Compound Annual Growth Rate (CAGR)
The CAGR formula calculates the rate of return required for an investment or business to grow from its beginning value to its ending value over the period of time specified, assuming the growth is constant over the period. The CAGR represents the average annual growth rate over the period, and it takes into account the effect of compounding.
The formula for Compound Annual Growth Rate (CAGR) is:
CAGR = (Ending Value / Beginning Value) ^ (1 / Number of Years) - 1
Where:
Ending Value: Final value of investment or business at the end of the period.
Beginning Value: Initial value of investment or business at the beginning of the period.
Number of Years: Number of years for which CAGR is being calculated.
For example, if an investment has a beginning value of $100,000 and an ending value of $150,000 after 5 years, the CAGR would be calculated as follows:
CAGR = ($150,000 / $100,000) ^ (1/5) - 1
CAGR = 8.14%
In this example, the CAGR for the investment is 8.14%, which means that the investment grew at an average annual rate of 8.14% over the 5-year period.
CAGR is useful for comparing the performance of different investments or businesses over different time periods, as it provides a standardized way of measuring the average annual growth rate. However, it is important to note that CAGR assumes a constant growth rate, which may not always be the case in real-world scenarios.
Time Value of Money (TVM)
WHAT
The time value of money (TVM) is the concept that a sum of money is worth more now than the same sum will be at a future date due to its earnings potential in the interim. Money can grow only through investing.
A sum of money in the hand is worth more now than the same sum in the future. This is a core principle of finance. An investment delayed is an opportunity lost. The time value of money is also referred to as present discounted value.
WHY
Why money today is worth more than money tomorrow?
Today's dollar is worth more than tomorrow's because of inflation (on the side that's unfortunate for you) and compound interest (the side you can make work for you). Inflation increases prices over time, which means that each dollar you own today will buy more in the present time than it will in the future, i.e. the decline of purchasing power of a given currency over time.
Inflation is a measure of the rate of rising prices of goods and services in an economy. It can occur when prices rise due to increases in production costs, such as raw materials and wages. A surge in demand for products and services can cause inflation as consumers are willing to pay more for the product.
In this context which happens most of the time (based on history so far), investors prefer to receive money today rather than the same amount of money in the future because a sum of money, once invested, grows over time.
HOW
For example, money deposited into a savings account earns interest. Over time, the interest is added to the principal, earning more interest. That's the power of compounding interest.
PV = FV
( 1 + r )
PV = present time value
FV = future value
r = rate of interest
Example: You have $1,000 on hand (PV), and interest rate is 1% per annum (r= 0.01).
FV = PV x ( 1 + r ) = 1,000 x (1.01) = $1,010 a year later if you have deposited the PV amount in the bank which promised the interest of 1% per annum.
If it is not invested, the value of the money erodes over time. If you hide $1,000 in a mattress for three years, you will lose the additional money it could have earned over that time if invested. It will have even less buying power when you retrieve it because inflation has reduced its value.
As another example, say you have the option of receiving $10,000 now or $10,000 two years from now. Despite the equal face value, $10,000 today has more value and utility than it will two years from now due to the opportunity costs associated with the delay.
In other words, a payment delayed is an opportunity missed.
Formula:
Generally, it considers 1) the amount of money, 2) its future value, 3) the amount it can earn, and 4) the time frame.
For savings accounts, the number of compounding periods is an important determinant.
FV = PV x [ 1 + (i / n) ] (n x t)
PV = Present value of money
i = interest rate
n = number of compounding periods per year
t = number of years
Assume a sum of $10,000 is invested for one year at 10% interest compounded annually. The future value of that money is:
FV = $10,000 x [1 + (10% / 1)] ^ (1 x 1) = $11,000
The formula can be rearranged to find the value of the future sum in present day dollars. For example, the present day dollar amount compounded annually at 6% interest that would be worth $5,000 one year from today is:
PV = $5,000 / [1 + (6% / 1)] ^ (1 x 1) = $4,717
Effect of Compounding Periods on Future Value
Taking
the $10,000 example above, if the number of compounding periods is
increased to quarterly, monthly, or daily, the ending future value
calculations are:
Quarterly Compounding: FV = $10,000 x [1 + (6% / 4)] ^ (4 x 1) = $10,614
Monthly Compounding: FV = $10,000 x [1 + (6% / 12)] ^ (12 x 1) = $10,617
Daily Compounding: FV = $10,000 x [1 + (6% / 365)] ^ (365 x 1) = $10,618
Hence,
TVM
depends not only on the interest rate and time horizon but also on
how many times the compounding calculations are computed each year.
