Yes, this picture was taken in Singapore!

A man scavenging for cupboards

Everywhere you go in Singapore, you cannot help taking your hat off to their government - Changi Airport is truly the best in the world; so is their MRT, bus service, public housing, etc. The city state seems so wealthy and well-managed. But beyond the awe-inspiring skylines, something is disturbing: Elderly people cleaning the toilets, serving in the food courts, etc. I took this picture while I was enjoying a great meal of crab in the Arab precinct. I also recalled running into a man in tatters eating his meal in one of the viaducts at Nicole Highway. You can’t blame the government though; there will always be some sad cases here and there.

Slogan, slogan, and slogan...

My attention was drawn to a slogan in a full page advertisement in The Star today.

“Your Financial Provider” screams loud and clear below the advertiser MBSB’s corporate logo. The first thought that crossed my mind was: How arrogant! Whose financial provide are you? Certainly not mine!

The self-exaltation advertisement was apparently put up to celebrate its being named one of Forbes Asia’s best 200 small to midsize companies in the region. However, it was thanking its customers for making the company one of the “top” companies in the region! I am not sure if the people in MBSB understand the difference between these two sets of adjectives: “small to midsize” and “top”.

I used to know a little about MBSB during its earlier days. Indeed it was the leading provider of housing loans in the country at one time. It went listing and I cannot remember what happened next; its shares tanked. We lost some good money!

Talking about sloganeering, Firefly is another name that comes straight into my mind.

I am still doing some advisory work for a firm that operates from Singapore. I find it too tiring to commute between Melbourne and Singapore between meetings. I therefore also maintain a small apartment at Subang Saujana. Firefly is obviously the most convenient carrier for me to count on.

It styles itself as “Your Community Airline”. Frankly, I really do not know what it means by that. Which community? The community that lives around Subang Airport? (If so, it is certainly not big enough to sustain the airline!) The community that wants cheap fares? (But the fares aren’t cheap at all! I usually have to pay between MYR300 MYR500 for a one-way journey.)

Besides its bizarre slogan, I also have a few things to say about Firefly.

1.      When you go into its website to purchase tickets on-line, it would ask you to enter your Enrich Number. Do try it to see if it works.

2.      If don’t un-check the insurance and sms offers, you will find yourself “slugged” by these two additional costs.

3.      Try to make a print-out of the e-ticket it sends to you. The IT personnel there either have not attempted to do one themselves, or they are still groping to do a proper job.

4.      At the airport, you need to fork out “penalty” charges if you want to board an earlier flight, even though it might be half empty. (Common sense would dictate that you fill up these unsold seats first, wouldn’t this is be so in Business Course 101?)

Otherwise, the aircraft are reasonable comfortable and punctual.

Many love sloganeering. This is the latest from the British Airways: To Fly. To Serve. Isn’t the first part superfluous? (Or it stays in the tarmac most of the time? And you believe the second part???

Amazing Macau

Macau had never been on my radar until my wife and I decided to “kill” our frequent flyer points with Singapore Airlines.

The ferry service from Hong Kong Airport to Macau was so-so, the only worth-mentioning thing was the usual Hong Kong efficiency. We didn’t even have to go through immigration and the hassle of personal baggage handling when we boarded the ferry to Macau. The ferry terminal at Macau was also so-so.

But Central Cotai (apparently short for Coloane-Taipa Island) is a totally different world. The hotels are luxurious. All the world’s brand names are there. And it is restaurants, restaurants everywhere! I reckon 85% of the guests are Chinese mainlanders. Notwithstanding, the entire dream city looks and smells clean, even the toilets! (I am not being mean to Chinese mainlanders; many of them have yet to learn the ABCs of social etiquette!)

There are a few things we can learn in Macau. The two pictures above – one taken in rural Macau and the other, at Cotai - speak volumes of the territory’s ability to sustain between the two extremes. And two: the level of public hygiene is second to few. Even the trays and cutlery in the food courts are dry and clean, something you don’t even see in Singapore!

