What is Annuity? Questions on annuity due, ordinary annuity, deferred annuity

What is ANNUITY in Finance Concept? 

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A lot of my students get confused with the concepts of annuity. So what exactly is annuity?

You can see annuity as a fixed amount of cash-flow that you will be getting or paying over a fixed interval. 

For instance, getting $100 in year 1, year 2 and year 3. $100 is the fixed amount of cash-flow and 1 year apart is the fixed interval. 

Having said that, getting $100 in year 1, year 3 and year 4 for instance is no longer an annuity as the interval is no longer one year apart since year 2 is being skipped. The interval is not limited to year, it can be monthly, weekly, 2 years interval etc as long as the same cash-flow is paid over same interval. 

There are a few types of annuity as follow:

1. Annuity Due - cash inflow or  outflow that occurs immediately     
2. Ordinary Annuity - cash inflow or  outflow that occurs at the end of the year
3. Deferred Annuity - cash inflow or  outflow that occurs only after a few years
4. Perpetuity Annuity - cash inflow or  outflow that occurs forever
    
Consider the questions as follow:

1. John has just been employed by a prestigious firm, drawing an annual salary of $300,000, paid at the end of each year. He plans to work for five years before retiring. He buys a new luxury home with mortgage repayments of $5,000 per month for the next 20 years (payable at the end of each month), and donates $10,000 per annum forever to his favourite charity. What annual amount, in present value terms, can John withdraw for the first five years of his retirement from the remainder of his savings? Assume an annual interest rate of 6% p.a.

• Is there annuity?
• What is the first step to tackling this question?
• Do you know what you are supposed to find?

2. Kristy has to make rental payments of $1,000 at the start of every month, throughout the four-year duration of her university course. Her university fees are $4,000 to be paid at the start of each year. She earns $1,500 per month (paid at the end of each month) from a part-time job. Assume an interest rate of 8% p.a. and that she keeps the part-time job for the next four years. How much money, in present value terms, can she withdraw each month for the next four years?

• What are the different annuity involved?

• Can you draw the timeline?

** If your school allows you to use financial calculator, please make use of your financial calculator to help you solve your annuity problem.

The next post will be on uneven cash flow. Stay Tune!

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CAPM Capital Asset Pricing Model - A brief Introduction

The article below talks about CAPM and the formula. Still have issues understanding CAPM? SMS +65 9758-7925 or email enquiry@starcresto.com for tuition!

CAPM: ASSUMPTIONS

Capital asset pricing model assumes that in an open market place, all investors are well-diversified and with homogenous belief, they hold on to the same risky assets. Additionally, there is a risk-free asset where the lending and borrowing rate is the same at rf and there is unlimited amount of capital that are available. Also, it is assumed that the market has perfect information and that all investors are rational and risk averse.

CAPM Illustration

Given the assumptions, it meant that everyone has the same assets to choose from, the same information about the assets and same decision methodology (from Markowitz mean-variance portfolio theory). Thus, everyone would be choosing a portfolio on the same efficient frontier with a mixture of risk-free asset and risky assets (M). That is, everyone sets up the same optimization problem, does the
same calculation, gets the same answer and chooses a portfolio accordingly.

Since everyone is holding on to the same, risky assets portfolio, that is also known as market portfolio. Also, the fact that the investors are well diversified implies that they do not look at standard deviation which measures total risk but only on systematic risk (non-diversifiable risk) which is measured by beta. Hence, CAPM formula can be presented by 

ri = rf + βi(rM − rf)

where 

1. ri --> required rate of return for the ith stock 

2. rf --> risk free rate

3. βi --> beta of the ith stock

4. rM --> return of an average stock / market index

5. (rM − rf) --> market risk premium

6. βi(rM − rf) --> risk premium

 

(C) Valerie Chai Hui Yee, 2014, Capital Asset Pricing Model

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Sample NPV questions - Need help in your finance module? Email enquiry@starcresto.com for tuition

Sample NPV Questions

Question 1
A two year project costs $500,000. There is a 70% chance that demand will be high in the first year in which case the net cash flow will be $80,000 and a 30% chance it will be low in which case the net cash flow will be -$40,000. If demand is high in the first year there is a 60% chance it will stay high in the second year with net cash flow of $60,000 and a 40% chance it will be low with net cash flow of -$10,000. If demand is low there is a 70% chance it will stay low with net cash flow of -$10,000 and a 30% chance it will be high with net cash flow of $20,000.

