3/3/2022
Finance
(FIN200)
Interest Rates and Security Valuation
Pierre Rostan, Ph.D.
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Business Cycle
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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The Business Cycle
• Recurring patterns of recession and recovery
• Peak
• Trough
Exercise 1: Define 1) A peak. 2) A trough 3) A Contraction 4) An
Expansion.
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
The Business Cycle
• Recurring patterns of recession and recovery
• Peak
• Trough
Exercise 1, solution: 1) A peak is the transition from the end of an expansion to the start of a
contraction. 2) A trough occurs at the bottom of a recession just as the economy enters a
recovery. 3) Contraction is the period from peak to trough. 4) Expansion is the period from
trough to peak.
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The Business Cycle
• Exercise 2: Industry relationship to business cycles
• Define…
• Cyclical industries
• Defensive
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The Business Cycle
• Exercise 2 (solution): Industry relationship to business cycles
• Define…
• Cyclical industries
• Industries with above average sensitivity to the state of the
economy
• Defensive
• Industries with below average sensitivity to the state of the
economy
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Exercise 3: For each pair of firms, choose the one that you think
would be more sensitive to the business cycle.
a. General autos or general pharmaceuticals.
b. friendly airlines or happy cinemas.
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Exercise 3, solution: For each pair of firms, choose the one that you
think would be more sensitive to the business cycle.
a. General autos or general
pharmaceuticals.
b. friendly airlines or happy cinemas.
• General Autos. Pharmaceutical purchases are less discretionary
than automobile purchases.
• Friendly Airlines. Travel expenditures are more sensitive to the
business cycle than movie consumption.
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Sensitivity to Business Cycle
• Factors affecting sensitivity of earnings to business cycles
• Sensitivity of sales of the firm’s product to the business cycles
• Sales:
• Cyclicals: durable goods, anything whose purchase is likely to be
delayed during a recession, this will include items that are less
likely to be purchased when income is not growing or falling.
• Exercise 4: Cyclicals, provide examples
• Defensive: provide examples
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Sensitivity to Business Cycle
• Factors affecting sensitivity of earnings to business cycles
• Sensitivity of sales of the firm’s product to the business cycles
• Sales:
• Cyclicals: durable goods, anything whose purchase is likely to be
delayed during a recession, this will include items that are less likely
to be purchased when income is not growing or falling.
• Exercise 4. solution: Cyclicals, provide examples These might
include discretionary goods like jewelry, expensive vacations, RVs,
machine tools, steel, autos and transportation
• Defensive: provide examples food producers and food processors,
pharmaceutical firms, medical services and public utilities, tobacco,
movies, cheap beers
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Industry Cyclicality
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• Exercise 5: Here are four industries and four forecasts for the
macroeconomy. Choose the industry that you would expect to
perform best in each scenario.
• Industries: housing construction, health care, gold mining, steel
production.
• Economic forecasts:
• Deep recession: falling inflation, falling interest rates, falling GDP.
• Superheated economy: rapidly rising GDP, increasing inflation and
interest rates.
• Healthy expansion: rising GDP, mild inflation, low unemployment.
• Stagflation: falling GDP, high inflation.
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• Exercise 5, solution: Here are four industries and four forecasts for the
macroeconomy. Choose the industry that you would expect to perform best in
each scenario.
• Industries: housing construction, health care, gold mining, steel production.
• Economic forecasts:
• Deep recession: falling inflation, falling interest rates, falling GDP.
• Superheated economy: rapidly rising GDP, increasing inflation and interest
rates.
• Healthy expansion: rising GDP, mild inflation, low unemployment.
• Stagflation: falling GDP, high inflation.
• Deep recession = Health care (non-cyclical)
• Superheated economy = Steel production (cyclical)
• Healthy expansion = Housing construction (cyclical, but interest rate sensitive)
• Stagflation = Gold mining (counter cyclical)
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Methods of government intervention Hint: FMEDCC
• Fiscal policy (budget and taxes): use of government revenue collection (mainly
taxes) and expenditure (spending) to influence the economy
• Monetary policy: monetary authority of a country controls the supply of
money, targeting a rate of interest for the purpose of controlling inflation,
promoting economic growth and stability. Expansionary (loose) policy increases
the total supply of money in the economy more rapidly than usual, and
contractionary (tight) policy expands the money supply more slowly than usual
or even shrinks it. 2 ways: open market operation, increase or decrease of the
Fed funds rate*, or Fed discount rate** for US.
• External policy (tariff and cap on fund flows)
• Direct legislation (corporate law)
• Competition policy (avoid oligo/monopolies)
• Consumer protection (ombudsman)
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Methods of government intervention
In the US, monetary policy in 2 ways: open market operation, Federal
Bank increases or decreases the Fed funds rate*, or Fed discount rate**
for US.
*Fed funds rate: The interest rate at which a depository institution lends
funds maintained at the Federal Reserve to another depository
institution overnight.
**Federal discount rate: The interest rate at which an eligible financial
institution may borrow funds directly from a Federal Reserve bank.
Banks whose reserves dip below the reserve requirement set by the
Federal Reserve's board of governors use that money to correct their
shortage.
