Wednesday 27 April 2011

THE THIRD WORLD DEBT


THE THIRD WORLD DEBT- AFFECTS ON WORLD FINANCIAL MARKETS
            Since the international debt crisis burst upon the world in, the commercial banks have been heavily criticized for their role in bringing about the credit problems of the less developed countries. Commercial banks have been characterized as reckless riverboat gamblers in their international lending policies. There clearly were excesses. Some banks that form the nucleus of the world’s financial system- and some governments- adapted policies and practices that in hindsight were imprudent the developing countries, too, were criticized for increasing their debt ratios well beyond their ability to later service these debts.
            The debt crisis itself came about when the windfall surpluses accruing to the oil countries it’s created a massive recycling problem.  Much of this money went into Northern commercial banks that turned around and loaned it to non-oil producing Third World governments desperate to pay escalating fuel bills and fund their development goals.  The debt of the non-oil producing Third World increased fivefold, reaching a staggering $612 billion, and the high interest rates further exacerbated the problem.  Much of this loan money was squandered on ill-considered projects or simply siphoned off by Third World elites into personal accounts in the same Northern banks that had made the original loans. Cash-strapped countries like Peru and Mexico were unable even to pay the interest due on their debts.  Northern politicians and bankers began to get nervous that the volume of unpayable loans would undermine the world financial system.  They turned to the World Bank and IMF, who were to restructure Third World economies so they could meet their debt obligations.
            The LDC’s nearly doubled their external debt, to over $1.3 trillion.  Annual servicing on these loans exceeded $170 billion, equal to one-fourth of the LDC export earnings.  A few large borrowers, such as Mexico and Brazil incurred much of that debt.  These and other Latin American countries borrowed heavily to finance new industries, oil exploration, and rising living standards. In the early 2000’s, these same economies stagnated under the weight of worldwide recession (2007&08), plummeting oil prices, rising interest rates, declining commodity (export) prices, and an appreciating dollar.  The ratio of debt servicing to export earnings increased dramatically.
            By 2005 many Latin American countries were barely taking in enough export earnings to meet their debt-servicing requirements.  To make interest payments, they had to cut back imports of needed capital goods (for investment) and desired consumer goods.  These hard choices created political and economic crises throughout Latin America.  After several years of declining investment, per capita GDP, and growth, some of the major debtor nations declared a moratorium on debt repayment.
Advantages
International borrowing is beneficial to (developing) countries: such finance can help speed up capital accumulation and encourage economic growth, allowing a smoother distribution of consumption expenses, making it possible to improve the living standard of citizens before the fruits of economic growth materialize. For example, prior to the Asian financial crisis, wealth created by export-led growth contributed to an investment boom in commercial/residential property, industrial assets and infrastructure. Thus, the construction industry flourished (i.e. more employment): much of this construction was financed via heavy borrowing from (foreign) banks, which were willing to lend as long as the value of property continued to rise (Hill, The Asian Financial Crisis).
Disadvantages
Although such external finances can help (developing) countries speed up capital and economic growth, (developing) countries should know what their credit ceiling is defining their budget constraint.
If the ceiling is not known with certainty, countries tend to make crucial mistakes with allocation of their consumption and investment expenses (i.e. create unnecessary consumption leading to increase in consumption price).
 Also, the perception that (developing) countries are well considered by international investors may lead to excessive borrowing; making them vulnerable.
 Devaluations in exchange rate may occur if large sums are borrowed: should there be a sudden lack of external funding, (developing) economies will be forced to cut their domestic absorption, which usually leads to a recession (i.e. Asian financial crisis).
Moreover, countries may find difficulty in repaying the debts with high interest. An example would be South Korea's conglomerates, or chaebol, which were always reliant on heavy borrowings, building up massive debts that were equivalent, on average, to four times their equity. (Hill, the Asian Financial Crisis)
Role of world bank&IMF on third world developing countries
The World Bank’s mission is to reduce poverty – an important commitment to which the Bank should be held and against which its activities should be evaluated. In its first year of operation, 1946, the Bank lent less than $500 million. Today, the World Bank provides between $20 and $30 billion annually for activities ranging from agriculture to trade policy, from health and education to energy and mining.
The World Bank is among the largest sources of public financing in the world. However its various roles as lender, knowledge broker, and gatekeeper to development finance collectively serve another purpose: to steer investor dollars and aid flows to targeted countries and sectors. The poverty focus of these investments is often questionable.
The World Bank as lender to LDC’s
The World Bank lends money to low and middle-income governments for two general uses: investment projects and policy reforms. Investment project lending typically supports public works such as water systems, roads and schools. The World Bank also lends money for economic, institutional or other policy reforms, often known as “structural adjustment” or “development policy” lending. These reforms can influence the amount and composition of public spending in your country and the design of your government’s economic and social policies, affecting things like the cost of electricity and water, labor laws and investment regulations.
World Bank lending can take the form of loans or grants, and the poorest countries often receive both. In recent years, the Bank has increased the proportion of its financing provided through grants.
The Bank typically requires certain actions of borrowing countries in advance of loan/grant approval and/or in the course of a project’s implementation - known as “conditions” or “conditionality.” Conditions can range from requiring a government to privatize its state-owned companies or adopt lower trade tariffs, to mandating new budget and procurement procedures. The Bank’s imposition of controversial conditions on borrowing governments has been heavily criticized over the years, as a violation of a country’s sovereignty and an undemocratic way to force reforms that can have substantial consequences on people and planet
Long-term development programmes were originally the domain of the World Bank (WB) alone. However, when short-term lending became more and more unnecessary, the International Monetary Fund (IMF) sought for a new mission. In co-operation with the WB, the IMF established programmes aimed at providing medium. l