Why is TVM important?
It can help guide investment decisions. Read on how TVM is being applied to property investment: property valuation math
How to check your BTO for defects list
In general, USE every thing in there and run checks during the afternoon with full natural light.
1. Check that all your keys (including letter box key) opens your main door properly.
2. Turn on all the lights (if it comes with) to make sure they are working perfectly, i.e. none of the lights are blown or any of the starters are faulty. If your wiring are hidden as some new flats are, pray that everything is wired properly.
3. Turn on all the taps, faucets, showers and let the water run. If water chokes in your sink, something's in its way (could be plaster etc).
Since BTOs do not come with showers installed, bring a hose along with you, stick it into the sink's tap and flood your floor. If water collects on the bathroom floor and takes forever to drain, your floor isn't sloped properly to encourage proper drainage.
4. Taste the water. While it may sound silly, it should taste... clean, and free from corrosion. Not that stainless steel pipes corrode easily, and this being a new flat and all. But just because the pipes are newly installed doesn't mean the pipes are new (they're not). Bring along a clear drinking glass. Fill it up and see if there are any unnatural particles.
5. Open ALL the windows to their fullest. Check to see if they function properly. Pay attention to the handles to ensure they are not loose. Also check that they all turn and lock properly. If you have to force the handle into lock position, the handle will loosen up within a short time. This is a problem because most handles are dead bolted onto the frames. And once they are loose, there is nothing to be done but re-bolt them onto another area, leaving unsightly holes on your frame and your handles will not be levelled with your other windows.
6. Use all the toilets by flushing them and ensure they work properly - see how long it takes for the water tank to fill up and flush again. Faulty water tank plumbing may hinder replenishment of the tank's water.
7. If your unit comes with a fancy accordion pole hanger for drying clothes, play around with it to ensure everything is bolted properly and its mechanisms are functioning smoothly.
8. If your walls are tiled, take a thick (a 50-cent works) coin or marble and start tapping on each of them to check if any of the tiles are hollow or loose.
9. Although you would not be able to confirm this within 7 days, be on a constant look out for water leakage/damage on your ceilings after your upstairs neighbor has moved in.
10. Always remember that just because it's a newly built flat doesn't mean everything in it is new. That means piping, gates, windows etc. Check for rust, LISTEN for defects, look for cracks (on the toilet bowls and sinks), and ensure window rubber linings are not dried or rotten.
Source
Co-ownership of Immovable Property
| Tenants-in-common | Joint Tenants |
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共享权益: 共 享 权 益 (Tenants-in-common) 是 联 名 业 主 的 一 种 , 联 名 的 利 益 是 以 份 数 分 明 , 例 如 是 甲 乙 各 占 一 半 , 甲 占 三 分 之 一 , 其 余 三 分 之 二 由 乙 拥 有 , 分 配 按 联 名 人 士 间 的 协 议 而 确 订 。 这 等 权 益 因 为 份 数 分 明 关 系 , 所 以 可 以 在 无 须 经 另 一 方 的 同 意 下 将 属 于 自 己 的 分 数 自 由 转 售 和 送 赠 他 人 , 及 由 后 人 来 承 继 。
共有权益人，联名业主: 共有权益人(Joint Tenants) 是联名业权的其中一类 ， 俗称「长命契」。共有权益是以「生还原则」(Principle Of Survivorship) 来作准 , 谁人过世,的权益便归其余还在生的人， 直至死剩最后一人, 共有权益便会消失。
Source
Useful Guide for Freelance Professional
Property Valuation Math – Using NPV and MIRR to Identify Good Deals
1. Net Present Value (NPV) and
2. Modified Internal Rate of Return (MIRR).
Here‘s a question:
- A property is priced at $1.4 million and is expected to generate a yearly net cash flow of $41,200.
- Assuming no leverage, would an investor with a Desired Rate of Return of 8% be wise to invest at the current price and sell @ $1.4 million (for simplicity) 5 years later with selling costs of 1% of the sales price?
