Personal Tax Planning

2009 is ending around the corner. Within these few days before approaching the year end. We need to optimize our tax relief/rebate for Y/A 2009. You may download the free tax booklet from PWC from this website http://iss2.etax.com.my/visitors/new_sitemap.nsf/pages/tax-booklet.html.

Example 1:
It is sad that for those who not yet marry. They can’t enjoy much tax relief/rebate.

Comment:
1. Medical check up relief: Go for personal medical check up.
2. Book relief: Subscribe some magazine or buy more books.
3. Sport equipment relief: Buy a bicycle???
4. Medical Insurance relief: emmmm.
5. Tax rebate from S110: Claim rebate from high-dividend yield investment from Section 110. However, government is smarter now. Single tier tax system eliminates this very soon.

For an unmarried man, it is really has nothing much for the tax rebate/relief.
Example 2:
For those who married, they can setup the income allocation in order to reduce tax. Rule of thumb is to allocate the income from high earner to low earner.
Comment:
1. Tax rebate from S110: Placing the high-dividend yield investment under lower earner account. Low tax bracket payer enjoy higher Section 110 dividend from Section 108. However, government is smarter now. Single tier tax system eliminates this very soon.
2. Income allocation: Business is registered for lower income earner e.g. Ong registered the new company under her wife’s name. Thus, business income will not contribute to his personal income.
3. Insurance premium/EPF tax relie: Let us said Ong’s wife have business income, with the new insurance programme taken up, the RM6,000 insurance premium/EPF tax relief for wife will be taken up. She can either choose EPF or insurance premium, RM500 per month will do. No point for Ong to buy life insurance for this relief because his salary is higher than RM 55,000 p.a (RM 6000/0.11).
4. Most of the relief e.g. child relief, book relief etc. shall always be placed under high earner as he/she is facing a much higher income tax bracket.
5. Parent medical relief: To advise their elderly parents to keep all receipts of medical treatments in order to seek tax relief on this item in which currently are not used at all.
6. Professional Education Relief: If the couple is attending any work-related courses on their own expenses such as training programmes or legal-related courses, they are advised to submit their course fees receipts for tax relief on this area of up to RM 5,000 per annum individually.
7. Computer relief: The couple is also recommended to keep any receipts for the purchase of a home computer or accessories as to claim tax rebate of RM 3,000 every 3 years individually.
8. Book relief: For books purchased in approved bookstores, the couple is recommended to keep receipts for books purchased for tax relief.

Diverted original posting from my facebook note dated 22-Nov-09.

Investment Planning: Asset Relocation

Investment planning is the optimization of the Ong’s portfolio accordingly to the Ong’s risk profile.
From the net worth statement, the investible items are sorted as below. Due to the weight of the different classes of the investment tool, the return of the portfolio is calculated by using this formula:

Example:

Return formula:
Saving account return: (New – Old)/Old
Fixed Deposits return: (New – Old)/Old
Share: (New – Old + dividend)/Old
Unit trust: (New – Old + distribution)/Old
Whole Life Cash Value: (New – Old + Bonus)/Old, for cash value accumulation, not the total premium
Investment-linked product: (New – Old + distribution)/Old, in the investment allocation, not the total premium
EPF: Declaration by EPF during financial year end

Saving account: risk free rate, said 2.5% is higher than 0.9%. It is not worth to park money into it. However, it is only served as cash for emergency. It is recommended to transfer it all to fixed deposits account. Alternatively, if Ong has credit card with the credit limit of RM 20,000, thus he has no worry in holding so much cash in the saving account. He can park the money to higher return investment tool.
Fixed Deposit: Best method to curb the inflation rate. It is at very low risk, low return but very secure. Thus, it serves as emergency fund. If Ong has bought life, personal accident and hospitalization & surgical insurance for all his family members (parents, children and spouse), the amount shall be reduced to RM 15,000.

Share: Highest return doesn’t mean to be the best share. For financial planning, Sharpe ratio is used to gauge the performance of the investment tool. Consistency in generating the expected return is the first choice of the plan. Thus, to increase the portfolio return, switching from share#1, share#2, and share#4 to share#1 can drastically increase the share portfolio return. However, 2 to 3 shares shall be recommended in order to reduce the systematic risk or market risk. If possible, regional good share shall be recommended in order to reduce the systematic risk.
Unit trust: Does your UT agent provide the analysis before advising you to switch your fund from one to another? UT is a very diversify product, it is not recommended to have too many type of UT. Thus, Unit trust#1 and Unit trust#2 shall be allocated to unit trust#3. The consistency of the return has higher possibility to achieve financial goal.