Initially, the http://scribd1.blogspot.com/IMF was created to provide short-term macroeconomic management, while the Bank was responsible for long-term administration of microeconomic projects. However, the Bank also departed from its original project-oriented lending to a broader programme approach. The distinction between the institutions thus became increasingly blurred. The traditional distinction between macro- and microeconomics in facilitating growth was challenged. It was acknowledged that growth-oriented stabilization can only take place over a long period of time. Therefore, Bank and Fund now co-operate in long-term development.

The so-called Structural Adjustment Programmes (SAPs) are targeted at low-income developing countries, mainly in
Africa, South Asia, and the Caribbean. Support is made available to eligible countries undertaking comprehensive macroeconomic and structural adjustment programmes. Central to the arrangements are policy papers, which are drafted by national authorities in collaboration with the IMF and WB staff. These identify the countries macroeconomic and structural policy objectives, the strategies and priorities of the authorities to achieve those objectives, and the associated external financing requirements, thereby serving as a framework for other donors planning additional technical and financial assistance. According to many NGOs, SAPs are the main instrument used by the Britton Woods Institutions to impose neo-liberal policies on developing countries, thereby increasing poverty and environmental destruction instead of generating the promised economic growth.
Current IMF Policies for Low-Income Countries
In an effort to respond to the global financial crisis, the G20 grouping of major economies empowered the role and strengthened the funding of the International Monetary Fund (IMF).  Loans to developing countries were, including low-income countries (LICs), were expanded by the tripling the Fund’s resource base from US$250 billion to US$750 billion.  The IMF’s concessional lending capacity to LICs will be ten times higher in 2014 than before the crisis.
The IMF has announced that it has drawn lessons from the East Asian crisis of 1997-98, when its emergency lending was tied to pro-cyclical policies, such as fiscal austerity measures and higher interest rates, which led borrowing countries into even deeper crisis, causing massive job losses and an economic recession that could have been avoided.  The Fund’s official position now is that it has reformed its programs and provided greater flexibility for LICs to adopt expansionary policies.
The IMF is still prescribing pro-cyclical policies that constrain public spending
Despite pledges to address the crisis in flexible and innovative ways, the IMF’s key objective in crisis loans remains “macroeconomic stability” through the “tightening of monetary and fiscal policies.”
Since the onset of the financial crisis in 2008, IMF crisis loans have required policies such as:
•        lowering fiscal deficits and inflation levels;
•        buffering international reserves (as they fell to dismal levels from the impact of the trade shock in this financial crisis);
•         reducing or restraining public spending (through public sector wage freezes and pension freezes, cutting minimum wages, eliminating subsidies to fuel, gas and power, and hiking utility tariffs and tax reforms);
•        increasing official interest rates or restraining the growth of the money supply;
•        preventing currency depreciation; and,
•        providing financial sector liquidity where needed.
Instead of increasing government expenditure and boosting domestic demand, local employment and economic activity to overcome the recession, the IMF is cutting spending and increasing tariffs and taxes in already contracting economies for the purpose of maintaining low inflation and fiscal deficit rates, flexible exchange rates, and trade and financial liberalization. The burdens of these questionable policies, intended to maintain investor confidence, access to external capital and sustainable debt situations, fall squarely on the shoulders of local taxpayers and consumers.
The impacts of the recent financial crisis have threatened key elements of the progress made by LICs over the past several decades. For LICs as a whole, economic growth decelerated to 7.2 percent in 2008, in which industry and manufacturing took the brunt of the contraction in world demand. Exports and imports were hit by the trade shock, falling to 25 and 36 percent of GDP, respectively.  Workers’ remittances decreased to 5.1 percent of GDP in 2008 from 5.7% in 2007.  Perhaps the largest decline was seen in the decline of foreign exchange reserves in LICs, which plummeted to 4.1 months of import payments in 2008, from a previous high of 6.2 months in 2002.
A study by academics at the School of Oriental and African Studies (SOAS) finds that in 13 LICs with IMF programs, pro-cyclical fiscal and monetary policies are still being imposed. During the brunt of the food and fuel price crisis of 2008, and the financial crisis of 2009, marginally higher deficits were permitted. However, the fiscal flexibility of the IMF proved to be short-lived, as the Fund has already begun advocating tighter fiscal policies starting this year (2010).
Latest IMF projections for the countries assessed show that the fiscal expansion projected for 2009 amounts to only 1.5 percent of GDP on average, and a fiscal tightening of 0.5 percent of GDP is projected for 2010. Eight of the 13 countries are facing tighter fiscal constraints in 2010 than in 2009. While this suggests greater flexibility compared to the Fund’s pre-crisis targets for lowering fiscal deficits, it is not a significant revision of the IMF’s framework, and cannot be equated to a genuine provision of fiscal policy space for LICs.
An alternative macroeconomic framework that would allow for policy space would incorporate the judgment that fiscal policy has to play a central role in driving the development process, and thus has to take the form of expansionary, public-investment-led fiscal policies. However, the IMF only assesses fiscal policy in terms of the costs of financing a fiscal deficit, while failing to factor in the costs of foregone growth and poverty reduction if the widening of the deficit were not allowed. The IMF also fails to dynamically assess the budgetary position of LICs based on the potential for mobilizing additional domestic revenue, or for creating greater fiscal space with additional debt relief initiatives or expanded grant assistance.
A recent study by academic John Weeks at the Centre for Development Policy and Research in London argues that the IMF is mistaken in emphasizing the reliance on monetary policies in many low-income countries in sub-Saharan African because of the absence of viable domestic markets for government bonds or commercial banking sectors interested in lending for private-sector investment. According to the study, “As a result, central banks often have to offer high rates of interest on government bonds to induce banks to buy them. Thus, a significant share of the public budget is diverted into debt servicing that ends up fattening banking profits.”
A study by the United Nations Children’s Fund (UNICEF) on 86 recent IMF country reports (Article IV agreements and loan documents) in both low- and middle-income developing countries has also concluded that the Fund advises governments to withdraw fiscal stimulus or cut public spending. In two-thirds of the 86 countries reviewed, the IMF recommends cutting total public expenditures in 2010.  
In all but a few countries, the Fund recommends further fiscal adjustment in 2011.  Furthermore, the IMF calls for curtailing wage bills, removing subsidies, especially those for fuel, and reforming and further targeting social programs. UNICEF states that fiscal austerity measures, particularly in a context where economic recovery has yet to gain traction, entails serious human and economic costs that undermine efforts towards achieving the Millennium Development Goals (MDGs). 
The United Nations (UN) has also critiqued the Fund’s contractionary policies in its flagship annual report, the World Economic Situation and Prospects 2010. The report stated: “Despite pronounced intentions, many recent IMF country programs contain pro-cyclical conditions that can unnecessarily exacerbate an economic downturn in a number of developing countries. Indeed, amid sharply falling global demand, the Fund has been advocating belt-tightening for many developing program countries. At the same time, it has been praising advanced economies for their unprecedented efforts in borrowing and spending their way out of recession. The IMF should expand the use of its resources to help support counter-cyclical measures in those developing countries that have sustainable public finances in the medium-term but are impeded in this effort by adverse market conditions.

