawn or received at equal intervals.
Periodic rents occur at the end of the period.
0 1
Present Value
2 3 4 19 20
$100,000 100,000 100,000 100,000 100,000
. . . . .
100,000
LO 4
Annuities (Present Value)
LEARNING OBJECTIVE 4
Solve present value of ordinary
and annuity due problems.
58. 6-58
Illustration: Assume that $1 is to be received at the end of
each of five periods, as separate amounts, and earns 5%
interest compounded annually.
Present Value of an Ordinary Annuity
ILLUSTRATION 6.28
Solving for the Present Value of an Ordinary Annuity
LO 4
59. 6-59
A formula provides a more efficient way of expressing the
present value of an ordinary annuity of 1.
Where:
Present Value of an Ordinary Annuity
LO 4
60. 6-60
Illustration: What is the present value of rental receipts of
$6,000 each, to be received at the end of each of the next 5
years when discounted at 6%?
ILLUSTRATION 6.30
Present Value of an Ordinary Annuity
LO 4
61. 6-61
Illustration: Jaime Yuen wins $2,000,000 in the state lottery.
She will be paid $100,000 at the end of each year for the next
20 years. How much has she actually won? Assume an
appropriate interest rate of 8%.
0 1
Present Value
What table do we use?
2 3 4 19 20
$100,000 100,000 100,000 100,000 100,000
. . . . .
100,000
Present Value of an Ordinary Annuity
LO 4
62. 6-62
$100,000
Receipts Factor Present Value
x 9.81815 = $981,815
i=8%
n=20
Present Value of an Ordinary Annuity
LO 4
TABLE 6.4 PRESENT VALUE OF AN ORDINARY ANNUITY OF 1
63. 6-63
Present Value of an Annuity Due
Present value of a series of equal amounts to be
withdrawn or received at equal intervals.
Periodic rents occur at the beginning of the period.
0 1
Present Value
2 3 4 19 20
$100,000 100,000 100,000 100,000
100,000
. . . . .
100,000
LO 4
Annuities (Present Value)
64. 6-64 LO 4
ILLUSTRATION 6.31
Comparison of Ordinary Annuity with an Annuity Due
Present Value of an Annuity Due
65. 6-65
Illustration: Space Odyssey, Inc., rents a communications
satellite for 4 years with annual rental payments of $4.8 million
to be made at the beginning of each year. If the relevant
annual interest rate is 5%, what is the present value of the
rental obligations?
ILLUSTRATION 6.33
Computation of Present Value of an Annuity Due
Present Value of an Annuity Due
LO 4
66. 6-66
0 1
Present Value
What table do we use?
2 3 4 19 20
$100,000 100,000 100,000 100,000
100,000
. . . . .
100,000
Present Value of Annuity Problems
Illustration: Jaime Yuen wins $2,000,000 in the state lottery.
She will be paid $100,000 at the beginning of each year for the
next 20 years. How much has she actually won? Assume an
appropriate interest rate of 8%.
LO 4
67. 6-67
$100,000
Receipts Factor Present Value
x 10.60360 = $1,060,360
i=8%
n=20
Present Value of Annuity Problems
LO 4
TABLE 6.5 PRESENT VALUE OF AN ANNUITY DUE OF 1
68. 6-68
Illustration: Assume you receive a statement from MasterCard with
a balance due of €528.77. You may pay it off in 12 equal monthly
payments of €50 each, with the first payment due one month from
now. What rate of interest would you be paying?
Computation of the Interest Rate
Referring to Table 6.4 and reading across the 12-period row, you find 10.57534 in the
2% column. Since 2% is a monthly rate, the nominal annual rate of interest is 24% (12
x 2%). The effective annual rate is 26.82413% [(1 + .02) - 1].
12
Present Value of Annuity Problems
LO 4
69. 6-69
Illustration: Juan and Marcia Perez have saved $36,000 to finance
their daughter Maria’s college education. They deposited the money
in the Santos Bank, where it earns 4% interest compounded
semiannually. What equal amounts can their daughter withdraw at
the end of every 6 months during her 4 college years, without
exhausting the fund?
Computation of a Periodic Rent
12
Present Value of Annuity Problems
LO 4
70. 6-70
Rents begin after a specified number of periods.
Future Value of a Deferred Annuity - Calculation same as
the future value of an annuity not deferred.
Present Value of a Deferred Annuity - Must recognize the
interest that accrues during the deferral period.
0 1 2 3 4 19 20
100,000 100,000 100,000
. . . . .
Future Value
Present Value
Deferred Annuities
Other Time Value
of Money Issues
LO 5
LEARNING OBJECTIVE 5
Solve present value problems
related to deferred annuities,
bonds, and expected cash
flows.