"Looking up to Whites" Mindset

I have accumulated some frequent flyer points with Singapore Airlines over the years. Singapore Airlines has the policy of deducting your points every year – if you don’t use them. My wife and I decided to use these points to visit Macau, which we had never been before, even though it is just a ferry away from Hong Kong. We flew through Hong Kong.

Something quite “un-Hong Kong” happened when we were about to board our flight at the Hong Kong airport, which prompted me to write this feedback to Singapore Airlines:

“My wife and I were on this flight from Hong Kong to Singapore on 4 November 2014. When we were about to board the aircraft at Gate 19, we experienced something that was very bizarre.

Being a holder of the Krisflyer XXX Card, we naturally wanted to take advantage of the priority lane accorded to this class of travelers and duly took our place there. We were the first two in the queue. The couple behind us were Caucasian. When the gate opened, the officer - apparently a young man of Chinese descent - instead of clearing us according to the queue status, reached out to the Caucasian man behind me and my wife to scan their passes first - as if we were invisible or not worthy to be XXX members! I naturally protested and although this male officer immediately to scan our passes to scan, I really felt slighted. Moreover, there was not even a word of apology.

This "looking up to the whites" mentally is most unbecoming and indeed disgraceful for a person of his age and colour. I do know that this particular officer is not a member of your staff, however, I urge you to help eliminate this discriminatory mind-set, since he was acting on your behalf at the material time.”

TABLE ETIQUETTE

In the old days it was socially correct for one to help guests or fellow diners first when a dish was served, especially if you were playing host in the table. Some would do so throughout the course of the meal. Fellow diners would also usually reciprocate. All these were supposed to be traits of good upbringing. Using your own pair of chopsticks to serve others was also not a big issue, even though they had been coated with your saliva many times over!

But friends, this is NO-NO in the present time, unless the person you want to help is a lady, or an elderly, or a young child! Even then, please DO NOT use your chopsticks, or fork, or spoon. Ask the restaurant helper for a common pair of chopsticks or a fork or a spoon if none is provided. It is still quite common to see Chinese eateries and restaurants the world over to overlook this need even today. (Yet we say we are the most cultured people on this planet!)

First of all, many people are quite health conscious or discerning about their food now. What is nice to you may not be great to your guests or fellow dinners. Second, you spoil people’s appetite with your “peasant” habit of wielding chopsticks left, right and centre.

Another peasant habit one commonly sees is this: dumping the bones and fats on the table. Thoughtful restaurants usually provide a small plate beside the main plate/bowl for the purpose. But if it is not available, do leave them at one corner of your plate. When you are done with the meal, don’t leave your chopsticks and cutlery all over the world. Place them neatly together - parallel to one another - on your plate.

Many of us Chinese still have a great deal to lean about table etiquette!

Lessons from Bhutanese

On our way out of the Monastery of Divine Madman in Wandue, Bhutan, my wife and I saw this young lady. “Where are you from, sir?” “Japan?” She asked in perfect English. I can understand why she thought we were Japanese. After all, how many tourists of Chinese descent ever bother to say hello to strangers?

My wife and the sweet young lady

I was intrigued by the cross she wore on her neck. She told us that her parents were Christians and there is also a church there. But didn’t our tour guide tell us that there was no church in Bhutan? Before we parted, she even said, “Have a good day!” How sweet of her! She is only 10 years old!

I was trying to bring home a point by relating this incident to friends. Bhutan was hardly a nation a couple of hundred years ago. Today its people practise a level of social etiquette much higher than ours.

I was also not very conscious about common courtesy until I decided to call Australia home in 2001. My wife and I took morning and evening walks around our apartment at Sydney’s Rushcutters Bay. We were always greeted by whoever we saw along the way. On roads, few would overtake you left, right and centre. Everyone seemed to be observing speed limit. And no random parking!  I began to realize how oblivious and inconsiderate we could be to fellow beings in our part of the world! And we boast about our five thousand years of civilization!