Towards growth- and development-oriented fiscal and monetary policies
A more development-oriented macroeconomic policy stance is necessary in order to generate the quantum leap in resources that LICs require to finance large-scale new investments in economic and social infrastructure, which includes the specific MDG goals in the health and education sectors, and job creation. Progress on poverty reduction and basic human development has historically required, and continues to require, such a critical degree of spending and investment in the domestic economy. The experience of the ‘Great Recession’ of 2007-2009 has altered the terms of the debate on macroeconomic policies. However, the current debate has been mostly limited to advocacy for expansionary (i.e., counter-cyclical) policies without any real debate about the need to emphasize the role of deficit-financing.
The social outcomes represented by the MDGs need to be made explicit and taken into account as part of the macroeconomic policy-making process; otherwise, the MDG development agenda will continue to collide with the stability-focused macroeconomic policies.
Furthermore, while the Fund has recommended and included social safety net spending in most of its loan programs, the presence of social protection systems should not become an effort to merely compensate for the social dislocations generated by a pro-cyclical and deflationary macroeconomic policy framework.  
Instead, social protection systems should be complementary and supplementary to an expansionary macroeconomic framework that prioritizes social and economic spending, even at the expense of higher inflation rates and deficit levels when appropriate analyses of the trade-offs are assessed.   Until the domestic economic and social infrastructure has built a healthy level of capacity and resources, the prioritization on spending with high economic and human returns should be supported by IMF, and other IFI, loans and grants to low-income countries.
In order to support inclusive and long-term economic development in low-income countries, IMF policies need to change:
•        The IMF should not only permit, but also support, the active use of fiscal policy to support public investments and public spending to build essential economic and social infrastructures, on which private investment too inevitably relies. Future revenues expected from the investment should pay off the debt that the government initially incurred;
•        The IMF should encourage more expansionary monetary options that better enable domestic firms and consumers to access affordable credit for expanding production, employment, and increased contributions to the domestic tax base. Monetary policy should thus maintain low real interest rates, rather than ineffectively trying to keep inflation low with high interest rates which dampen aggregate demand and growth prospects;
•        The IMF should support exchange rate management in its developing-country member states in order to foster broad-based export competitiveness that can lead to greater structural diversification of the domestic economy; and,
•        The IMF should permit the regulation of the capital account to confront the continuous inflow, as well as outflow, of private capital from national economies, i.e. ‘capital flight.
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The World Bank and International Monetary Fund (IMF) are two of the most powerful international financial institutions in the world. They are the major sources of lending to African countries, and use the loans they provide as leverage to prescribe policies and dictate major changes in the economies of these countries. The World Bank is the largest public development institution in the world, lending over $24 billion in 2007 of which over $5 billion (or 22 percent) went to Africa.
The World Bank and IMF are controlled by the world's richest countries, particularly the U.S., which is the main shareholder in both institutions. The World Bank, headquartered in Washington, DC, follows a "one dollar, one vote" system whereby members with the greatest financial contributions have the greatest say in decision making. The U.S. holds roughly 17% of the vote in the World Bank and the 48 sub-Saharan African countries together have less than 9% of the votes. The Group of 7 rich countries (G-7) control 45% of World Bank votes. Highlights in the Evolution of IMF Lending
2000