Whole Life cash value: Traditional insurance product does a better security as the insurance company has to strictly follow Bank Negara guideline. The cash value from the whole life serves as the final resource of the liquid cash for Ong. This investment component in the insurance has a good cash value that always has higher return than the fixed deposits.

Investment-linked product: Choosing the unit trust by the insured is under insured liability. It does not have a better security as whole life insurance. Regular premium investment-linked product has a very low unit trust allocation that erodes the ability of the asset growth. The objective of the investment shall be studies before making any decision. Single premium investment-linked product has a higher ratio (e.g. 1.2 times, 1.25 times) compared with unit trust that coupled with free insurance (e.g. 1.0 times). However, Sharpe ratio shall be used to make the decision.

EPF: EPF is the best tool for retirement. With no confident that you can generate a higher return from the withdrawal, then you better not to withdraw it for investment, housing loan reduction, education etc. Most Malaysian “invests” in their children as the safety net for his retirement. What if the safety net fails to commit to return your retirement income? If you are an employee, you may request HR to divert your annual increment to EPF contribution (max 19% for tax exemption). This is a way of conversion from taxable income to non-taxable income in order to reduce your tax.

Diverted original posting from my facebook note dated 21-Nov-09.

Investment Planning: XNPV and XIRR

For uneven cashflow, the best method to calculate the IRR and NPV, excel is the best.
NPV is the net of the discounted CF,j at expected return which relative to present day.
NFV is the net of the compounded CF,j at expected return which relative to future.

Expected return could be risk free rate, inflation, or anything that yu think you need for other evaluation.

This means every project has a NFV and NPV that is use to evaluate the profitability of a project. The project that we discuss here may be investment in equity, UT, real estate, business... that I will share it to you later.

Example 1: A project with 8-years cash flow is tabulated in the table. The table indicates the project have a positive NPV@15% p.a and a positive NFV@15%.
Rules of thumb, based on your expected return input to NPV, said 15%, the discounted for net cashflow produces a positive value. Then, we might accept the project. However, to be specific, IRR has a better meaning than NPV.

IRR is calculated based on the assumption of NPV=0. It is the powerful decision making tool that help me to make the judgment what investment instrument is preferred. IT is termed as CAGR, annualized return, APR, ROI...

However, that was taught from lecturer. I met CFP module 1-6 lecturers, they never mention about XIRR and XNPV. It maybe they do not use XIRR in investment module or maybe they do not even know about EXCEL.

Example 2: In reality, our actual cashflow is complicated (see table 2).The inflow and outflow of a portfolio with different counter are sorted in the table (NOTE: No sorting will return with a wrong IRR, Microsoft shall improve on this XIRR function).Thus, this portfolio has a positive NPV at expected return 15% p.a CAGR. Now, date of transaction is considered in calculation too. You have to liquidate your portfolio, said now.

XIRR is higher than my expected return 15% CAGR but in CFP, lesser than 12% is recommended in calculation. In bullish market, IRR of an aggressive portfolio could simply over 30% p.a, while in bearish it could even lower than -15% p.a We use IRR to compare with the economic indicator not direct return. Direct return has not specific time frame.

Example 3: Bond's coupon rate versus yield-to-maturity. To calculate the CAGR, we all use XIRR for the semiannual coupon. Thus, XIRR takes into the consideration of actual date payment while YTM assumes 360 days a year, or 30 days a month.

Example 4: Project A, B and C comparison.

Obviously,IRR evaluation for the uneven cashflow indicates project A has higher IRR than others. This is how decision is made.


Example 5: Deferred Annuity
You will surprise that the example of the deferred annuity will have a slightly higher IRR that FD rate. However, the only advantages that it could provide is the insurance component built-in inside the policy. For cost effectiveness, UT+termed life maybe have a better return then the annuity.