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Federal funds rate (April 12, 2000 – January 1, 2022)
Fed Funds Rate (Current target rate 0.00-0.25%)
On January 1, 2022 = 0.08%
Federal funds rate: The interest rate at which a depository institution lends funds maintained at
the Federal Reserve to another depository institution overnight https://fred.stlouisfed.org/graph/?g=14Et
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European economy
https://fred.stlouisfed.org/series/CLVMEURSCAB1GQEA19
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
European economy: AAA rated bonds: Feb. 14, 2022
Buying negative yielding debt
might be considered similar to
paying a government to guard
your money in a vault. ... Cash
is the most liquid of assets.
But central banks have
imposed negative interest
rates on cash deposits
(-0.50% since 18 Sept. 2019).
The euro area yield curve on
Sept. 17, 2021 shows AAArated euro area central
government bonds
Source:
https://www.ecb.europa.eu/stats/financial_markets_and_interest_rates/euro_area_yield_curves/html/index.en.html
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Exercise 6:
Why using negative
LIBOR interest rates?
• Source: http://www.bbc.com/news/business-32284393
https://www.global-rates.com/en/interest-rates/libor/libor.aspx?mid=949
• First, for banks any excess funds parked at the central bank involve paying the ECB's
negative deposit rate (-0.50%)
• Buying a government bond might be less costly; the German Government Bond 2 Year
Yield was trading at -0.428% (last update 14 Feb. 2022)
• That is part of the reason some banks are lending to each other at negative interest rates including some of the rates known as Libor, in euros, Swiss francs and yen.
• It may be preferable to lend money to another bank or a government rather than paying to
keep it at the central bank.
The London Interbank Offered Rate (LIBOR) is the cost of short-term borrowings on the overseas interbank
market for prime bank borrowers (top 50). When the bank borrowing money from another bank does not
belong to the top 50 banks, a spread is added to the base rate. For example -0.64957% + 0.20% = -0.44957%
https://en.wikipedia.org/wiki/List_of_largest_banks
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Fiscal Policy
• Government spending* and taxing actions to stabilize or spur growth in
the economy
• Most direct policy method in terms of its effect on the economy
(Keynesian policy)
• Often implemented too slowly due to political process
• Leaky budget analogy*
• Fiscal Policy may be insufficient to fine tune an economy, it can be
inflationary
• May be necessary when monetary policy is ineffective such as in the
Financial Crisis of 2008
(*) Government spending are government purchases of goods and services. Examples
include road and infrastructure repairs, national defence, schools, healthcare, and
government workers' salaries. Transfer payments are government payments to individuals.
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Fiscal Policy
• (*)Leaky budget analogy: Government spending is very inefficient and
it can be likened to carrying a leaky bucket to fill up the trough.
• The process is highly politicized and government does not have a profit
motive; hence, it is rarely an efficient operation and much money is
poorly spent, resulting in little growth.
• If growth does not occur, then future taxpayers will face higher taxes to
repay the debt used to finance the spending.
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Monetary Policy
• Manipulation of the money supply to influence economic activity by
influencing the demand for goods and services to be produced and
consumed
• Initial & long run effects
• Potentially long lags
• It changes the incentives to purchase and invest, but may not lead
to desired effect on demand
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Central Bank action: open market operations
e.g. Central Bank sells government bonds
• Decrease in supply = Q1 to Q2
• Rates go up = r1 to r2
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Monetary Policy
The Fed can increase the money supply and lower interest rates in the short term
(albeit with lags up to 18 months to full policy effect), but many believe money
supply creation is inflationary in the long run and the inflation would push interest
rates back up.
This is the expectations problem of monetary policy and it can be self-fulfilling.
In the inflationary periods in the 1970s when the Fed increased the money supply
interest rates fell, but quickly began to rise again due to inflationary expectations in
the economy.
For this reason the Fed tries to keep inflation out of the system.
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Economic cycle
Source: http://ygraph.com/businesscycle
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Monetary policy
•Loose Monetary policy
•Monetary Easing
•Expansionary Monetary policy
•Accommodative monetary policy
•Loose credit
•Easy money policy
•Money supply increases
•Interest rates decrease
•Stimulates economic activity
•Tight Monetary policy
•Monetary Squeeze
•Contractionary Monetary policy
•Tight Monetary policy
•Credit squeeze
•Tight money policy
•Money supply decreases
•Interest rates increase
•Moderates the speed of
economic growth through higher
interest rates.
•Reduces inflation.
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Methods of government intervention
• What is the DAB's Monetary Policy Objective? Da Afghanistan Bank is
responsible and fully empowered to make the monetary policy
decisions in Afghanistan. According to Article 2.1 of DAB Law: "The
primary objective of Da Afghanistan Bank shall be to achieve and to
maintain domestic price stability."
• The other objectives of Da Afghanistan Bank, which shall be
subordinated to the primary objective of Da Afghanistan Bank, shall be
to foster the liquidity, solvency and effective functioning of a stable
market based financial system, and to promote a safe, sound and
efficient national payment system.
• https://dab.gov.af/
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Methods of government intervention
How Does Monetary Policy Work?
• DAB signals its monetary policy stance through adjustments in money supply in the market.