Even though the dwellings of their common folks are pretty simple, Bhutanese are a clean lot. Their grounds are neat and tidy. The same holds true for their public places and monasteries. I particularly appreciate their restaurants. The cutlery is thoughtfully laid out; there is always a common spoon for dishes that are meant to be shared. The food, though Spartan, was generally tasty. And the best of all, the toilets are clean and not smelly!

There is a great deal we Chinese have to learn from Bhutanese!!!

Kathmandu, what happened?

The Kathmandu I visited in 1974 - a city thinly populated, without much traffic, dissected by clean rivers and guarded by the majestic Himalayas - is long gone. Today it is a city of some 4 million inhabitants. Traffic is chaotic, air dusty and garbage piles up everywhere. Fortunately, the people are still as friendly as before. But from the way they speak English, they sound not very different from their southern neighbours now. 

No wonder the electricity supply is so erratic!

Kathmandu's Oxford Street

So pristine!

A smiling Gurkha - a potential Victorian Cross recipient.

Kathmandu's MRT



This picture should be rotated 90 deg anti-clockwise. But does it matter?
Isn't true that Kamasutra can be performed in any position?
(Carvings on a pillar in one of the temples at Patan)

 

 

Gross National Happiness: Bhutan

My wife and I did a cursory tour of the country that counts on Gross National Happiness to measure its people's well-being than anything else and we came back thoroughly impressed, not just by the looks of their superstar royal couple, but by what we saw. The whole country is pristine - lush forested mountains and blue-water rivers everywhere. Their architecture is distinctive - from humble dwellings to majestic fortresses and monasteries. But what we enjoyed most was their people - so ready to break into smiles and help. They must have the highest per-capita English proficiency outside the English-speaking world - thanks to their very enlightened monarch. Apparently, every subject in school in taught in English, except their Dzongkha language and culture. They speak English without any heavy trace of South Asian accent. Even though the meals that were organized for us by the local tour organiser were quite simple, they tasted good. Their national dress, which Bhutanese wear on all social occasions, make them look like samurais (maybe more elegantly so - with their black high stockings).

Some tourists might find their roads "third-world" but I was quite prepared to overlook this discomfort. After all, it is a land-locked country with a population of only about 700,000. Everything has to be imported!


Nepal to Bhutan, from the window of the aircraft




At Bhutan's Paro Airport, very safe indeed!



To Bhutanese, this is knowledge!



The real Shangri-La?



Even the figurines are happy! Salt or Pepper?

Sauna, Bhutan style



Welcome to my land!



No wonder he is so happy!



Sonam, the most witty tour guide I have come across!

Nepalese's national dress; don't they look like samurais?

Marijuana, what a surprise!
But smoking is banned in Bhutan

If you can reach it by foot, you don't need doctors anymore

Truly happy!!!

 

Cheap Money - Good for the Economy???

Central bank governors are falling head-over-heels to reduce interest rates, which appears to be their only super weapon to help grow economies. Japan led the way in the 1990s. Their economy has never been in a worse shape after this. I am not an economist, but I hold dearly to this belief: don't expect free lunch! 

To me, there must be a cost attached to any business borrowing. Without a cost, there is simply no pressure for the business borrower to work hard! Easy and cheap money stifles productivity. It feeds real estate and stock market frenzies. Retirees suffer, but ultimately, it does irreparable damages to the economy at large.

Yet, many central bankers are competing to show who is the fairest of them all, meaning, who can dish out the lowest rate! I suspect many are patronizing Ben Bernanke’s tailor.

This crude thought of mine focusses on a micro-aspect of easy and cheap monies in business management.