For 1ook investment, IRR,low = 1.63%, IRR,high = 4.76%, IRR,- = 1.34%
Total,low = RM151,972, Total,high = RM 422,917, Total,- = 140,000.
How about I put 100k to FD and I withdraw 7k yearly at my age 56?
so, what do you think about this annuity product? hmmm.... does your agent know about the fact? hmmm....

Example 6: Have you ever heard about the crab breeding? How NPV and IRR are used in the decision making. Crab breeding is just a background. Capture all the inflow and outflow that expected in the operation. Budget for the business, duration, escape plan .... can be considered inside the plan.
From the plan, you would notice that you have no income that can last for at least 6 months!!! So then you enjoy the value of IRR!!!

Diverted original posting from my facebook note dated 13-Nov-09.

Chilren Education Fund Planning

In near future, most people is graduated at least master/PhD as the literacy of the country increase. Education fees is the best benchmark of inflation. And, it is already happened at our neighbor country.


Maxix awares about the important of the education for his child. He starts to plan his one-year old son's education plan. Present speeding on tertiary education, said education fees + Living = 25,000. Let's take 6% p.a. for educational and cost of living inflation.

Educational fees@18 years old = FV(0.06,18-1,0,-25000,0) = $67,319.32 p.a

Total funding for Bachelor, Master, PhD for 8 years university study with 8% fund performance:
= PV((0.08-0.06)/(1+0.06),8,67319.32,0,0)/(1+0.06),begin = $467,510.72

Funding Strategies:
1) Lump sum now investment at the end of the year
PV(0.08,18-1,0,-467510.72,0) = $126,353.63

2) Yearly payment for 18 years
PMT(0.08,18-1,0,-467510.72,0) = $13,852.08

3) Existing Resource 20,000 investment and yearly payment
PMT(0.08,18-1,20000,-467510.72,0) = $11,659.49

Adapted original posting from my facebook note dated 11-Nov-09.

EPF Fund Projection at Retirement Age

Figure 1: Last 5 year EPF performance (http://www.kwsp.gov.my/index.php?ch=p2reports&pg=bm_p2reports_statistic&ac=986&tpt=32enenenenbmenen)

Based on the previous note there was no shortfall strategy that we could discuss. Thus, let us simulate a person who has a shortfall of retirement fund.

Said,33 years old Maxix annual income 120k p.a. Expected salary increment is 4%p.a. EPF dividend is 5%p.a.
He has 130k in the EPF deposit now.
How much is the EPF fund@55 years old without the withdrawal?

PV((0.05-0.04)/(1+0.04),55-33,-0.23*120000,0,0) = $544,926.97

PV,begin = $544,926.97/(1+0.04) = $523,968.24
FV(0.05,55-33,0,-130000-523968.24,0) = $1,913,027.60

If his retirement need is 2.5m.
Shortfall = $586,972.40

Strategy:
1) Increase Maxix investment
PMT(0.05,55-33,0,586972.40,0) = ($15,243.97), end of the year
2) Set aside of existing cash amounted 200k with 5.016%
RATE(55-33,0,-200000,586972.4,0,0.1) = 5.016%

....many more depends on what resource and limitation he has

Diverted original posting from my facebook note dated 10-Nov-09.

Retirement Plan Construction

3 Steps to construct retirement plan: Retirement income need, retirement fund required and funding/accumulation.

Step 1: Retirement income needed
Retirement income approaches: (A) Target replacement ratio (TRR) and (B) Expense Method
For TRR, 50%-70% of expected last drawn salary is calculated in order to replace the expenses. It is assumed that less commitment approaches retirement age. Once retired, you no need to pay tax, EPF, loan (depends on housing and car loan are cleared) and Educational fund (depends on your funded resource). Different person has different ratio. Thus, it is proposed based on the personal objective, net worth and cash flow.