The UN Millennium Development Goals are agreed by world leaders at the UN Millennium Summit.

2001
2005

Argentina suffers a financial crisis and a deep recession, defaults on its debt, and is forced to abandon its currency board pegging the peso to the U.S. dollar.
The G-8 launch the Multilateral Debt Relief Initiative and the IMF agrees to forgive 100 percent of the $3.3 billion debt owed to it by 19 of the world's poorest countries.




World Bank Role on South Asia
Ø  Nepal
Ø  Bangladesh
Ø  Sri lanka
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Program (GFRP) to help ease the pressure on the country’s budget, under which the government was struggling to fund the expansion of food-related spending, including social protection programs. Under GFRP, Afghanistan received $8 million for the rehabilitation of about 500 small, traditional irrigation schemes.
The Bank is also focused on helping South Asian countries cope with the impact of the global economic crisis. In Pakistan, the Bank approved $500 million to support the government’s program to regain and maintain economic stability and steer the economy back onto a higher growth path. In India, the Bank approved a $400 million loan to improve access to finance for the country’s small and medium enterprises, which face serious challenges in accessing adequate and timely financing on competitive terms, particularly long-term loans
The Bank is working to address South Asia’s vast urban and rural infrastructure deficits, which often are cited as the greatest constraint to sustained, rapid growth. More than 40 percent of India’s population, for example, is without electricity, and the high cost of erratic and insufficient power supply hurts industry as well as households. The new country strategy for India plans to fast-track much-needed infrastruc­ture development. In fiscal 2009, the Bank approved a $400 million loan to the Power Grid Corporation of India, financing designed to increase reliable power exchange between regions and states.
Bangladesh faces similar energy sector problems. Manufacturers surveyed in the Bank’s most recent Investment Climate Assessment estimate that power shortages reduce sales by about 12 percent a year. To help address the problem, the Bank approved $350 million in fiscal 2009 for the Siddhirganj Peaking Power Project, designed to increase reliable power during periods of peak demand. The project builds on the Bank Group’s long history of involvement in Bangladesh’s energy sector, including support to the successful Rural Electrification and Renewable EnergyDevelopment Program, which has helped bring power to hundreds of thousands of consumers through grid connections and solar home systems. And in Nepal, the Bank committed $89.2 million in response to the country’s unprecedented energy crisis, in which grid-based consumers were supplied with electricity for only eight hours per day.
Inadequate road infrastructure is also a critical constraint for sustainable and inclusive growth in South Asia. In Sri Lanka, national roads carry more than 70 percent of all traffic. But uncontrolled roadside development, years of neglect and poor road maintenance have resulted in low travel speeds and poor levels of service. To help improve the country’s roads, the Bank approved $98 million in additional financing for the ongoing Road Sector Assistance Project, which has so far improved and completed 420 kilometers of national roads across the island
South Asia suffers from some of the worst human deprivation in the world. It has the largest number of undernourished children in the world, and an estimated 26 million children remain out of school. But the region has also made impressive gains. Bangladesh, for example, has achieved gender parity in secondary schools. Building on this achievement, the Bank approved a $130.7 million credit to improve quality and increase access to and equity of secondary education in the country in fiscal 2009.
Similar progress has not been realized in higher education in Bangladesh: at 6 percent, the country’s tertiary enrollment rate is one of the lowest in the world. In fiscal 2009, the Bank provided $81 million to improve the quality and relevance of teaching and research in higher education institutions in Bangladesh.
The Bank continues to be heavily engaged in South Asia’s health sector. In a major new attack on malaria, kala azar, and polio, the Bank provided $521 million to boost prevention, diagnosis, and treatment.
Pakistan’s external debt and liabilities reduced by $942 million or 1.7 per cent to $54.32 billion by end of March 2010 as compared with $55.26 billion in January 2010, according to latest official data.
However, the external debt and liabilities, which were $43.14 billion in 2008, have now reached $54.32 billion, showing 26 per cent increase in the last two years.
The total medium and long-term external debt and liabilities on March 31, 2010 reached $41.83 billion and short-term debt remained at $600 million. The total sum of these two loans is $42.43 billion and is known as Public and Publicly Guaranteed Debt. By January 2010 the sum total of these two types of external debts was $43.23 billion, which reduced by $0.79 billion in the last two months.
It further consists of external loan taken from sources like multilateral, bilateral, issuing of bonds, commercial banks and defence.