To deliver a high Return on Equity (RoE) to please shareholders, one only has to make sure that his cost of borrowing is lower than his Return on Total Assets (RTA). The latter is really what a CEO is paid to manage. By gearing up, he can achieve extraordinary RoE.

The formula is simple, really:

RoE = RTA + D/E(RTA - CoD)

If the cost of borrowing is 5% and your RTA is 7%, you will have a spread of 2%. If your Debt to Equity is 5, which means your use $5 of borrowed capital and $1 of own capital to do the business, your RoE will be [7+(5x2)]% or 17%! Your contribution as a manager of the business is only 7% and OPM (other people's money) helps boost the rest of the glowing result for you! But the source of this 5% bank rate is the life-long savings of many old men and women. How much do they get? Probably 2 to 3%! Both the mediocre manager in you and your bank manager literally laugh all the way to where? The bank!!!

In reality, few banks would allow their borrowers to have too high a debt-to-equity ratio. A ratio of 2 or 3 is probably the max you could go for. However, in Japan, a ratio of 15 is not uncommon – there, banks and big businesses tend to lean on each other. Coupled with the fact that competition is intense (and hence margins thin), even though the cost of borrowings are low, the outcome can be fatal. I suspect this is the real reason behind Japan's overall decline.

Many have also been floored by this concept too. In the heyday of high interest rates, (RTA - CoD) turns negative and multiplying this by your D/E, you will have to cry all the way to the bank instead! As an illustration, if your D/E is 2 and your RTA is 5% and your cost of borrowing is 8%, your RoE becomes [5+2x(5-8)] = -1%! How not to cry all the way to the bank!

 
History tends to repeat itself. Economic cycles are for real. It is not for me to cry wolf, but surely you don’t need a PhD in economics to exercise common sense?

INTERNAL RATE OF RETURN – WHAT IS IT?

I gave this talk in February 1994. I thought it is still useful...

Internal Rate of Return (IRR) is a term that is often heard in executive suites and boardrooms. The general perception is that the mathematics involved is too complex or forbidding and the task should best be left to one of those bright-eyed MBAs in the office. One result is that many decision-makers do not quite go beyond the figure to form conclusions, as if IRRs are absolute indicators of financial viability in project investments. What does it really mean?

The concept is actually quite simple. And IRR has many limitations.

Let me try to explain it in the plainest manner.

Say, you have $1,000 and are looking for a good place to grow your money. The easiest and most risk-free way is to put the money in a neighbourhood bank to earn interest. Banks used to pay reasonable interests on deposits, but not now. Many are paying close to zero these days! But for illustration sake, let’s assume a certain Goodie Bank is prepared to pay you an interest rate of 10% per annum. After one year, your balance should show $1,100. Let’s assume this scenario: (a) at the end of the year, you decided to withdraw the $100 interest you had earned to spend and started the new year with a balance of $1,000 in your savings book again, (b) the bank gives you the same interest rate for the next four years, and (c) you also repeat the process of withdrawing $100 at the end of every year for the next four years, and (d) at the end of the fifth year, you close the account and take back your $1,000 together with the interest of $100 that is due to you.

	Beginning Balance ($)	Ending Balance ($)	Withdrawal ($)
Year 1	1,000	1,100	100
Year 2	1,000	1,100	100
Year 3	1,000	1,100	100
Year 4	1,000	1,100	100
Year 5	1,000	1,100	1,100

Assuming that the $100 interest income that you take out every year is not subject to any form of tax, you are effectively getting a return of 10% every year for five years out of the $1,000 you put in; do not forget, though, you are also getting your $1,000 back at the end of the period.

This 10% is an IRR in its simplest form.

Is the 10% return good for you? Foremost in your mind, I suppose, is the question of inflation. True, the $1,000 you get back five years later does not have the same purchasing power as it now has. Even the $100 you take out at the end of every year also seems to be getting “smaller and smaller”. In a real life situation, bank interest rates also fluctuate from time to time. In the 1970s and 1980s, more-than-10%-a-year rates were the order of the day; now you are lucky to get 1 or 2% a year!