Step 1(A): Retirement income needed – Target replacement ratio (TRR)
Cat, 32 years old, she earns 10,000 monthly. Her yearly increment is 5%. She plans to retire around 65 year old.
Her last drawn salary, FV(5%, 65-32-1,0,-120000,0) = $571,792.98
Assumption:
TRR(50%, e.g. less commitment) = $285,896.49
TRR(60%, e.g. child educational funded by own, bad health family members etc) = $343,075.79
TRR(70%, e.g. loan not clear yet, child educational funded by own, bad health family members etc) = $400,255.08
Higher TRR produces higher security but high cost too. Thus, another method is studies.
Step 1(B): Retirement income needed – Expenses method
Cat’s outflow is 45,000. Let’s add 10% buffer. Thus, it is assumed as 50,000. Inflation is 5%.
Future annual expenses at age 65 year old is FV(5%, 65-32,0,-50000,1) = $250,159.43

Step 2: Retirement Fund calculation
Let’s take future annual expenses at age 65 year old is $250,159.43.
Life expectancy (Malaysian: 75 years old, Singaporean: 85 years old). Medical development human life is getting more advances. Thus, it will be reviewed time from time.
Two approaches for the retirement fund calculation: (A) principal liquidation and (B) Principal intact.

Step 2 (A): Retirement Fund calculation – principal liquidation
Cat is a Singaporean PR. She plans to stay and work at Singapore for the rest of her life.

Figure 1: Malaysian 30-years historical fixed deposit rate and consumer price index

With ROI 8% p.a, Inflation = 0%. Retirement fund, 2Ai, = PV(0.08,85-65,-250159.43,0

,1) = $2,652,590.33
With ROI 8% p.a, Inflation = 5%. Retirement fund, 2Aii, = PV((0.08-0.05)/(1+0.05),85-65,-250159.43,0,1) = $3,879,129.82

Step 2 (B): Retirement Fund calculation – Principal intact.
With ROI 8% p.a, Inflation = 0%. Retirement fund, 2Aiii, = PV(0.08,999,-250159.43,0,1) = $3,377,152.31 or (250159.43/0.08)+250159.43 = $3,377,152.31
With ROI 8% p.a, Inflation = 5%. Retirement fund, 2Aiv, = PV((0.08-0.05)/(1+0.05),999,-250159.43,0,1) = $9,005,739.48 or (250159.43*(1+0.05)/(0.08-0.05))+250159.43 = $9,005,739.48

From 2Ai, 2Aii, 2Aiii and 2Aiv, it is recommended 2Aii, $3,879,129.82 realistically.

Scared?

Step 3: Retirement Funding Calculation
Insurance/UT agent will based on the $3,879,129.82 to work out the annual payment, PMT(0.1,65-32,0, 3879129.82,0) = ($17,453.78) annually in order to close the deal fast.

Professionally, net worth that we had discussed earlier will be use to off the retirement fund funding.
Item in the present value of Net Worth will be projected at year 65 years old to offset the retirement fund because financial plan implement. It might be the additional add-on to net worth e.g inherit of parent assets. Thus, it is advised to have a review if net worth has changed.
Cat has share/unit trust – 200,000, own-occupied house – 130,000, car – 35,000, CPF – 150,000. Her insurance has no cash value because she bought term insurance. She doesn’t invest in any houses. She has no car loan but house loan – (76,000).

Current asset that we discuss over her is net investment asset, NIA.
NIA is the total sum of asset that exclude of house and car. Thus, NIA is 200k+150k =350k@32 years old.

Share/UT’s ROI is 10% p.a while CPF is 2% p.a. Increment 5.5%p.a
FV@65, Share/UT = FV(0.1,65-32,0,-200000,1) = $4,645,030.88
FV@65, CPF = FV(0.02,65-32,0,PV((0.02-0.055)/(1+0.055),65-32,120000*(0.2+0.15),0,0)/(1+0.055),0) = $4,716,156.49 with no withdrawing.
Total NIA@65 = $9,361,187.38, Requirement retirement fund@65 = $3,879,129.82
Thus, NIA>required fund, she doesn’t need to have a retirement fund. She must be very careful in taking care of her investment.

Let us upgrade the scenario, may she stop her employment? Another words, can she retire now by taking dividend to support 50k living?
FV@65, Share/UT = FV(0.1,65-32,0,-200000,1) = $4,645,030.88
FV@65, CPF = FV(0.02, 65-32,0,-150000,0)= $288,334.71
NIA@65 = $4,933,365.59, Requirement retirement fund@65 = $3,879,129.82
Thus, NIA>required fund, she doesn’t need to worry about her retirement plan. She must be very careful in taking care of her investment. But, she need to source for another income to support her 50k p.a living.