Changes in money supply will impact demand in the economy. To maintain its primary
objective of domestic price stability, Da Afghanistan Bank has adopted a framework which is
known as the Monetary Aggregate Targeting Framework. Controlling liquidity condition is
highly important in the economy; hence any changes in the rate of liquidity have a direct
impact on the overall economic activities in the country. Therefore, changes in liquidity rate
should be consistent with the rate of economic growth as well as the demand for the national
currency in the economy
MP Operational Target
• Under this monetary policy framework, DAB has been using reserve money (RM) as the
primary liquidity indicator since 2010, and projects its precise amount based on the expected
growth rate, the average annual inflation rate, and changes in the aggregate demand for
Afghani during the year. Considering the expansion of the banking sector in the country and its
role in creation of money as well as taking into account the economic conditions, Da
Afghanistan Bank determined Reserve Money (RM) as the key operational target, while
Currency in Circulation (CiC) is set as an indicative target.
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Methods of government intervention
MP Operational Target
• To achieve the operational target, DAB primarily uses Open Market
Operations (OMOs) to manage liquidity in the money market. In case
of excess liquidity available in the market, DAB mops up this surplus
liquidity by using the monetary policy instruments. DAB conducts
Foreign Currency Auctions on weekly basis to sell foreign currency to
licensed Money Service Provides (MSPs) and Capital Notes (CNs)
Auction to sell CNs to commercial banks (https://dab.gov.af/capitalnote) usually with the agreement to purchase the same on the
transaction maturity date. On the contrary, if there is shortage of
liquidity in the system, DAB injects Afghani in the system through
OMOs.
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Monetary Policy Tools
• Central Bank of Afghanistan: As primary instruments for monetary policy, the
Central Bank of Afghanistan uses the sale of currency and the capital note
auction to control the reserve money. http://old.dab.gov.af/en/page/monetary-policy/inflation-rate-outlook
1. Auction Sale of Currency: Under currency trading regulation, the Central Bank of
Afghanistan sells foreign currencies to licensed commercial banks and authorized
money exchange dealers through a free and transparent auction process on biweekly basis.
2. Capital Note Auction: the second tool the Central Bank uses to control the RM
(Reserve Money) is the auction of capital note, which is sold to commercial banks
once a week. To further use the latter instrument that help decreases dependence
on the sale of foreign currencies, the Central Bank announced the capital note with
7 day maturity along with capital notes with 28, 182 and 364 days of maturity,
leading to an increase in investment on the capital notes.
Source: https://dab.gov.af/sites/default/files/2019-01/29RegulatoryCapitalWorksheetIns22112015153521749553325325.pdf
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Reserve money
• Reserve money = Currency in Circulation + Bankers' Deposits with Da Afghanistan
Bank + 'Other' Deposits with Da Afghanistan Bank .
• Among these components, the most important one is currency in circulation. It
includes notes in circulation and coins.
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Monetary Policy Formulation and Decision Making
Monetary Policy Committee
• Monetary Policy Committee (MPC) is established and is chaired by the
Governor of DAB, First Deputy Governor acts as Deputy Chairman,
members of the Supreme Council as members and Monetary Policy
Director General acts as the Secretary of the Committee. The monetary
policy committee closely works with the Monetary Policy Department,
Market Operations Department and Financial Supervision Department.
• MPC responsibility: Monetary Policy Committee is primarily
responsible for setting the stance of monetary policy, which meets four
times a year. MPC vigilantly monitors the developments in the
economy of the country as well as in the international economic arena
and set the targets for Reserve Money and Currency in Circulation and
Net International Reserves. Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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• Aug. 23, 2021: Taliban spokesperson
Zabihullah Mujahid said that Haji
Mohammad Idris - the acting head of
Afghanistan's central bank, will address the
"looming banking issues" of the country.
• The announcement comes at a time when
banks reportedly remain closed in the
country, ATMs are running out of cash and
prices of essential items have risen by as
high as 35 per cent since the group took
over.
• February 11, 2022: US to split $7 billion in Afghan assets between relief, 9/11
victims
US President Joe Biden signed an executive order unfreezing billions in Afghan
funds in US banks. The frozen Afghan central bank assets will be split between
humanitarian aid and the victims of the September 11 attacks.
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
2022: DAB leadership holds meeting with the high ranking official of commercial
banks
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Monetary Policy Formulation and Decision Making
Monetary Policy Committee
MPC Tasks: Monetary Policy Committee's main task is to execute the main tasks of Da
Afghanistan Bank as per the law of Da Afghanistan Bank which are:
1. Formulation, adoption and execution of monetary policy;
2. Formulation of reserve policy and DAB's reserve position in accordance with DAB's Law;
3. Imposing regulations on execution of exchange rate policy and open market operations;
4. Decision making on keeping and management of DAB's reserves as determined in DAB's
law;
5. Approval of regulations to facilitate e-transactions among DAB, banks and their customers;
6. Approval of regulations to regulate repo rates and interest rates;
7. Signing international clearing and payments agreements.
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Monetary Policy Formulation and Decision Making
Monetary Policy Committee.
• MPC Meetings: MPC meetings are held on quarterly basis four times a year. The
supreme council assigns a meeting on monetary policy issues during its quarterly
meetings and its approvals are valid under the approvals of the Supreme Council.