- $1.4M is overpriced since return does not meet Desired Rate of Return of 8%.
- The Net Present Value (NPV) is -$292,212 and therefore not a wise investment.
- Even though the Net Rental Yield is 2.9%, it is a wealth decreasing investment hence I should not invest in such project. The property will not meet my expected rate of return of 8% and I should look for other options where I can get more than 8% returns or I should reduce my expected rate of return.
Tip: The Net Present Value method means that money now is more valuable than money later on. Confused? Here‘s a simpler explanation: you can use money to make more money! You could run a business, or buy something now and sell it later for more, or simply put the money in the bank to earn interest.
Example 1:
A friend needs $1,000 now, and will pay you back $1,140 in a year. Is that a good investment when you can get 10% returns elsewhere? (Hypothetical example, since we know lending money to friends is never a good investment!)
Money Out - $1,000 today:
You invested $1,000 today, so Present Value (PV) = -$1,000
Money In - $1,140 next year (Future Value or FV):
Present value (PV) of $1,000 at 10% interest rate = -$1,036.36
Net amount is:
Net Present Value (NPV) = $1,036.36 - $1,000 = $36.36
So, at 10%, the investment is worth $36.36.
In other words, it is $36.36 better than a 10% investment, in terms of today's money.
Your choice of interest rate can change too.
Suppose that you are offered an investment which will pay the following cash flows at the
end of each of the next five years:
How much would you be willing to pay for this investment if your required rate of return is 12% per year? Suppose that you were offered the investment at a cost of $800. What is the NPV?
Answer: NPV is $200.18.
Since the NPV is 0, the value of this investment at $800 is a good investment as it meets your Required Rate of Return of 12%.
Suppose that you were offered the investment at a cost of $800. What is the IRR?
Answer: IRR is 19.54%
The Internal Rate of Return 19.54% > Required Rate of Return 12%. Therefore, the value of this investment at $800 is a good investment.
Putting It All Together and the Modified Internal Rate of Return (MIRR)
The Internal Rate of Return (IRR) has been a popular metric for evaluating investments for
many years — primarily due to the simplicity with which it can be interpreted. However, the
IRR suffers from a couple of flaws.
The most important flaw is that it implicitly assumes that the cash flows will be reinvested for the life of the investment at a rate that equals the IRR.
The Modified Rate of Return (MIRR) and Net Present Value (NPV) solve this problem by using an explicit reinvestment rate (i.e. bank deposits).
| Period | Cash Flow |
| 0 | 0 |
| 1 | 100 |
| 2 | 200 |
| 3 | 300 |
| 4 | 400 |
| 5 | 500 |
From the above table, suppose that you were offered the investment at a cost of $800. What is the MIRR if the reinvestment rate is 10% per year?
Answer: MIRR is 16.48%
So, we‘ve determined that our investment valued at a cost of $800 is acceptable. It has a positive NPV, the IRR is greater than our 12% required return, and the MIRR is also greater than our 12% required return.
Reinvestment Rate
The reinvestment rate refers to the annual yield at which cash flows from an investment can be reinvested.
For example: Ryan owns one rental property. After the payment of all expenses and debt
service, Ryan has cash flows of $1,000 per month, which is a 15 percent return on his
money.
The Internal Rate of Return (IRR) for this property assumes that Ryan will take his
entire $1,000 worth of cash flows per month and reinvest that money in something else at
the same 15 percent rate he is earning on the property. This reinvestment rate of 15% is
highly unlikely and unrealistic for the average investor.
A more realistic scenario: Ryan puts the $1,000 per month in a savings account earning 0.25% interest, or uses it to pay off personal expenses, such that his reinvestment rate is 0.25%.
Two realistic reinvestment rates for the average property Investor would be Bank Deposits at prevailing rates or CPF Ordinary‘account at prevailing 2.5% interest.
Concluding Comments
To conclude, all this property ―math we have learnt so far – Cap Rates, Cash-on-Cash Return, IRR, NPV and MIRR are used mutually to:
1. Assess the performance of one‘s property (value) and desired ROI;
2. Rank and choose between different properties;
3. Rank and choose between different investments.
All smart investors will do their sums before putting their hard-earned money to work.