Said, dividend yield is 6%p.a. share/UT = 200k. Thus, dividend paid = 12k p.a
PV, begin = (50000/0.06)+50000 = $883,333.33. She needs to accumulate current value of $683,333.33.

Conclusion: Cat has no worry in retirement. She doesn’t even require a retirement plan. If she wants to immediately quit the current job and taking the dividend as her income, she requires current value of $683,333.33.
*Study
PV, begin = (50000/0.06)+50000 = $883,333.33. She needs to accumulate present value of $683,333.33.
PV, begin = (50000/0.07)+50000 =$764,285.71. She needs to accumulate present value of $564,285.71.
PV, begin = (50000/0.08)+50000 =$675,000.00. She needs to accumulate present value of $475,000.00.
PV, begin = (50000/0.09)+50000 =$605,555.56. She needs to accumulate present value of $405,555.56.
PV, begin = (50000/0.1)+50000 = $550,000.00. She needs to accumulate present value of $350,000.00.

Note: her annual income is $120,000 with 19.32% saving ratio from cashflow/net worth analysis.

Diverted original posting from my facebook note dated 8-Nov-09.

Insurance Planning - Required Sum Insured Calculation

Sum insured is calculated in order to tabulate your scheduled premium payment. Three methods are discussed here.

1) Rule of Thumb method:
It provides a brief idea of sum insured: 5-10 times annual income
This method is used by insurance agent to close the deal fast, too rough, not accurate as different individual has different expense/income ratio). 5 to 10 times of annual income may be very subjective.

Example 1: Let's take 8 times. Amy earns 10,000/month. Thus, annual income is 120,000/month.

Rule of thumb's sum insured = 8*10k*12 = 960k.
Current life insurance coverage = 100k
The shortfall shall be 860k.

Then insurance agent will recommend her to buy another 860k sum insured.
It will be very funny if Amy's dependence expenses is said 40k which the agent do not consider her net worth that can be off set for the high sum insured. It is baseless to make the assumption that causes a big gap between 5 times and 10 times sum insured.

Further more, higher earner will end up with higher sum insured.

2) Human Life Value or Economic Life Value method:
Another slightly improved method but flaw is still exist. As my lecturer said, if a person is symbolized as a money printing machine, will you protect this machine? Human has a value. SS Huebner first expounded the concept of a human value. The economic value of a human being may be taken to be the present value or discounted value of anticipated net earning of the individual during the productivity year. But, it is a good method for those who do not has a fix income, not yet perfect approximately.
To get the highest commission or promising commission, agent uses the method wont be very-wrong or commission-guaranty. It is due to no matter how high or low of a person's income, it will sure work out with a sum insured that higher that income replacement method. Thus, over insured might be exist if you view it from the method 3. However, the advantage of this method would be the most secured way to calculate the sum insured...because it wont be the scenario that expense more than income. Thus, the failure rate is low but might be a burden to the insured.

Example 2: 33-year-old Amy earns 10,000/month. Her commitment to her dependence is 25 years. What would be the sum insured that she required if the policy has ROI of 5%?

Answer:
PV(.05,25,-120000,0,0) =$1,691,273.35 without salary increment.

Growth adjusted rate of return, I,adj = (r-g)/(1+g)
I,adj = (0.05-0.04)/(1+0.04) = 0.009615385, or 0.9615%

PV((0.05-0.04)/(1+0.04),25,-120000,0,0)/(1+0.04)

= $2,553,253.71 with 4% salary increment.

Remember that premium has to be paid first before u enjoy the coverage. so, it is divided by (1+.04).

which one is realistic? $2,553,253.71.

Net worth statement from CFP step 2/3 will be used to offset the sum insured requirement, said 350k.

Current life policy (validity till 25 years) = Current bought life policy#1 + Current bought life policy#2 + Current bought life policy#3 + Current bought life policy#4 + Company group policy till retire
= 32k + 100k + 10k + 115k + 3*120K = 617k

shortfall = $2,553,253.7- (350k + 617k)
= $1,586,253.71.

Conclusion: She requires 1.6 million sum insured.

For this method you would always notice that you need to have a high net worth in order to have a zero shortfall.

3) Income replacement method:
Insurance agent wants to close the deal fast, they most likely wont spend mush time for this method. To understand this, you will lost your patient if your agent tell you so.