At the end of each MPC meeting, the Chairman holds a press conference to
communicate the decisions made on recent monetary policy issues and
macroeconomic situation as a whole.
• You want to know more about the implementation of DAB’s monetary policy:
https://dab.gov.af/Monetary-Policy-Implementation
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Exchange Rate Policy (Annual)
• In the light of Article 69 of the Da Afghanistan Bank law, formulating, adopting and execution of
exchange rate policy is one of the main responsibilities of Da Afghanistan Bank. Among the
eight exchange rate regimes in the world, Da Afghanistan Bank has adopted the Managed
Floating Exchange Rate regime. Under this exchange rate framework, the exchange rate is
determined by the demand and supply factors in the market.
• This exchange rate regime is adopted based on the economic condition, balance of payments
(exports and imports), and taking into account the degree of openness of the economy
(currency inflow and outflow).
• Under this framework, DAB does not target the exchange rate. Meanwhile, considering the
negative impacts of the exchange rate fluctuations on investors, consumers, and other
economic agents' expectations as well as the level of overall domestic prices; the bank
monitors the exchange rate behavior and puts its efforts to prevent serious fluctuations in the
exchange rate using its monetary policy instruments.
https://www.worldbank.org/en/country/afghanistan/overview
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Overview of economic indicators
The current account consists of the balance of trade, net primary income or factor income and net unilateral
transfers, that have taken place over a given period of time. Balance of trade = exports of goods and
services minus imports. Factor income is income received from the factors of production: the inputs used
in the production of goods or services in order to make an economic profit. Factor income on the use of
land is called rent, income generated from labor is called wages, and income generated from capital is
called profit. net unilateral transfers = remittances, loans from IMF.
Overview
Last
Reference
Previous
GDP Annual Growth Rate (%)
4.03
Dec/19
1.58
Unemployment Rate (%)
11.1
Dec/19
11.1
6.4
Nov/20
6
-18.39 : 13.97
Balance of Trade (USD Million)
-5913
Dec/19
-6531
-8518 : -1661
Current Account (USD Million)
-894
Sep/20
-413
Current Account to GDP (%)
-21.2
Dec/19
-21.7
6.1
Dec/19
7.4
-0.9
Dec/19
-0.4
20
Dec/20
20
Inflation Rate (%)
Government Debt to GDP (%)
Government Budget (% of GDP)
Corporate Tax Rate (%)
Personal Income Tax Rate (%)
Coronavirus Cases (Persons)
Coronavirus Deaths (Persons)
Coronavirus Recovered (Persons)
20
Dec/19
20
55008
Jan/21
54939
2400
Jan/21
2399
45912
Jan/21
45868
Range
-1.8 : 17.2
6.7 : 12.4
-7558 : -413
-75.2 : -20
6.1 : 23
-26.8 : -0.4
0 : 20
20 : 20
0 : 55008
0 : 2400
0 : 45912
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
https://tradingeconomics.com/afghanistan/indicators
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GDP
The Gross Domestic Product (GDP) in Afghanistan was worth 19.81 billion US dollars in 2020, according to official
data from the World Bank. The GDP value of Afghanistan represents 0.02 percent of the world
economy. source: World Bank
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
There are 12 banks operating in Afghanistan consisting of 3 state
banks, 7 private banks and 2 branches of foreign banks.
Name
Bank Millie Afghan
State Owned Bank
2
Pashtany Bank
State Owned Bank
Licensed date
Relicensed 26 July
2004
Relicensed 26 June
2004
Kabul
PIBA AF KA
3
New Kabul Bank
State Owned Bank
18-Apr-11
Kabul
KABU AF KA
4
Private Bank
13-Jun-06
Kabul
AZBAAFKA
5
Azizi Bank
Afghanistan International
Bank
Private Bank
22-Mar-04
Kabul
AFIB AF KA
6
Islamic Bank of Afghanistan
Private Bank
18 March, 2009
Kabul
N/A
1
HQ
Swift
Kabul
BMAFAFKA
7
Maiwand Bank
Private Bank
31-Dec-08
Kabul
N/A
8
Afghan United Bank
Private Bank
4-Oct-07
Kabul
AFGUAFKA
9
The First Micro Finance Bank
Private Bank
18-Mar-04
Kabul
FMFBAFKA
10
Ghazanfar Bank
11
National Bank of Pakistan
12
Bank Alfalah ltd
Private Bank
1-Mar-09
Kabul
Branch Of Foreign Permitted 1st October
Bank
2004
Kabul
Branch Of Foreign
Bank
21-May-05
Kabul
N/A
NBPA AF KA
ALFHAFKA
email
website
info@bma.com.af
www.bma.com.af
info@pashtanybank.
com
www.pashtanybank.com
info@newkabulbank.
www.newkabulbank.af
af
info@azizibank.af
www.azizibank.af
info@aib.af
www.aib.af
info@ibafg.af
www.ibafg.com
info@maiwandbank.
www.maiwandbank.com
com
info@afghanunitedb www.afghanunitedbank.co
ank.com
m
info@fmfb.com
www.fmfb.com.af
info@ghazanfarbank
www.ghazanfarbank.com
.com
nbpkbl.operations@
yahoo.com
www.nbp.com.pk
naeems@bankalfala
www.bankalfalah.com
h.com
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Central bank action: reserve requirement
• The reserve requirement (or cash reserve ratio) is a central bank regulation employed by most, but not
all, of the world's central banks, that sets the minimum amount of reserves that must be held by a
commercial bank.