See: Net Present Value Calculator
Reference1: Propwise.sg, Contributor: Gerald Tay
Reference2
SALE Residential Landed Prices by District - Recent Transactions
| 19 | Hougang | 37 | 8,500,000 | 1,820,000 | 3,350,000 | 1,788 | 616 | 1,212 | 7,018 | 1,582 | 2,799 |
| 10 | Holland | 32 | 40,500,000 | 2,730,000 | 6,165,000 | 3,899 | 787 | 1,272 | 33,691 | 2,260 | 4,930 |
| 15 | Katong | 28 | 12,000,000 | 1,960,000 | 4,740,000 | 1,673 | 389 | 1,279 | 8,600 | 1,389 | 3,935 |
| 28 | Seletar | 18 | 11,118,000 | 1,750,000 | 3,020,000 | 1,870 | 602 | 1,050 | 10,032 | 1,615 | 3,321 |
| 16 | East Coast | 18 | 6,200,000 | 548,000 | 3,464,000 | 1,563 | 127 | 911 | 7,599 | 1,744 | 3,305 |
| 11 | Thomson | 17 | 20,000,000 | 2,750,000 | 9,000,000 | 2,548 | 704 | 1,493 | 13,390 | 2,723 | 6,049 |
| 23 | Choa Chu Kang | 16 | 13,200,000 | 1,620,000 | 3,632,000 | 1,629 | 618 | 1,031 | 10,699 | 1,615 | 3,310 |
| 20 | Ang Mo Kio | 14 | 7,000,000 | 1,720,000 | 3,740,000 | 1,869 | 900 | 1,162 | 5,317 | 926 | 3,278 |
| 27 | Yishun | 11 | 5,700,000 | 1,600,000 | 3,158,000 | 1,502 | 484 | 1,118 | 5,102 | 1,808 | 3,305 |
| 13 | Macpherson | 11 | 11,500,000 | 2,700,000 | 4,050,000 | 1,282 | 851 | 1,088 | 10,538 | 2,648 | 3,735 |
| 14 | Eunos | 10 | 5,300,000 | 160,000 | 3,025,000 | 1,707 | 221 | 1,156 | 7,546 | 721 | 2,514 |
| 21 | Clementi | 7 | 13,800,000 | 1,680,000 | 3,828,000 | 1,780 | 445 | 1,073 | 10,398 | 1,765 | 3,767 |
| 26 | Upper Thomson | 6 | 3,800,000 | 2,450,000 | 3,290,000 | 1,138 | 754 | 941 | 3,767 | 3,208 | 3,251 |
| 22 | Jurong | 4 | 3,688,888 | 1,750,000 | 1,784,000 | 1,083 | 717 | 944 | 5,145 | 1,615 | 1,932 |
| 25 | Kranji | 3 | 5,008,000 | 2,138,888 | 2,888,888 | 966 | 604 | 606 | 8,288 | 2,217 | 4,768 |
| 18 | Tampines | 3 | 5,000,000 | 2,900,000 | 3,700,000 | 1,042 | 582 | 605 | 8,590 | 2,788 | 6,114 |
| 17 | Changi | 2 | 4,750,000 | 1,500,000 | 3,125,000 | 758 | 459 | 609 | 6,265 | 3,272 | 4,769 |
| 5 | Pasir Panjang | 2 | 4,238,000 | 3,600,000 | 3,919,000 | 1,319 | 1,236 | 1,278 | 3,218 | 2,917 | 3,068 |
| 12 | Toa Payoh | 1 | 1,000,000 | 1,000,000 | 1,000,000 | 250 | 250 | 250 | 4,004 | 4,004 | 4,004 |
| 9 | Orchard | 1 | 6,400,000 | 6,400,000 | 6,400,000 | 3,216 | 3,216 | 3,216 | 1,991 | 1,991 | 1,991 |
| 8 | Little India | 1 | 3,100,000 | 3,100,000 | 3,100,000 | 1,021 | 1,021 | 1,021 | 3,035 | 3,035 | 3,035 |
| 4 | Harbourfront | 1 | 2,400,000 | 2,400,000 | 2,400,000 | 541 | 541 | 541 | 4,435 | 4,435 | 4,435 |
| Grand Total | 243 | 40,500,000 | 160,000 | 3,830,000 | 3,899 | 127 | 1,132 | 33,691 | 721 | 3,531 |