Required
If the required return is 10% should the project go ahead? What is the chance of a negative NPV? 

Question 2

There is a new product to be manufactured and it has a life of five years. The project requires a land worth $650,000. New machinery with a purchase cost of $360,000 with freight cost of $10,000 and installation cost of $30,000 is needed. Salvage value is expected to be $50,000 at the end of year 5. 

The company plans to borrow the money needed to purchase the machinery from its bank at an interest rate of 6% per annum. It will use retained earnings to fund the purchase of the land and this funding will reduce its dividend payments by $70,000 per year.

EBITDA from operations are expected to be: $350,000; $400,000; $580,000; $400,000; $340,000 respectively.
Working capital requirements are expected to be 10% of EBITDA. Working capital is assumed to be needed at the start of the year. To promote the new product the company will spend $53,000 on direct marketing in the first year.

The company’s effective tax rate is 30% and the capital allowances are at 25% of the written down value of the machinery at the beginning of each year. Any unrelieved capital allowance will be given in full in the year of disposal. Tax is payable in the same year to which it is related. To keep things simple assume the net cash flow per year is treated as the taxable profit before capital allowance.
The after-tax cost of capital for the company is 15%. 

Should you buy the machine?

Question 3

ABC Ltd is considering the purchase of a new photocopying machine that will enable its photocopy products to be printed with more vibrant colours. 

The new machine costing $184,000 is expected to have a useful life of 12 years and be able to be sold at that time for $3,000.  ABC Ltd forecasts that the improved quality of its products will generate an additional $80,000 in revenue in each of the next 12 years. The new machine will also require additional costs in colour toner each year. These are expected to b $6000 per year.

ABC current printing machine if replaced can be sold for $16,000 today. It has a book value of $10,000 for tax purposes. 

The new printing machine will require an additional injection of $5,000 in working capital, which will be recouped at the end of 12 years. In the first two years additional service costs of $2000 per year will be incurred.  These service costs are not tax deductible. Tax rates are 30% and the required rate of return is 10%. Capital allowances are at 25% of the written down value of the machinery at the beginning of each year. Any unrelieved capital allowance will be given in full in the year of disposal. Tax is payable in the same year to which it is related. 

Required:

Calculate the NPV and give your advice as to whether Fine Fabrics Ltd should proceed and purchase the new machine?

QUESTIONS TO ASK YOURSELF:

Can you do the questions?
If not, where are you stuck?
Have you grasp the concept of relevant costs, sunk costs, opportunity costs, incremental costs?
Do you understand the role of depreciation in cash flow?

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Finance / Financial Management / Corporate Finance Tuition in Singapore for University and Masters Students

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Background
I have been teaching Business and Corporate Finance full time and have grasp what is important for the test and exam. I have successfully spotted questions that will come out over the past years and this has helped my students scored an average of distinction to high distinction.

I have a total of 10 years experience in teaching and tutoring.

I offer both one-to-one and group tuition. For group tuition, the optimal number of students per class is between 4 to 6. Please form your own group because this will facilitate my teaching methodology.


Teaching Methodology:

1. Understanding concepts and application of concept to questions
2. Developing graphing skills
3. Identifying exam trends and skills (Questions spotting)
4. Practising varierty of questions to prepare you for your exam
5. Simplifying difficult concepts
6. Identifying and improving your weakness

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I have been teaching Business and Corporate Finance full time and have grasp what is important for the test and exam. I have successfully spotted questions that will come out over the past years and this has helped my students scored an average of distinction to high distinction.

I have a total of 9 years experience in teaching and tutoring.

I offer both one-to-one and group tuition. For group tuition, the optimal number of students per class is between 4 to 6. Please form your own group because this will facilitate my teaching methodology.