• The minimum reserve is generally determined by the central bank to be no less than a specified
percentage of the amount of deposit liabilities the commercial bank owes to its customers.
• The commercial bank's reserves normally consist of cash owned by the bank and stored physically in
the bank vault (vault cash), plus the amount of the commercial bank's balance in that bank's account
with the central bank.
• The required reserve ratio is sometimes used as a tool in monetary policy, influencing the country's
borrowing and interest rates by changing the amount of funds available for banks to make loans with.
• Western central banks rarely increase the reserve requirements because it would cause immediate
liquidity problems for banks with low excess reserves; they generally prefer to use open market
operations (buying and selling government-issued bonds) to implement their monetary policy.
• The People's Bank of China uses changes in reserve requirements as an inflation-fighting tool, and
raised the reserve requirement ten times in 2007 and eleven times since the beginning of 2010.
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
How to calculate the minimum reserve requirements?
• European Central Bank: [Overnight deposits + deposits with agreed maturity or period of
notice up to 2 years + debt securities issued with maturity up to 2 years + money market
paper] * 1%
(since 18 Jan. 2012)
Source: https://www.ecb.europa.eu/mopo/implement/mr/html/calc.en.html
• Central Bank of Afghanistan: Da Afghanistan Bank holds other monetary instruments like
Required Reserves, which is also used for the implementation of monetary policy in
addition to ensuring contingency-surveillance objectives.
• At the moment, in Afghanistan, the required reserve ratio is 8 percent on AFN and 10% on
USD.
• Objective of holding a Required Reserve at the Central Bank: to protect depositors.
• Reserves: 9,400 million USD
In view of the economic situation of the country, all banks, FXDs and companies including national merchants will soon adjust
their operations in a normal and regular manner and will conduct their business affairs with complete surety. In the same
manner, Da Afghanistan Bank assures the people that the banking sector is providing banking services to Afghans with
unwavering commitment, transparency and new banking programs. I would like to express my gratitude to the noble people
of Afghanistan for their patience. Regards, Alhaj Abdul Qahir (Mohammad Idrees) Acting Governor of Da Afghanistan Bank
Copyright AUAF 2022 - Pierre Rostan, Ph.D. (15 September 2021)
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Additional information on minimum reserve
requirements in Afghanistan
1. Referenced to Banking Law, Article (11), part (2), the paid-in capital and minimum capital is
one billion AFN.
2. Reference to Circular No. 9172 dated 1399/10/10, upon completion of Jan 2021, the
required reserve rates for AFN and USD are done based on a bank's CAMEL rating, as follow:
Required Reserve Based on CAMEL Ratings of Banks
CAMEL*
1
2
3
4
5
Rating/Currency
USD
8%
9%
10%
12%
14%
AFN
6%
7%
8%
10%
12%
(*) CAMELS is an international rating system used by regulatory banking authorities to rate financial institutions,
according to the six factors represented by its acronym. The CAMELS acronym stands for "Capital adequacy,
Asset quality, Management, Earnings, Liquidity, and Sensitivity."
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Azizi bank as at March 31, 2021
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Minimum regulatory capital ratio
• The Central Bank of Afghanistan: the minimum financial capital requirement of
AFN 250 million (about 2.7 million USD = how much liquid capital -easily sold
assets- they must keep on hand)
• The minimum Tier 1 capital ratio of 6 percent, and
• The minimum regulatory capital ratio of 12 percent.
• The tier 1 capital ratio measures a bank’s core equity capital against its total riskweighted assets—which include all the assets the bank holds that are
systematically weighted for credit risk. For example, a bank’s cash on hand and
government securities would receive a weighting of 0%, while its mortgage loans
would be assigned a 50% weighting.
Source: https://dab.gov.af/sites/default/files/2019-01/29RegulatoryCapitalWorksheetIns22112015153521749553325325.pdf
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Capital adequacy ratio
The capital adequacy ratio is calculated by dividing a bank's capital by its riskweighted assets. The capital used to calculate the capital adequacy ratio is divided
into two tiers.
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Rostan, Ph.D. -
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Yield curve shapes
Expansion, 85% of
the time*
indicator of a pending
economic recession,
5% of the time
Uncertainty, 6% of
the time
Uncertainty, 4%
of the time
(*) Rostan, P. and Rostan A. 2013. Testing quasi-random versus pseudorandom numbers on
Copyright AUAF 2022 - Pierre Rostan, Ph.D. bond option pricing, The IEB International Journal of Finance, vol. 6, pp. 96-115.
Theories of the Term Structure
• Expectations Theory: forward rates equal expected future zero rates,
there is a mathematical relationship between spot rates and forward
rates
• Market Segmentation Theory: short, medium and long rates
determined independently of each other, dynamics of supply and
demand independent on each segment.
• Liquidity Preference Theory: forward rates higher than expected
future zero rates = investors demand a premium for securities with
longer maturities, which entail greater risk, because they would
prefer to hold cash, which entails less risk.