71. 6-71
Future Value of Deferred Annuity
Deferred Annuities
Illustration: Sutton Corporation plans to purchase a land site in six
years for the construction of its new corporate headquarters. Sutton
budgets deposits of $80,000 on which it expects to earn 5% annually,
only at the end of the fourth, fifth, and sixth periods. What future value
will Sutton have accumulated at the end of the sixth year?
ILLUSTRATION 6.37
LO 5
72. 6-72
Present Value of Deferred Annuity
Illustration: Bob Boyd has developed and copyrighted tutorial software
for students in advanced accounting. He agrees to sell the copyright to
Campus Micro Systems for six annual payments of $5,000 each. The
payments will begin five years from today. Given an annual interest
rate of 8%, what is the present value of the six payments?
Two options are available to solve this problem.
LO 5
Deferred Annuities
73. 6-73
Present Value of Deferred Annuity
ILLUSTRATION 6.38
ILLUSTRATION 6.39
Use Table 6.4
LO 5
75. 6-75
Two Cash Flows:
Periodic interest payments (annuity).
Principal paid at maturity (single-sum).
0 1 2 3 4 9 10
140,000 140,000 140,000
$140,000
. . . . .
140,000 140,000
2,000,000
Valuation of Long-Term Bonds
LO 5
Other Time Value of Money Issues
76. 6-76
BE6-15: Wong Inc. issues HK$2,000,000 of 7% bonds due in
10 years with interest payable at year-end. The current market
rate of interest for bonds of similar risk is 8%. What amount will
Wong receive when it issues the bonds?
0 1
Present Value
2 3 4 9 10
140,000 140,000 140,000
HK$140,000
. . . . .
140,000 2,140,000
Valuation of Long-Term Bonds
LO 5
77. 6-77
TABLE 6.4 PRESENT VALUE OF AN ORDINARY ANNUITY OF 1
HK$140,000 x 6.71008 = HK$939,411
Interest Payment Factor Present Value
PV of Interest
i=8%
n=10
Valuation of Long-Term Bonds
LO 5
78. 6-78
HK$2,000,000 x .46319 = HK$926,380
Principal Factor Present Value
Valuation of Long-Term Bonds i=8%
n=10
LO 5
TABLE 6.2 PRESENT VALUE OF 1
PV of Principal
79. 6-79
BE6-15: Wong Inc. issues HK$2,000,000 of 7% bonds due in
10 years with interest payable at year-end.
Present value of Interest HK$ 939,411
Present value of Principal 926,380
Bond current market value HK$1,865,791
Account Title Debit Credit
Cash 1,865,791
Bonds payable 1,865,791
Date
Valuation of Long-Term Bonds
LO 5
80. 6-80
Cash Bond Carrying
Interest Interest Discount Value
Date Paid Expense Amortization of Bonds
1/1/12 1,865,791
12/31/12 140,000 149,263 9,263 1,875,054
12/31/13 140,000 150,004 10,004 1,885,059
12/31/14 140,000 150,805 10,805 1,895,863
12/31/15 140,000 151,669 11,669 1,907,532
12/31/16 140,000 152,603 12,603 1,920,135
12/31/17 140,000 153,611 13,611 1,933,746
12/31/18 140,000 154,700 14,700 1,948,445
12/31/19 140,000 155,876 15,876 1,964,321
12/31/20 140,000 157,146 17,146 1,981,467
12/31/21 140,000 158,533 * 18,533 2,000,000
* rounding
Schedule of Bond Discount Amortization
10-Year, 7% Bonds Sold to Yield 8%
BE6-15:
Effective-Interest Method of Amortization
LO 5
Year
1
2
3
4
5
6
7
8
9
10
81. 6-81
IFRS 13 explains the expected cash flow approach that uses
a range of cash flows and incorporates the probabilities of
those cash flows.
Choosing an Appropriate Interest Rate
Three Components of Interest:
Pure Rate
Expected Inflation Rate
Credit Risk Rate
Risk-free rate of
return. IASB states a
company should
discount expected
cash flows by the risk-
free rate of return.
Present Value Measurement
LO 5
82. 6-82
E6-21: Angela Contreras is trying to determine the amount
to set aside so that she will have enough money on hand in 2 years to
overhaul the engine on her vintage used car. While there is some
uncertainty about the cost of engine overhauls in 2 years, by conducting
some research online, Angela has developed the following estimates.
Instructions: How much should Angela Contreras deposit today in an
account earning 6%, compounded annually, so that she will have enough
money on hand in 2 years to pay for the overhaul?
LO 5
Present Value Measurement
83. 6-83
Instructions: How much should Angela Contreras deposit today in an
account earning 6%, compounded annually, so that she will have enough
money on hand in 2 years to pay for the overhaul?
LO 5
Present Value Measurement