Teaching Methodology:

1. Understanding concepts and application of concept to questions
2. Developing graphing skills
3. Identifying exam trends and skills (Questions spotting)
4. Practicing variety of questions to prepare you for your exam
5. Simplifying difficult concepts
6. Identifying and improving your weakness

Do contact me at 9758-7925 or email val@starcresto.com or tutor@tertiarytuition.com for tuition.

Student's Profile:

> Tertiary Student --
**Poly / JC (NYP, RP, SP, TP, NP, MDIS, Informatics, SIM, SAS, ACSI)
**University (NTU, NUS, SMU, Imperial College, London School of Economics, University of Durham, Uni SIM, UOL, RMIT, SAS, MDIS, University of Southern Australia, James Cook University, University of Newcastle, London School of Economics, Manchester Business School, University of Nottingham, Melbourne Business School)
**Master (Insead, Singapore Management University, NTU, UCLA, UC Berkeley, Manchester, Uni of Southern Australia, Uni of Buffalo, Uni of Adelaide, NUS, University of State of New York)
> Working Adults -- Managers, Deputy Directors, Managing Directors, Doctors, Divisional Directors, Auditors, Analyst, Credit Advisor, AVP

Tutor's Profile:

> Name -- Valerie Chai Hui Yee
> O Level -- 8 Distinctions for O'Level
> Diploma -- Singapore Polytechnic: Merit Diploma, Honours Roll, SIM Award, Singapore Polytechnic and School of Business Scholar
> Degree -- Nanyang Business School (Top Business School in Asia), NTU: First Class Honours, Dean List, C.H. Wee Gold Medal, Sumitomo Banking Corporation Scholar
> Post Graduate -- Certified Financial Analyst: CFA L1
> Experience -- 9 years of tutoring, Corporate Trainer
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Background
I have been teaching Business and Corporate Finance full time and have grasp what is important for the test and exam. I have successfully spotted questions that will come out over the past years and this has helped my students scored an average of distinction to high distinction.

I have a total of 9 years experience in teaching and tutoring.

I offer both one-to-one and group tuition. For group tuition, the optimal number of students per class is between 4 to 6. Please form your own group because this will facilitate my teaching methodology.


Teaching Methodology:

1. Understanding concepts and application of concept to questions
2. Developing graphing skills
3. Identifying exam trends and skills (Questions spotting)
4. Practicing varierty of questions to prepare you for your exam
5. Simplifying difficult concepts
6. Identifying and improving your weakness

Do contact me at 9758-7925 or email val@starcresto.com or tutor@tertiarytuition.com for tuition.

Student's Profile:

> Tertiary Student --
**Poly / JC (NYP, RP, SP, TP, NP, MDIS, Informatics, SIM, SAS, ACSI)
**University (NTU, NUS, SMU, Imperial College, London School of Economics, University of Durham, Uni SIM, UOL, RMIT, SAS, MDIS, University of Southern Australia, James Cook University, University of Newcastle, London School of Economics, Manchester Business School, University of Nottingham, Melbourne Business School)
**Master (Insead, Singapore Management University, NTU, UCLA, UC Berkeley, Manchester, Uni of Southern Australia, Uni of Buffalo, Uni of Adelaide, NUS, University of State of New York)
> Working Adults -- Managers, Deputy Directors, Managing Directors, Doctors, Divisional Directors, Auditors, Analyst, Credit Advisor, AVP

Tutor's Profile:

> Name -- Valerie Chai Hui Yee
> O Level -- 8 Distinctions for O'Level
> Diploma -- Singapore Polytechnic: Merit Diploma, Honours Roll, SIM Award, Singapore Polytechnic and School of Business Scholar
> Degree -- Nanyang Business School (Top Business School in Asia), NTU: First Class Honours, Dean List, C.H. Wee Gold Medal, Sumitomo Banking Corporation Scholar
> Post Graduate -- Certified Financial Analyst: CFA L1
> Experience -- 9 years of tutoring, Corporate Trainer
> Status -- Full time tutor


For more information, you can visit www.tertiarytuition.com or www.tuition.starcresto.com