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Expectation Theory
0r1
0
1r2
1
0r2
Annual Percentage Rate with annual compounding
2
(1 +0 r1 )1 (1 +1 r2 )1 = (1 +0 r2 )2
Annual Percentage Rate with continuous compounding
(e1x0 r 1 )(e1x1 r 1 ) = (e2x0 r 2 )
Simple Interest
1 +0 r3/12 ∗
3
3
6
1 +3/12 r6/12 ∗
= 1 +0 r6/12 ∗
12
12
12
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Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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Segmented market approach
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Expectations plus liquidity premium
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Forward Rates
• The forward rate is the future zero rate implied by today’s term
structure of interest rates
• Forward rates are used in Forward Rate Agreements
• FRAs = Over-the-counter contracts between parties that determine
the rate of interest to be paid on an agreed-upon date in the future. The
notional amount is not exchanged, but rather a cash amount based on
the rate differentials and the notional value of the contract.
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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Forward Rates
Assume
8% spot one-year bond
10% expected one-year bond spot rate in 12
months time
11% expected one-year bond spot rate in 24
months time
0r1
0
1r2
1
2r3
2
3
0r3
•Exercise 7: Which of the following today’s rate explains market expectations theory:
a) One year Bond 8.5 %
b) Two year Bond 8 %
c) Three year Bond 9.66%
d) Two year bond 9.66 %
e) Three year Bond 8.5 %
(assume Annual Percentage Rate annually compounded)
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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Forward Rates
Assume
8% spot one year bond
10% expected one year bond spot rate in 12
months time
11% expected one year bond spot rate in 24
months time
0r1
1r2
1
0
2r3
2
3
0r3
•Exercise 7 (solution): Which of the following today’s rate explains
market expectations theory:
a) One year Bond 8.5 %
b) Two year Bond 8 %
c) Three year Bond 9.66%
d) Two year bond 9.66 %
e) Three year Bond 8.5 %
(assume Annual Percentage Rate annually compounded)
Answer: (1+0r1)1(1+1r2)1 (1+2r3)1 =(1+0r3)3
1.08*1.10*1.11 = (1+ 0r3) 3
(1.08*1.10*1.11)1/3 -1 = 0.0966 = 9.66%
55
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Exercise 8: APR compounded annually
Year (n)
Spot rate for
nth-year
(% per annum)
1
3.0
2
4.0
5.0
3
?
5.8
4
5.0
6.2
5
5.5
6.5
0r1
0
Forward rate for
nth- year
(% per annum)
1r2
1
2r3
2
3
0r3
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Exercise 8 (solution): APR compounded annually
0r1
0
Year (n)
Spot rate for
nth-year
(% per annum)
1
3.0
Forward rate for
nth- year
(% per annum)
2
4.0
5.0
3
? = 4.59% =
(1.03*1.05*1.058)1/3 1
5.8
4
5.0
6.2
5
5.5
6.5
1r2
1
2r3
2
(1+0r1)1(1+1r2)1 (1+2r3)1 =(1+0r3)3
1.03*1.05*1.058 = (1+ 0r3) 3
3
(1.03*1.05*1.058)1/3 -1 = 0.0459 = 4.59%
0r3
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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Exercise 9: APR compounded annually
Year (n)
Spot rate for
nth-year
(% per annum)
1
3.0
2
4.0
?
3
4.59
5.8
4
5.0
6.2
5
5.5
6.5
0r1
0
Forward rate for
nth- year
(% per annum)
1r2
1
2
0r2
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Exercise 9: APR compounded annually
Year (n)
Spot rate for
nth-year
(% per annum)
1
3.0
2
4.0
?
3
4.59
5.8
4
5.0
6.2
5
5.5
6.5
0r1
0
1r2
1
0r2
Forward rate for
nth- year
(% per annum)
(1+0r1)1(1+1r2)1 =(1+0r2)2
2
1.03*(1+1r2)1 = (1+ 0.04)2
1r2
= [(1+ 0.04)2 / 1.03]-1
1r2 =
5%
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
59
Debt versus Equity
•There is a wide variety of debt, equity and hybrid
securities currently available in the capital market
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Debt versus equity (cont)
In general, debt is a security which:
1. Pays a contractually fixed rate of return (interest).
2. Has a finite life.
3. In the event of default on payment of interest, the
owners have first call on the assets of the issuer. Debt =
strong claim of creditors against the company assets.
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Debt versus equity (cont): Equity
• Common stock
• Residual claim
• In the event of bankruptcy, what will stockholders receive? Residual ClaimLowest priority in case of bankruptcy. First Debt holders, then preferred, then common.
• Limited liability
• What is the maximum loss on a stock purchase? Limited Liability- Can only lose
your initial investment
• Pays a dividend
• Has an infinite life (based on going-concern concept)
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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The Balance Sheet: definitions of its components
Assets
•Asset = ?
Liabilities
•Liability = ?
•Current assets = ?
•Current liabilities = ?
•Intangible asset = ?
•Noncurrent liabilities = ?
•Fixed assets = ?
Equity
•Equity = ?
•Paid-in capital = ?
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
The Balance Sheet: definitions of its components
Assets
•Asset = valuable item that is owned or
controlled by the entity and that was acquired
at a measurable cost.