We are now enjoying a period of relatively low inflation, if the people compiling the CPIs are to be believed. The rate obviously also does not stay static. In the above example, with adjustment for inflation, the real IRR to your $1,000 investment for five years is much less than 10%.

In the corporate world, IRR is commonly used, sometimes very indiscriminately so, to measure the viability of a project. To be meaningful, it has to be expressed in a manner such as this: The project yields an IRR of 21.3% over an 8-year period – meaning, two elements must be present: a percentage and a time frame. There must also be other qualifications. But let us not get carried away with too many technicalities first.

IRR can be defined as the expected average yearly rate of return you will get for your investment over a given period of time, taking into account that a dollar you receive tomorrow is different in value from the dollar you receive today.

Associated with IRR is the term “discounted cash flow”. Let me try to illustrate with an example.

Let’s say someone comes to you with a seemingly interesting proposal: A project that calls for a total investment of $10 million:

            Fixed Assets                $6 million

            Working Capital         $4 million

Unless you do not believe in bank borrowings, you normally would go to a bank to raise a loan to help finance part of the capital requirement for this project. (Debt actually improves your Return on Equity – provided the cost of your debt is lower than the Return on Total Assets; mathematically expressed, ROE = RTA + D/E [RTA – CoD].) You will also want suppliers to extend credit to your purchases of supplies, raw materials, services etc to reduce your working capital needs. However, if you borrow from banks, you will have to make provisions for the payment of interests and repayment of principal on a regular basis. Mind you, the banks are not a very forgiving lot. If you make a profit, you also have to pay taxes. You have also to set aside a good sum every year to “rejuvenate” your fixed assets. In accounting jargon, you say this is a “depreciation” or “amortization” provision. There is actually no cash flowing in and out of this provision, though.

Whatever cash coming in less whatever cash going out over a fixed period is the NET CASH FLOW for the period which, for planning purposes, is usually one year. Though not exactly correct, net cash flows can also be derived as follows:

            Profit from operations

            Add     : Depreciation
            Less     : Loan repayment
            Equals : Net cash flow
               
If you prefer to leave income taxes out (which is not unreasonable since government can change tax rates and incentives from time to time), the IRR you work out is that of a before-tax one. Next is your investment horizon. It is of course your intention to make your business a going concern. There is really no question of your winding it up after a predetermined period. But let’s be realistic. If you were investing in a snooker parlour, a business where every Tom, Dick and Harry can go into, you would certainly want to make your money fast and be happy to call it quits after just a couple of years. However, if you venture into a steel mill, you are unlikely able to see any profit for the first three years. You would also hope that the state-of-the-art plant you invest in will probably remain efficient for the next ten to fifteen years. Ditto if you go into large scale cultivation of oil palms which take about three years to mature and a couple more years to reach their peak yields. For the steel mill or the palm oil business, your financial people would have to project a 20-30 year cash flow table to plan your capital needs, especially during the gestation period, and be comfortable with the level of cash flows once the project is on stream. From this cash flow, you can calculate the IRR, and see what its NPV is – if you already have a hurdle rate in mind – and estimate the payback period. You would obviously want a high IRR, a robust positive NPV and a payback period that is as short as possible. For very high risk undertakings, such as oil and gas explorations, anything less than 40% over the field life might not be tenable to one; however, most people are happy if see IRRs of 15% after-tax or so.