In the last two months, multilateral external debt and liabilities reduced to $23.22 billion from earlier $23.73 billion. The break-up of this category is $11.06 billion from Asian Development Bank (ADB), $1.7 billion from International Bank for Reconstruction and Development (IBRD) and $9.83 billion from International Development Association (IDA).
From other sources the government took $616 million by March 31 2010. These sources are European Investment Bank (EIB) $63 million, Islamic Development Bank (IDB) $319 million, International Fund for Agricultural Development (IFAD) $187 million, NORD Development Fund $15 million, and OPEC fund $23 million.
Total loan from bilateral bases reached $16.57 billion on March 31 2010, which was $16.66 billion by January 2010, showing a decrease of $93 million in the last two months. The bilateral external debt composed of two sources-Paris Club Countries ($14 billion) and Non-Paris Club Countries ($2.55 billion) by end of March 2010.
Paris Club Countries included various countries, which are Austria $67 million, Belgium $34 million, Canada $531 million, Finland $6 million, France $2.17 billion, Germany $1.82 billion, Italy $105 million, Japan $6.67 billion, Korea $476 million, Netherlands $117 million, Norway $21 million, Russia $121 million, Spain $80 million, Sweden $153 million, Switzerland $108 million, United Kingdom $10 million, United States $1.51 billion.
Non-Paris Club Countries’ external debt and liabilities reached $2.55 billion till end of March 2010. These countries are China $1.88 billion, Kuwait $105 million, Libya $5 million, Saudi Arabia $442 million and United Arab Emirates $121 million.
Total liabilities on issuing different bonds etc reached $1.57 billion by end of March 2010, which was $2.15 billion in January 2010.
The foreign debt and liabilities from the commercial banks reached $275 million by end of March 2010, while it was $166 million in January 2010.
On defence, external debt and liabilities remained $199 million by end of March 2010 and the same amount was recorded on January 1, 2010 while total short-term debt from IBD reached $600 million by end of March 2010, which was $320 million in January 2010.
Total banking sector debt of the country reached $262 million till end of March 2010, which consists of long-term $120 million and short-term $142 million. While in January 2010 the banking sector debt of the country reached $196 million, which consists of long-term $126 million and short-term $70 million.

the government has geared up its efforts to borrow from both the State Bank and scheduled banks accumulating the domestic debt to record new peaks as it added over Rs800 billion in a year.
It looks that the government is in a fix as higher borrowing from the State Bank attracts stern warning from the International Monetary Fund (IMF) while borrowing from schedule banks catches the attention of State Bank.
The IMF restricts government borrowing from the Central Bank as it is inflationary while borrowing from scheduled banks is criticised by the SBP which is issuing cautions that borrowing leaves little room for private sector credit growth.
The serious shortage of revenue compelled the government to borrow from the banking system which resulted in a new record last year. The situation during the first four months of the current fiscal year looks more compelling for the government to borrow from all possible resources.
The government made drastic cut in the allocated funds for development programmes during the last fiscal year while the officially available indictors show that the situation is grimmer this year.
The latest report shows that the government has so far borrowed about Rs200 billion from the State Bank while it has collected Rs71 billion from the scheduled banks.
If government continues to borrow at this pace, another Rs1 trillion would be added into the domestic debt.
Economists believe that the government could hardly generate Rs1.7 trillion as revenue during this fiscal year primarily due to expected poor economic growth.
The domestic debt rose to Rs4.863 trillion by August 2010 while it was Rs4.050 trillion in August 2009.
In 12 months, Rs813 billion were added to domestic debt.
While the government is busy to raise its revenue and imposed flood surcharge, the heavy borrowing seems to have already set new records.
Last year the government set new record of borrowing from scheduled banks which attracted wide criticism by the SBP and independent economists and blamed the government for poor performance of the private sector.
The borrowing from the State Bank during the first four months was much higher than the same period of last year indicating that a new record has already been set. Last year, in the first four months the government borrowing from SBP was minus 17 billion while this year it has reached Rs200 billion.
However, borrowing from scheduled banks was lower. It was Rs71 billion in first four months while it was Rs131 billion during the same period of last year.The heavy borrowing accelerated the growth of broad money which is double than the last year.
The SBP reported the monetary growth was 2.74 per cent from July to Nov 5 against 1.48 per cent during the same period of last year.