Two approaches for your requirement for your principal, A) Principal Liquidation method and B) Principal Intact Method. In mathematics, A means FV=0 at the targeted period while B means n=infinity,9999 with FV=constant.

Example 3: 33-year-old Amy earns 10,000/month. 40k expenses per year. Her commitment to her dependence is 25 years. What would be the sum insured that she required if the policy has ROI of 5%?

Answer:
Principal Liquidation = PV(0.05,25,-40000,0,1)
= $591,945.67 without considering Inflation.
Principal Intact = PV(0.05,9999,-40000,0,1) = $840,000.00, or (40000/.05)+40000
=840,000 without considering inflation

Figure 1: Malaysian 30-years historical fixed deposit rate and consumer price index

Inflation adjusted rate of return, I,adj = (r-i)/(1+i)
I,adj = (0.05-0.04)/(1+0.04) = 0.009615385, or 0.9615%

Now, it become more realistic if we consider the inflation.
Principal Liquidation = PV((0.05-0.04)/(1+0.04),25,-40000,0,1)
= $893,638.80 with considering Inflation 4%.
Principal Intact = PV((0.05-0.04)/(1+0.04),9999,-40000,0,1)
= $4,200,000.00 or (40000/((0.05-0.04)/(1+0.04)))+40000 =4200000 with considering inflation 4%.

Which one is more realistic and practical among the four figures?
$893,638.80

Net worth statement from CFP step 2/3 will be used to offset the sum insured requirement, said 350k.

Current life policy (validity till 25 years) = Current bought life policy#1 + Current bought life policy#2 + Current bought life policy#3 + Current bought life policy#4 + Company group policy till retire = 32k + 100k + 10k + 115k + 3*120K = 617k

shortfall = $893,638.80 - (350k + 617k)
= (73,361)

Conclusion: No need to buy insurance because no short fall.

Quit Job Scenario:
Amy quits the current company and join another new company. The new company has no life insurance provided.

Then, the sum insured to be revised as below:

shortfall = (73,361) + 3*120k = 286,638. In order to protect her family expenses, she need to buy additional 286 k life insurance because there is a short fall.

As a conclusion, changing a job might seriously affect your insurance planning. The premium of the additional 286k is, 0.005*286000 = 1500 per annual for non-participating insurance.

Diverted original posting from my facebook note dated 4-Nov-09.

Amortization in Excel: Do You Know Your Loan Well?

100,000 home loan with 7% p.a for 10 years servicing.

1) What is the monthly payment?
2) What total interest paid for 10 years loan?
3) What is the ratio of interest paid and principle over loan?
4) What is the total interest paid, total principle paid, total payment and loan balance by the end of 3rd year servicing?
5) How much I have to pay more if base lending rate (BLR) increase from 7% p.a. to 7.5% p.a.

In excel:
1) Monthly Payment = PMT(rate,nper,pv,fv,type)

= PMT(0.07/12,12*10,100000,0,0) = -1,161.08.

2) Total Interest Paid for 10 years loan = CUMIPMT(rate,nper,pv,start_period,end_period,type)
= CUMIPMT(0.07/12,12*10,100000,1,12*10,0) = -39,330.20.

3) Ratio = (interest paid + principle)/principle
= (39,330.20+100000)/100000 = 1.39.

4) Total Interest paid, end of 3rd year = CUMIPMT(rate,nper,pv,start_period,end_period,type)
= CUMIPMT(0.07/12,12*10,100000,1,12*3,0) = -18,729.38.

Total principle paid, end of 3rd year = CUMPRINC(rate,nper,pv,start_period,end_period,type)
= CUMPRINC(0.07/12,12*10,100000,1,12*3,0) = -23,069.67.

Total payment, end of 3rd year = 3*12*(-1,161.08) or (-18,729.38)+(-23,069.67) = -41,799.05.
Loan balance = FV(rate,nper,pmt,pv,type)
= FV(0.07/12,12*3,-1161.08,100000,0) =($76,930.33).

5) Total Extra Interest = CUMIPMT(0.075/12,12*10,100000,1,12*10,0) - CUMIPMT(0.07/12,12*10,100000,1,12*10,0)
= (-42,442.12) - (-39,330.20)
= -3111.92

Figure 1: Historical Malaysian BLR

Diverted original posting from my facebook note dated 21-Oct-09.