Let’s go back to the $10 million project. Let’s assume that you plan for a 12-year investment horizon and your accountant suggests that you finance the project with an equity capital, viz., money from your own pocket, of $7 million and raise the rest from a supportive bank. In corporate finance, you say you are going for a 30-70 debt-to-equity ratio. Your accountant lays out the following net cash flow projection for you:

End of Year	Surplus/Deficit) $ million
1	(1.5)
2	0.2
3	1.5
4	1.5
5	1.5
6	1.5
7	2.9
8	2.0
9	2.0
10	2.0
11	2.0
12	2.0

You will want to attach some value to your fixed assets at the end of your investment horizon. Let’s say you reckon they can fetch 20% of their original cost at the end of the day. You must also not forget that you have also had some net working capital in the business by then. We call these the residual or terminal values:

            Fixed Assets, 20% of M$6 million    $1.2 million

            Working Capital                                  $4.0 million
                                                                          __________
                                                                           $5.2 million

Now let me introduce the concept of “discounting”. $1.00 put in a bank today will become $1.10 if the bank pays an interest of 10% per annum. Conversely, $1.00 received a year from now is only worth $1.00/1.10 or about $0.91 today. If you apply this principle to “bring” all the future yearly net cash flows to their “present” value, you will see the following:

Period	Net Cash Flow $ million	“Present” Value $ million
1	(0.5)	-1.5/1.1 =-1.36
2	0.2	0.2/(1.1x1.1) or 0.2/(1.1)2 =0.17
3	1.5	1.5/(1.1x1.1x1.1) or 1.5/(1.1)3 =1.13
4	1.5	Repeat Process
5	1.5	Ditto
6	1.5	Ditto
7	2.0	Ditto
8	2.0	Ditto
9	2.0	Ditto
10	2.0	2.0/(1.1)10 =0.77
11	2.0	2.0/(1.1)11 =0.70
12	2.0	2.0/(1.1)12 =0.64

You will find that the factor used is simply:

 

1/(1.1)ⁿ or (1.1)^-n         where n is the period in question.

The process of bringing these future yearly net cash flows to the present time is called “discounting”. If you sum up the present values of these yearly cash flows for the twelve years, you will get:

                        $7.65 million.

By the same token, the terminal or residual value of $5.2 million has also to be discounted by dividing it with a factor of (1.1)¹², which gives

                        $1.66 million

This figure has also to be included, making the Net Present Value a total of

$9.31 million.

Compared this total with the amount of equity capital you propose to put in, which is $7 million, you see a surplus of

                    
                        $2.31 million

Obviously, the project yields an averagely more than 10% per year.

Now, if you repeat the exercise by using a factor of 1.2, i.e., you discount the future yearly cash flows by 20%, you will find that the sum of these two present values, i.e.,

                        $4.40 million

is not sufficient to cover the $7 million you propose to put in as equity capital. You have a negative NET PRESENT VALUE situation of:

                        $2.60 million

An obvious conclusion from the last exercise is that your investment cannot give you an average yearly rate of return of 20%. If that is your expectation, which may be your “hurdle” rate, then the project is, on a prima facie basis, a NO-GO for you.

The actual average yearly rate of return must therefore be somewhere between 10% and 20%. The rate which gives you a net present value of ZERO, i.e., the summation of all the cash flows – both in and out – “discounted” appropriately, is the internal rate of return of your investment in the project. You can try 12%, 14%, 15.5%, so on and so forth. But the work is simply too laborious. There are ready tables in financial management textbooks to help you with the discounting, but they normally come in whole numbers, nothing fractional ones like 1.5%. For those who are more mathematically inclined, you can use graphs to determine the rate. However, with the advent of Excel, all you need is to type =IRR(Cell A:Cell Z) and out comes the answer! The internal rate of return of this project over 12 years based on a debt-to-equity of 30-70 is

                        13.7%

I have for the sake of clarity illustrated the concept with a simple example. There is really more to it than meets the eye. For instance, your project may take a year or two to complete. You may not have to come up with all capital you need to put up in one go. To be consistent, the installments have also to be discounted according to the period they are put in to conform to this “time-value” concept of money.

