Inflation and NPV

An important aspect of project valuation is the discounting of future cash flows using an appropriate opportunity cost of capital.
When cash flows and the opportunity cost of capital are given, obtaining the net present value is straightforward using either a financial calculator or a spreadsheet.
However, under inflationary economy, good care must be given to both cash flows and the opportunity cost of capital to obtain the same net present value in either nominal or real terms.
Only today I realize why my students were finding it difficult to deal with inflation in discounting real cash flows. The exercise involving a constant inflation rate was well understood, but I got only 1 right over 42 students on the exercise involving varying inflation rates.
I thought it may be good to demonstrate for the unknown student how to deal with the term structure of inflation rates. But as for every thing else in life, let start with the easiest case and end with the most involved case.
Suppose the following:
Investment (I(t=0)) = $800, real cash flow at time 1 (RCF(t=1)) = $500, RCF(t=2) = $700, and RCF(t=3) = $800. Assume an opportunity cost of capital of 25%.

What is the net present value in nominal terms when the expected inflation rate is 10% and constant over the three years?

Step 1: Convert real cash flows into nominal cash flows using
RCF(t)(1+i(t))^t,
where i(t) is the expected inflation rate at time t.
Step 2: Discount nominal cash flows using the nominal discount rate (the opportunity cost of capital).

Applying the two steps at once we obtain:

NPV = -$800 + $500(1+0.1)/(1+0.25)  + $700(1+0.1)^2/(1+0.25)^2 + $800(1+0.1)^3/(1+0.25)^3 = $727.26

What is the net present value in real terms?

Step 1: Adjust the nominal opportunity cost of capital for inflation rate by using
r(t) = [(1 + R(t))/(1 + i(t))] - 1,
where r(t) is the real rate at t, R(t) is the nominal rate at t, and i(t) is the expected inflation rate at t.

Doing so, we obtain, [(1+0.25)/(1+0.1)] - 1 = 0.1364 or 13.64%, which is constant over t.
Step 2: Discount real cash flows in terms of real opportunity cost of capital
-$800 + $500/1.1364 + $700/1.1364^2 + $800/1.1364^3 = $727.26

Conclusion: We obtain the same NPV in both nominal and real terms.

The following part is the more involved, and you will see why.

What if inflation rate is not constant over the years? How can we be consistent?
Let now assume that the expected inflation rate is 10%, 12%, and 15% at time 1, 2, and 3, respectively. We keep the rest of the given unchanged.

In nominal terms, we get:
-$800 + $500*1.1/1.25 + $700*1.1*1.12/1.25^2 + $800*1.1*1.12*1.15/1.25^3 = $772.26
So the formula is: RCF(t)(1+i(1))*(1+i(2))*...*(1+i(n)/(1+R)^t)

In real terms
step 1: Get the nominal rates at each t using R(t)(1+i(t))^t
step 2: Adjust R(t) for inflation using r(t) = [R(t)/((1+i(1))*(1+i(2))*...*(1+i(n)))^(1/n)]-1
So, in our cases
r(1) = [(1+0.25)/(1+0.1)] - 1 = 0.1364 or 13.64% as before
r(2) = [1.25^2/(1.1*1.12)^(1/2)] - 1 = 0.1262 or 12.62%
r(3) = [1.25^3/(1.1*1.12*1.15)^(1/3)] -1 = 0.1130 or 11.30%

We now use these real discount rates to discount our real cash flows to obtain the following:
-$800+$500/1.136 + $700/1.1262^2 + $800/1.1130^3 = $772.26

Conclusion: We are consistent. Both methods agree.

I hope this helps.

Extreme life style

Boko Haram is not a disease. It is a rebellious movement whose methods combine traditional military combats, suicide attacks, forced labor, and civilian subordination. Peoples of different backgrounds are today members of Boko Haram, a baby whose face concentrates the misery of Africa. Those in Boko Haram could be any African who at one time or another thought enough is enough.
I have seen people all over the continent searching for new ways to make a living for themselves and their loved ones. These ways are often extreme. All extreme ways are not alike. Boko Haram is an extreme way to make a living at other peoples' cost. Crossing the Mediterranean sea is another extreme way to make a living at oneself's cost. Serving as housemaid in the Middle East is yet another extreme way at oneself's cost to make a living. Many other extreme ways are hidden in every one of us. We have left behind us without always valid reasons aging parents, vulnerable brothers and sisters, and fragile societies. We have traveled miles for almost no impact. We are not as Europeans conquering America. We did not conquer a thing.
But who to blame for our misery, our quest for extreme to make a living of very little impact on ourselves and our community? Shall we blame our governments? Shall we blame Westerns? Since we are part of these constituted groups, it will be a shame to exclude ourselves for common failures.
Our education has one purpose: "live by standards." A life at extremes is not a standard life. Being part of Boko Haram is not a standard. Crossing the Mediterranean sea is not a standard. Travelling all the way from Ethiopia to Lebanon to work in-house is not a standard.
Extreme events will never be normal events. They are risky events with very little probability mass of occurrence. There will always be the lucky event among many events. It is the law of probability. The point to be made is that extremes are very costly for our continent. Losses through extremism are by far higher than gains. Extremism is about a person, standard is about common good. We must learn to live by standards.