•Current assets = cash and assets that are
expected to be converted into cash or used up
within 1 year.
•Intangible asset = asset with no physical
substance, such as goodwill, or the protection
provided by an insurance policy.
•Fixed assets = tangible , noncurrent assets.
Liabilities
•Liability = strong claim against all assets
•Current liabilities = obligations (claims) due
within 1 year
•Noncurrent liabilities = obligations (claims)
due within more than 1 year
Equity
•Equity = ownership, capital obtained by Paidin capital and Retained earnings. Residual
Claim.
•Paid-in capital = amount of capital "paid in" by
investors during common or preferred stock
issuances, including the par value of the shares
themselves = Stocks + additional Paid-in
capital
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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Financial Institutions versus Financial Markets:
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Financial Institutions versus Financial Markets
• Firms that require funds from external sources can obtain them
in three ways:
• through a bank or other financial institution;
• through financial markets;
• through private placements: typically bonds or preferred
stocks to an investor or group of investors, such as insurance
companies or pension funds.
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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Direct Debt Finance
•Corporations issue financial securities to raise
funds in the Debt Capital market
•This is obtained by issuing bonds
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Finance
(FIN200)
Bond Valuation
Pierre Rostan, Ph.D.
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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Valuation of corporate debt
• A standard (senior) bond is collateralized by the assets of the
company (debenture = not collateralized, full faith of the
issuer)
• is a contract between the issuer (borrower) and the investor
(lender) stipulating the issuer’s obligations to make
specified payments on specified future dates
• has a value equal to the present value of all cash flows
associated with holding the bond
‘Cash flows’ consist of periodic interest payments and the
repayment of the face value upon maturity
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
“REGISTERED” BOND: A registered bond is a debt instrument whose bondholder's information
is kept on record with the issuing party. By archiving the owner's name, address, and other
details, issuers ensure they're making the bond's coupon payments to the correct person.
Other type: bearer bond
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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“COUPON” BOND
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Key features of a standard bond
• Typical bond has the six following characteristics:
• Face (maturity) value
• The amount to be repaid on maturity
• Coupon rate
• The annual rate of interest on the bond
• Interest is paid semi-annually/annually, etc.
• Maturity Date
• The date on which the bond matures
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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Key features of a standard bond (cont)
• Term to maturity
• The period of time between now and the maturity date
• Price
• The present value of the cash flows to be received by the
bond holder
• Yield
• The rate of return if the bond is held to maturity
• Yield is a function of current market interest rates and the
riskiness of the bond
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Indentures and Covenants
• An indenture is a formal debt agreement that establishes the terms of a
bond issue, while covenants are the clauses of such an agreement.
• Covenants specify the rights of bondholders and the duties of issuers,
such as actions that the issuer is obligated to perform or is prohibited
from performing.
• In the U.S., federal and state securities and commercial laws apply to the
enforcement of these agreements, which are construed (i.e. interpreted)
by courts as contracts between issuers and bondholders.
• The terms may be changed only with great difficulty while the bonds are
outstanding, with amendments to the governing document generally
requiring approval by a majority (or super-majority*) vote of the
bondholders.
(*)anywhere from 67-90% Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
37
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Indentures and Covenants
(formal debt agreement)
(clauses of such an agreement)
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Variations to a standard bond
Main variations are:
Floating rate (notes) bonds (FRNs)
•The coupon (interest) rate varies periodically, and is
based on a “benchmark” market rate such as LIBOR
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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Variations to a standard bond (cont)
•Deferred coupon bonds
•There are no coupon (interest) payments for a fixed
period after the bond issue
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Variations to a standard bond

Zero-coupon bonds
 no
interest payment. The only cash flow is the face value on
maturity
these bonds are sold at a steep discount
PV 
FV
 r
1  
 n
n*T
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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Exercise 10:
• The value of a 17-year, zero-coupon bond with a maturity
(face) value of $100,000 and a semi-annual-pay yield of
8.22% APR is closest to:
A. $24,618
FV
B. $25,425
PV 
n*T
 r
C. $26,108
1  
 n
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Exercise 10 - solution
Answer: B
PV 
FV
100,000
 0.0822 
1 

2


2*17
 $25,424.76
N
I/Y in percent
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
40
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Copyright AUAF 2022 - Pierre
Rostan, Ph.D. -
Variations to a standard bond (cont)
•Convertible bonds (notes)
•A hybrid security (=mix of debt and equity).
•The bondholder has the option to convert to equity
(shares at a fixed price at a fixed date)
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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Convertible bonds: value
Value of a convertible bond =
MAX(Straight bond or Conversion value) + Option value
Value of the
convertible bond
VALUE OF A CONVERTIBLE BOND
Convertible bond value
Conversion value
Option value
Bond value
Exercise price
Value of the share
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
83
Convertible bonds
Example 1
• A conversion ratio of 45:1 means one bond (with a $1,000 par value) can be
exchanged for 45 shares of stock.
• Or it could be specified at a 50% premium, meaning if the investor chooses to
convert their shares they have to pay the price of the common stock at the time of
issuance plus 50%.
• Basically, these are the same thing said two different ways.