The mechanics of working out IRRs is really a figure crunching exercise. Your assumptions must be able to live up to scrutiny; otherwise, it is simply a garbage-in-garbage-out exercise. Projects done devoid of business understanding and entrepreneurial foresights are not worth the paper on which they are written on. However, it has also to be accepted that no one can really foretell what will become of things in the next three to five years, let alone twelve to fifteen years! We can only rely on prevailing knowledge and sentiments to project prices and costs. How many cash flow projections have lived up to their authors’ forecasts? Few really! You may have the capacity, but would you be able to achieve the level of volume objectives you have in mind for the next so many years? Can you predict what your competitors will do? What about the impact of currency fluctuations? Can duties and taxes remain static for the next five to ten years? Your bank may revise its asking rate. Your product can also become obsolete, so on and so forth.

You may also decide to sell your business to a listed company which offers a premium that you cannot rationally refuse. Or you may want to take the business public yourself. Try taking a look at your work years later, if you know what I mean!

It is therefore also quite irrelevant to calculate IRRs to three or four decimal places.

I always caution the blind use of this investment appraisal tool. Remember the rubber glove frenzy in the mid-1980s? So many investors got carried away by a high, yet seemingly realistic, internal rate of return in the wake of a very strong demand for rubber gloves. By all account, cost of product was low; analyst would also tell you this: “You can’t go wrong with this project, IRR is fantastic. I have also done a sensitivity test. Even if I bring down the price by 10% and push the cost up by 10%, we still get an IRR of 60%.” Ditto on people who go into projects based on conventional wisdom or people who embark on businesses or products the business cycle for which are already well past the take-off phase. They will surely go wrong. (If everybody is doing discounted cash flows based on the same set of conventional assumptions, how can the conclusions be different? What many analysts failed to realize is, once the “glut” stage is reached, prices can go down by 50% and cost up by 50%, all within a year or two! No wonder so many always get their fingers burnt.)

In the world we live in today, IRR as a sacrosanct viability indicator is really suspect. But IRRs do have their usefulness.

Where of when?

Comparative analysis is one area where IRR is helpful.

Say you have three investment options in terms of plant configurations. There are all subject to the same external and internal environmental variables. For this illustration, we assume their capital cost is the same - $100,000 – but their net cash flow estimates are different, and the investments have negligible residual value at the end of Year 6:

	Option A M$’000	Option B M$’000	Option C M$’000
Original investment:	100	100	100
Net cash flow:
Year 1	40	25	10
Year 2	38	25	30
Year 3	26	25	30
Year 4	18	25	30
Year 5	16	25	30
Year 6	12	25	20
Total	150	150	150

IRR under the situation can help you to evaluate the three options in a more objective manner. Their IRRs over a six-year period are as follows:

Option A	Option B	Option C
16.9%	13.0%	12.1%

Although the original investments are the same for the three options and cash flows over the six years also all add up to $150,000 in absolute terms, the choice is very clear.

IRR is a useful quantitative method to appraise investments, but it is NOT a be-all-and-end-all one. It should be used in conjunction with a few others.

Modified Internal Rate of Return

Some argue that IRR is flawed. Firstly, it assumes that interim positive cash flows are being continuously reinvested at the same rate of return that the project is generating them. This may not be realistic. A more realistic rate, say the firm’s cost of weighted average cost of capital, should instead be used. Secondly, cash flows in the initial years are usually negative. To correct these two, a version called the Modified Internal Rate of Return is also used. The formula is:

,

For example, if an investment gives the following cash flow projection:

Period	0	1	2	3	4	5
Cash Flow	-4,000	-1,000	3,000	3,500	3,500	4,000

then, the “r” from the following IRR formula, will yield 37.5%

To calculate the MIRR, we have to know our financing cost and to assume our reinvestment rate. Let’s say they are respectively 10% and 12%. The formula above will give us a rate of 27.5%, which is significantly lower than its IRR of 37.5%.

But MIRR, like IRR, is also not a be all, end all formula in investment analyses.