Monday 25 April 2011

Balance Scorecard


*      Which types of goods produced here?

*      What is unit cost which goods are produced here?


*      If company launched new product what is the procedure?


*      Whose are the main customers of your products?


*      Time of delivery goods to customers?


*      What your company preferred your main customer?


*      What the suppliers of your company corporate with your company?

*      Which type of technology is used here? Latest or old.


*      What the main customers are satisfied with your company?

*      What your company gives training of new employees?


*      What is the value of your company in market?
*      What is the sale of your company per month?

*      What is the revenue of your company?


*      What is the internal environment of your company like (behavior between senior management and employees?)

*      What is the learning of your company from previous year?


*      What are the expectations of your company in future?

*      How the company introduced new product in market?


*      Whose are the main competitors of your company in market?

*      What is the percentage of ROI(return on investment)?


*      What was the profit of your company in last year?


Thursday 14 April 2011

Time value of money


Time value of money
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The time value of money is the value of money figuring in a given amount of interest earned over a given amount of time.
For example, 100 dollars of today's money invested for one year and earning 5 percent interest will be worth 105 dollars after one year. Therefore, 100 dollars paid now or 105 dollars paid exactly one year from now both have the same value to the recipient who assumes 5 percent interest; using time value of money terminology, 100 dollars invested for one year at 5 percent interest has a future value of 105 dollarsThis notion dates at least to Martín de Azpilcueta (1491–1586)
The method also allows the valuation of a likely stream of income in the future, in such a way that the annual incomes are discounted and then added together, thus providing a lump-sum "present value" of the entire income stream.
All of the standard calculations for time value of money derive from the most basic algebraic expression for the present value of a future sum, "discounted" to the present by an amount equal to the time value of money. For example, a sum of FV to be received in one year is discounted (at the rate of interest r) to give a sum of PV at present: PV = FV − r·PV = FV/(1+r).
Some standard calculations based on the time value of money are:
Present value The current worth of a future sum of money or stream of cash flows given a specified rate of return. Future cash flows are discounted at the discount rate, and the higher the discount rate, the lower the present value of the future cash flows. Determining the appropriate discount rate is the key to properly valuing future cash flows, whether they be earnings or obligations.[2]
Present value of an annuity An annuity is a series of equal payments or receipts that occur at evenly spaced intervals. Leases and rental payments are examples. The payments or receipts occur at the end of each period for an ordinary annuity while they occur at the beginning of each period for an annuity due.[3]
Present value of a perpetuity is an infinite and constant stream of identical cash flows.[4]
Future value is the value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today.[5]
Future value of an annuity (FVA) is the future value of a stream of payments (annuity), assuming the payments are invested at a given rate of interest
Present value of a future sum
The present value formula is the core formula for the time value of money; each of the other formulae is derived from this formula. For example, the annuity formula is the sum of a series of present value calculations.
The present value (PV) formula has four variables, each of which can be solved for:
  1. PV is the value at time=0
  2. FV is the value at time=n
  3. i is the interest rate at which the amount will be compounded each period
  4. n is the number of periods (not necessarily an integer)
The cumulative present value of future cash flows can be calculated by summing the contributions of FVt, the value of cash flow at time=t
Note that this series can be summed for a given value of n, or when n is .[7] This is a very general formula, which leads to several important special cases given below.
[edit] Present value of an annuity for n payment periods
In this case the cash flow values remain the same throughout the n periods. The present value of an annuity (PVA) formula has four variables, each of which can be solved for:
  1. PV(A) is the value of the annuity at time=0
  2. A is the value of the individual payments in each compounding period
  3. i equals the interest rate that would be compounded for each period of time
  4. n is the number of payment periods.
To get the PV of an annuity due, multiply the above equation by (1 + i).
[edit] Present value of a growing annuity
In this case each cash flow grows by a factor of (1+g). Similar to the formula for an annuity, the present value of a growing annuity (PVGA) uses the same variables with the addition of g as the rate of growth of the annuity (A is the annuity payment in the first period). This is a calculation that is rarely provided for on financial calculators.
Where i ≠ g :
To get the PV of a growing annuity due, multiply the above equation by (1 + i).
Where i = g :
[edit] Present value of a perpetuity
When , the PV of a perpetuity (a perpetual annuity) formula becomes simple division.
[edit] Present value of a growing perpetuity
When the perpetual annuity payment grows at a fixed rate (g) the value is theoretically determined according to the following formula. In practice, there are few securities with precise characteristics, and the application of this valuation approach is subject to various qualifications and modifications. Most importantly, it is rare to find a growing perpetual annuity with fixed rates of growth and true perpetual cash flow generation. Despite these qualifications, the general approach may be used in valuations of real estate, equities, and other assets.
This is the well known Gordon Growth model used for stock valuation.
[edit] Future value of a present sum
The future value (FV) formula is similar and uses the same variables.
[edit] Future value of an annuity
The future value of an annuity (FVA) formula has four variables, each of which can be solved for:
  1. FV(A) is the value of the annuity at time = n
  2. A is the value of the individual payments in each compounding period
  3. i is the interest rate that would be compounded for each period of time
  4. n is the number of payment periods
[edit] Future value of a growing annuity
The future value of a growing annuity (FVA) formula has five variables, each of which can be solved for:
Where i ≠ g :
Where i = g :
  1. FV(A) is the value of the annuity at time = n
  2. A is the value of initial payment paid at time 1
  3. i is the interest rate that would be compounded for each period of time
  4. g is the growing rate that would be compounded for each period of time
  5. n is the number of payment periods
[edit] Derivations
[edit] Annuity derivation
The formula for the present value of a regular stream of future payments (an annuity) is derived from a sum of the formula for future value of a single future payment, as below, where C is the payment amount and n the period.
A single payment C at future time m has the following future value at future time n:
Summing over all payments from time 1 to time n, then reversing the order of terms and substituting k = nm:
Note that this is a geometric series, with the initial value being a = C, the multiplicative factor being 1 + i, with n terms. Applying the formula for geometric series, we get
The present value of the annuity (PVA) is obtained by simply dividing by (1 + i)n:

Another simple and intuitive way to derive the future value of an annuity is to consider an endowment, whose interest is paid as the annuity, and whose principal remains constant. The principal of this hypothetical endowment can be computed as that whose interest equals the annuity payment amount:
Principal = C / i + goal
Note that no money enters or leaves the combined system of endowment principal + accumulated annuity payments, and thus the future value of this system can be computed simply via the future value formula:
FV = PV(1 + i)n
Initially, before any payments, the present value of the system is just the endowment principal (PV = C / i). At the end, the future value is the endowment principal (which is the same) plus the future value of the total annuity payments (FV = C / i + FVA). Plugging this back into the equation:
[edit] Perpetuity derivation
Without showing the formal derivation here, the perpetuity formula is derived from the annuity formula. Specifically, the term:
can be seen to approach the value of 1 as n grows larger. At infinity, it is equal to 1, leaving as the only term remaining.
[edit] Examples
[edit] Example 1: Present value
One hundred euros to be paid 1 year from now, where the expected rate of return is 5% per year, is worth in today's money:
So the present value of €100 one year from now at 5% is €95.24.
[edit] Example 2: Present value of an annuity — solving for the payment amount
Consider a 10 year mortgage where the principal amount P is $200,000 and the annual interest rate is 6%.
The number of monthly payments is
and the monthly interest rate is
The annuity formula for (A/P) calculates the monthly payment:
This is considering an interest rate compounding monthly. If the interest were only to compound yearly at 6%, the monthly payment would be significantly different.
[edit] Example 3: Solving for the period needed to double money
Consider a deposit of $100 placed at 10% (annual). How many years are needed for the value of the deposit to double to $200?
Using the algrebraic identity that if:
then
The present value formula can be rearranged such that:
(years)
This same method can be used to determine the length of time needed to increase a deposit to any particular sum, as long as the interest rate is known. For the period of time needed to double an investment, the Rule of 72 is a useful shortcut that gives a reasonable approximation of the period needed.
[edit] Example 4: What return is needed to double money?
Similarly, the present value formula can be rearranged to determine what rate of return is needed to accumulate a given amount from an investment. For example, $100 is invested today and $200 return is expected in five years; what rate of return (interest rate) does this represent?
The present value formula restated in terms of the interest rate is:
see also Rule of 72
[edit] Example 5: Calculate the value of a regular savings deposit in the future.
To calculate the future value of a stream of savings deposit in the future requires two steps, or, alternatively, combining the two steps into one large formula. First, calculate the present value of a stream of deposits of $1,000 every year for 20 years earning 7% interest:
This does not sound like very much, but remember - this is future money discounted back to its value today; it is understandably lower. To calculate the future value (at the end of the twenty-year period):
These steps can be combined into a single formula:
[edit] Example 6: Price/earnings (P/E) ratio
It is often mentioned that perpetuities, or securities with an indefinitely long maturity, are rare or unrealistic, and particularly those with a growing payment. In fact, many types of assets have characteristics that are similar to perpetuities. Examples might include income-oriented real estate, preferred shares, and even most forms of publicly-traded stocks. Frequently, the terminology may be slightly different, but are based on the fundamentals of time value of money calculations. The application of this methodology is subject to various qualifications or modifications, such as the Gordon growth model.
For example, stocks are commonly noted as trading at a certain P/E ratio. The P/E ratio is easily recognized as a variation on the perpetuity or growing perpetuity formulae - save that the P/E ratio is usually cited as the inverse of the "rate" in the perpetuity formula.
If we substitute for the time being: the price of the stock for the present value; the earnings per share of the stock for the cash annuity; and, the discount rate of the stock for the interest rate, we can see that:
And in fact, the P/E ratio is analogous to the inverse of the interest rate (or discount rate).
Of course, stocks may have increasing earnings. The formulation above does not allow for growth in earnings, but to incorporate growth, the formula can be restated as follows:
If we wish to determine the implied rate of growth (if we are given the discount rate), we may solve for g:
[edit] Continuous compounding
Rates are sometimes converted into the continuous compound interest rate equivalent because the continuous equivalent is more convenient (for example, more easily differentiated). Each of the formulæ above may be restated in their continuous equivalents. For example, the present value at time 0 of a future payment at time t can be restated in the following way, where e is the base of the natural logarithm and r is the continuously compounded rate:
This can be generalized to discount rates that vary over time: instead of a constant discount rate r, one uses a function of time r(t). In that case the discount factor, and thus the present value, of a cash flow at time T is given by the integral of the continuously compounded rate r(t):
Indeed, a key reason for using continuous compounding is to simplify the analysis of varying discount rates and to allow one to use the tools of calculus. Further, for interest accrued and capitalized overnight (hence compounded daily), continuous compounding is a close approximation for the actual daily compounding. More sophisticated analysis includes the use of differential equations, as detailed below.
[edit] Examples
Using continuous compounding yields the following formulas for various instruments:
Annuity
Perpetuity
Growing annuity
Growing perpetuity
Annuity with continuous payments
[edit] Differential equations
Ordinary and partial differential equations (ODEs and PDEs) – equations involving derivatives and one (respectively, multiple) variables are ubiquitous in more advanced treatments of financial mathematics. While time value of money can be understood without using the framework of differential equations, the added sophistication sheds additional light on time value, and provides a simple introduction before considering more complicated and less familiar situations. This exposition follows (Carr & Flesaker 2006, pp. 6–7).
The fundamental change that the differential equation perspective brings is that, rather than computing a number (the present value now), one computes a function (the present value now or at any point in future). This function may then be analyzed – how does its value change over time – or compared with other functions.
Formally, the statement that "value decreases over time" is given by defining the linear differential operator as:
This states that values decreases (−) over time ( ) at the discount rate (r(t)). Applied to a function it yields:
For an instrument whose payment stream is described by f(t), the value V(t) satisfies the inhomogeneous first-order ODE ("inhomogeneous" is because one has f rather than 0, and "first-order" is because one has first derivatives but no higher derivatives) – this encodes the fact that when any cash flow occurs, the value of the instrument changes by the value of the cash flow (if you receive a $10 coupon, the remaining value decreases by exactly $10).
The standard technique tool in the analysis of ODEs is the use of Green's functions, from which other solutions can be built. In terms of time value of money, the Green's function (for the time value ODE) is the value of a bond paying $1 at a single point in time u – the value of any other stream of cash flows can then be obtained by taking combinations of this basic cash flow. In mathematical terms, this instantaneous cash flow is modeled as a delta function δu(t): = δ(tu).
The Green's function for the value at time t of a $1 cash flow at time u is
where H is the Heaviside step function – the notation ";u" is to emphasize that u is a parameter (fixed in any instance – the time when the cash flow will occur), while t is a variable (time). In other words, future cash flows are exponentially discounted (exp) by the sum (integral, ) of the future discount rates ( for future, r(v) for discount rates), while past cash flows are worth 0 (H(ut) = 1 if t < u,0 if t > u), because they have already occurred. Note that the value at the moment of a cash flow is not well-defined – there is a discontinuity at that point, and one can use a convention (assume cash flows have already occurred, or not already occurred), or simply not define the value at that point.
In case the discount rate is constant, this simplifies to
where (ut) is "time remaining until cash flow".
Thus for a stream of cash flows f(u) ending by time T (which can be set to for no time horizon) the value at time t, V(t;T) is given by combining the values of these individual cash flows:
This formalizes time value of money to future values of cash flows with varying discount rates, and is the basis of many formulas in financial mathematics, such as the Black–Scholes formula with varying interest rates