Last but not least

Why we have failed as Africans of all walks of life? Because we are stubborn peoples scattered across the African continent.
We are not worse than others. May be we are the last if continent must be ordered in terms of its success to solve human problems. But being the last among the best is not always a bad outcome. There must always be a first and a last thing. If I am not, someone else is. When you consider a group of people, the notion of last is meaningless. Last makes only sense if you have a linear view of things or peoples. A nonlinear view eliminates the last effect. It much depends from which perspective you look at things. A last thing for one may be a first thing for another person. May be this is why people travel around the globe to discover the last they do not know. They pay to visit the last thing, the last civilization, the last beast, the last of the last.
The last thing is mysterious to me. Once the last thing is known, it becomes a thing among other things. A profound sense of search makes the last thing, a think to add to other things. No human will try to destroy the last thing. No human will aim to eliminate the last people. If such a mistake is intentionally done, then the next to last become the last. May be some of the brilliant minds who know who is intellectually last are afraid to walk a mile and discover the truth of the last. Obviously, they must be the last.
So being last is not all bad. In many situations to be last is to be first. Consider the European struggle in experimenting different economic, political and technological systems. Consider now African countries we gained their political independence in the 60s. Normally, those who were last should have been the first to improve the old systems. Unfortunately, the last went further back. They got their inspiration from Machiavelli. Some went even further to resuscitate Cesar and the Pharaohs. Obviously the last was still the least. Considering that a human is a completion of another human being, it is a conundrum that dictators were born to Africans.
I asked myself why we did not learn from others. Our fathers thought they were different from others. In their misery, they run away from the past of those we came to colonize their minds, to tame their spirit, and to brutalize their body. They were much afraid to be like them. But were they better? If they were better in which ways? We have to go back in history to find out what kinds of people our African ancestors were before the arrival of colonizers. Did not they brutalize their fellows?
We are now in the 21st century. Still we know very little about others. We are still in the path of our own. We still believe in our differences. Just because we were colonized, does not mean we are better. Just because we are victim of racism, does not mean we are not racists. Just because we were enslaved, does not mean we are not abusers of our fellow Africans. We are all those things. We are exactly like them. May be worse.
I believe peoples are complementary beyond what we can imagine. Without this complementary, human being would have destroyed himself long ago. Therefore, learning from others is essential. You learned from others, if you believe that you are like others. You do not learn from others, if you believe you are different. History only serves the minds of those who humble themselves. So being last is not a big deal. The harder you try to separate yourself from the rest of the world, the quicker you fall backwards.

A thought for my people

I was born in Kinshasa in the Democratic Republic of Congo (DRC). My parents are from the coastal province of the Nether Congo. Neither too politicized nor too militarized, the Nether Congo is symbolically important in the making of the Congo. Congolese do not travel a lot, but for those we can and do, the cities of the province are privileged. The proximity to the capital Kinshasa is surely an advantage. But the province lacks a real political influence. To exist as a province in DRC, you need to be in the military. The true power is in the hands of the gunmen. The inhabitants of the Nether Congo known as NeKongo are not trained to violently impose their views. They tried lately with Moanda Ne Nsemi, but went nowhere. The strong and bloody military action against the NeKongo was silently supported by many fellow Congolese who feared the idea of another Congo with an independent Nether Congo.
It is difficult to both mourn and understand. When you hear that your people was murdered because their opinions found no place in the minds of those in power, you walk silently, and questioned the sense of belonging. You want to find excuses for your fellow Congolese who went to re-install the rule of fear. You convince yourself that anyone who speaks against the existence of the Congo as it is known to all of us should die. If they are few, they can be imprisoned. If they are more than hundreds they should be killed. In the shoes of those in power, the order is re-established when the jungle is silenced. No one speaking out his mind is the state of mind that should help fellow Congolese in power to work harder for the better. After all, if the sacrifice of hundreds killed in the Nether Congo can serve the interest of the majority why not. I hope really that those souls resting from the misery of the Congo are not better than those still in power inventing new methods to tyrannize the mortal among all mortals of the earth.  