Rule of 78, Hire Purchase

Car hire purchase for 3 years loan, 4.1% p.a. for MYR 27,000. If I want to settle my car loan one shot after the 16th payment, how much I had to pay for 17th payment and how much I had saved for the interest? Is the settlement worth to be executed? (assume FD = 3% p.a)

Let me introduce basic calculation in hire purchase. It is based sum of digit, or called as rule of 78.
One year monthly installment consists 12 months. Thus, if you add up at the number from 12nd to 1st numbers, it results 78. Sum of 12+11+10+9+8+7+6+5+4+3+2+1

= (12*(12+1))/2 = 78. Thus, it is also called as sum of digits.

Similarly, 2 years monthly installment, 3 years, 4 years, 5 years, 6 years, 7 years and 8 years results 300, 666, 1176, 1830, 2628, 3570 and 4656 respectively.

Term charges of the HP = Principle*interest*number of years
= 27000*0.041*3 = 3321.

Sum of digit = N*(N+1)/2
= 36*37/2 = 666.

Monthly installment = Principle+Term charges/(number of years*12)
= (27000+3321)/(3*12) = 842.25

For Rebate = n(n+1)*term charges/N(N+1)
= (36-16)*(36-16+1)*3321/(36*(36+1)) = 1047.16.

Outstanding installment = (36-16)*842.25 = 16845.
Thus, redemption sum = 16854 – 1047.16 = 15806.84.

Interest saving = Old HP – settled HP
= 842.25*36-(15806.84+16*842.25) = 1038.16.

Effective interest for old plan = 12*RATE(nper,pmt,pv,fv,type,guess)
= 12*RATE(36,-842.25,27000,0,0,0.15) = 7.692% p.a

Effective interest for old plan = using IRR from Cash flow see image = 7.515% p.a

Diverted original posting from my facebook note dated 21-Oct-09.

Rule of 72, Flash Feeling Compounding/Discounting Rate

Rule of 72 is used to have a flash idea of how it can double or halve your present value, PV in compounding or discounting manner respectively. It links the relation between rate and year of holding with the 72, in discounting and compounding manner.

Formula:
n=72/rate

n=holding year in compounding and discounting
rate=annual rate

Example 1: Make it simple to be understood, how long your bank fixed deposits needed to double its value if bank offer 3%p.a?

Based on rule of 72, it requires 24 years.
Working: 72/3 =24.

Actual period is 23.45 years.
Working: in Excel, NPER(0.03,0,-1,2,0)).

Example 2: if the current inflation rate is 6%, how long my favorite coffee price will increase to double from current price?

Based on rule of 72, it requires 12 years from now.
Working: 72/6 = 12.

Actual period is 11.89 years.
Working: in Excel, NPER(0.06,0,-1,2,0))

The basic theory behind the magic 72 is natural logarithm of 2. To get a relationship of double your PV for your FV, let us see the derivation.

FV=PV(1+r)^t, where FV, PV, r and t denote future value, present value, rate and period in year.

2=1*(1+r)^t;
ln(2)=t*ln(1+r), with ln(1+r) approximates to r
thus, 0.693147=t/r (approximation)

Due to 72 is a special number, that has high number of factor of 72 (2, 3, 4, 6, 8, 9, 12, 18, 24 and 36) compared to 69 (3,23) and 71, thus number 72 is chosen to be the flash calculation to capture the idea of how the rate feel like.

How do we use it in daily life?
Example 3: Malaysia credit card charge is 18% p.a, while Singapore is 24% p.a. Does the different of 6% p.a. make a big different?
Let us compare it with rule of 72.

Malaysia rate requires 4 years to double your outstanding balance.
Working: 72/18 = 4.

Singapore rate only requires 3 years to double your outstanding balance.
Working: 72/24 = 3.

Finally, benchmark those rates with local FD rate 2.5%p.a. It requires 28.8 years to get your FD double.
Working: 72/2.5 = 28.8.

So, which one better, to be a lender or borrower? My advice is….be the banker not to be the slave of bank especially credit card.

Diverted original posting from my facebook note dated 22-Oct-09.

Comment:
To understand more, please read the Time Value of Money basic.