Lost comparative advantage

The law of comparative advantage is a law of relative maximum. Countries can choose the best production combinations among all available possible production combinations. But such a combination must not be rudimentary in the sense of a best single combination of two commodities. The best combination must be at a point where production possibilities curve cross. Such a combination represents an interesting  portfolio combination point.
In introductory economic courses, only one production curve is drawn and shown. However, policy makers see many possible economies coexisting at different levels. Such a view is not a blue-sky contemplation since these curves are forcefully nonlinear. Multiplicity and non-linearity are due to variation of different orders.
A first order variation gives rise to an exposed economy. Not because nature is first-order, but because our perception limits our view, understanding, and action. Such an economy is rudimentary with curves best represented by vertical lines crossing horizontal lines. I guess before the industrialization era, economies around the globe were not leveraging on uncertainty, risk, and the unknown. These economies produced simple production combinations that possibly could be moved along an horizontal line.
A combination of the first order and a second order variation gives rise to a satisfactory economy in a world where human being is excused for extreme events. The 18th, the 19th and the first part of the 20th century were dominated by the view that the economic structure is both first and second order. Tools and institutions were introduced and developed to set up and to manage new economic structures. Unfortunately, many countries in Africa kept the first-order view as a benchmark in dealing with economic and political affairs. Worst people in these countries are afraid of leveraging on uncertainty, the unknown, and the hidden. Since beliefs are important vehicles of thoughts, these countries lost the comparative advantages they had prior to the emergence of the first and the second view elsewhere in the world.
In fact, we have already moved away from a paternalistic view of the economy. Policy makers became aware of the existence of a third and a fourth order of economic variation. We are almost there in modelling a world economy that is resilient to the first, second, third and fourth orders of economic variation. Clearly, we do not excuse ourselves for extreme events. We do not say is not our fault. We know now that extreme events can be prevented. We know we have to be prepared to face extreme events when they arrive. We take full responsibility in what may happen.
The point of what was said, is that a country that ignores the management of risk is in trouble. The country has no a comparative advantage. It will produce at higher costs. Importing is cheaper than producing. This may explain why African countries are getting poorer. They have lost the comparative advantage of pushing themselves into the future.

Devastating Internet

According to the Congolese Constitution, there will be a presidential election in 2016 in the Democratic Republic of Congo (DRC). The Congolese diaspora cannot wait the day and the time, the incumbent president will leave the office. The year 2016 is in the mind of the Congolese diaspora, the beginning of a new era for the country as a whole. Some believe with Kabila stepping down, Congolese will come together and establish the rule of law.
President of the Congo since 2001, Joseph Kabila's reign coincide with the use of Internet at a large scale. He and his staff were not prepared to communicate through Internet. They came from a generation who believed in hardware, not in software. They missed the whole point of being leaders in the 21st century. Unable to develop a modern strategy, they mocked people who insulted the president. They were unable to use Internet as a tool to reach out, as a converter of dark thoughts. They badly failed to cat short damaging rumor. They surely have succeeded to keep Kabila alive. The Congolese Diaspora could not reach the president physically, but they did bring his presidential image down. They have counterfeited his Internet image. As a result, Congolese has a perception of Joseph Kabila that is surprising for someone who has been president for 14 years. He is a complete stranger to his fellow Congolese. Since nature abhors a vacuum, stories were invented, stories were perverted, and a new image was developed.
Joseph Kabila will step down soon or later. However, he will not go down in history as a Congolese who fought for other Congolese. This could be wrong. But what can you do against an image that is broadcast when there is no one else to convince you to the contrary. The Congolese diaspora has defeated the president team. They have corrupted the minds of the majority of the Congolese leaving abroad. They have put in the mind of thousands of people that Joseph Kabila is a traitor. They have convinced a large number of Congolese that he is an usurper. Those around the president do not obviously care in line with the saying "the dog bark but the caravan moves". The question is who is in the caravan? Where the caravan is moving about?
It was in 2001 I met Joseph Kabila when he visited Finland. Me and my fellow Congolese did what we could to meet the young president. There is no much to say about what he said then. I think he could not believe his eyes that Congolese was living in a country known for his supposedly cold winter. Some of my fellow did try to make this visit a beginning of something, but as far I know most of the initiatives did not go very far. Anyway, when Kabila came to Finland, I was doing my PhD at HANKEN, and did not give much thought to what he said or he was.
People who met Mobutu like to say that Mobutu was charming and warming. He will make himself a fanatic supporter of the Congo. The same thing cannot be said about Kabila. Now people cannot be compared in terms of either what they say or how they look. Nonetheless, it is a shame that the team around Joseph Kabila did not fabricate a better image for their champion.