• Example: conversion ratio of 45:1 means that: 1000 / 45 = $22.22 (exercise price of
the option)
• 50% premium means that: price of the common stock at the time of issuance of the
convertible bond (=14.81$) plus 50% = 14.81*1.50 = $22.22
•Assume today that the stock market price is $20.
•Conclusion: in this example, it is not worth converting into stocks.
•It is better to wait until the stock price is $22.22 (breakeven) of greater.
•The investor starts making profit when stock price > $22.22
•Example: stock price = $32.22 at the time of the conversion: Profit $32.22 - $22.22 =
$10 per stock
84
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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Convertible bonds
Example 2
•TSJ Sports issues $10 million in three-year convertible callable bonds with a 5% coupon yield
and a 25% premium.
•This means that TSJ will have to pay $500,000 in interest annually, or a total $1.5 million over
the life of the converts.
•If TSJ’s stock was trading at $40 at the time of the convertible bonds issue, investors would
have the option of converting those bonds for shares at a price of $50 ($40 x 1.25 = $50).
Conversion price is $50.
•Therefore if the stock was trading at say $55 by the bond's expiration date, that $5 difference
per share is profit for the investor.
•However there is usually a cap on the amount the stock can appreciate through the issuer’s
callable provision. For instance, TSJ executives won’t allow the share price to surge to $100
without calling the converts (i.e. convertible bonds).
•Alternatively, if the stock price tanks to $25 the convert holders would still be paid the face
value of the $1,000 bond at maturity.
•This means that convertible bonds limit risk should the stock price plummet, while limiting
exposure to upside price movements of the underlying common stock.
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
85
Variations to a standard bond
(cont)
• Bonds with embedded options
• the bond-holder may have the option to sell the bond back
to the issuer (puttable)
• or the bond-issuer may have the option to buy it back from
the holder (callable) before the maturity date
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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Bonds with embedded options
Puttable bond: the bondholder buys
from the issuer a bond + 1 long put
(cont)
on the bond.
• The bondholder has the right to sell the bond back to the issuer with 1
short put at the face value when interest rates increase and the bond
price is lower than the face value (makes a profit), or whenever the
bondholder is not happy with the management of the firm.
Callable bond: the bondholder buys from the issuer a bond + 1 short call
on the bond.
• 1) When interest rates decrease and bond price is higher than the face
value, the issuer with 1 long call buys back the bond at the face value
from the bondholder (makes a profit); 2) The issuer issues new bonds at a
lower coupon making the cost of borrowing cheaper.
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Options
• Holder, buys = long option; Writer, sells = short option
• Long Call = right to buy the underlying asset for the holder;
obligation to sell for the writer (short call)
• Long Put = right to sell the underlying asset for the holder;
obligation to buy for the writer (short put)
• European option can be exercised only at the end of its life;
• American option can be exercised at any time during its life.
• The holder pays a premium to the writer.
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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Valuation of corporate debt (cont)
• The value of a bond can be determined using the following equation:
  r   n*T  
1  1  

FV
n



PV  PMT 
r

  r  n*T 

 1  
n

  n
where:
T = maturity of the bond
n= number of periods in one year
PMT= the interest payments
FV = the face value of the bond
r
= the cost of debt capital
Copyright AUAF 2022 - Pierre
Rostan, Ph.D. -
Valuation of corporate debt (cont)
Exercise 11:
• Lisholm Ltd has issued bonds earning a 7% APR coupon rate.
The interest is paid semi-annually and the bonds mature in
eight years. The bond face value is $1,000.
• If your required rate of return (=yield) is 8% APR, what is the
current price of the bond?
_______________________________________________
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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Valuation of corporate debt: Exercise 11 (solution)
  r   n*T  
1   1  

FV
n


PV  PMT  
r

  r  n*T 

 1  
n

  n
1  1  .04 16 
16
PV  35
  1000(1  .04)
.04


 407.83  533.91
 $941.74
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Copyright AUAF 2022 - Pierre
Rostan, Ph.D. -
46
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Valuation of corporate debt (cont)
Exercise 12:
• You have just purchased 10 newly issued $100 five-year
ABC Company Ltd. debentures at par (i.e bond price =
face value).
• These debentures pay $6 (per debenture) in interest semiannually.
What is your rate of return (yield) APR?
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Valuation of corporate debt (cont)
Exercise 12: solution
You have just purchased 10 newly issued $100 five year
ABC Company Ltd. debentures at par (i.e bond price =
face value).
These debentures pay $6 (per debenture) in interest
semi-annually.
What is your rate of return?
Since it is at par: Coupon rate = Yield To Maturity = 0.06*2
= 12% coupon = 12% YTM APR semi-annually
compounding.
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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Copyright AUAF 2022 - Pierre
Rostan, Ph.D. -
Valuation of corporate debt (cont)
Exercise 13:
You are also negotiating the purchase of 10 $100 debentures
issued by the DEF Company Ltd. 4 years ago, that return $3 per
debenture in semi-annual interest payments and have six years
remaining to maturity.
What is the maximum price you should offer for the DEF
Company Ltd. debentures, assuming the DEF company is in the
same risk class as the ABC company?
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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Copyright AUAF 2022 - Pierre
Rostan, Ph.D. -
Valuation of corporate debt (cont)
Solution exercise 13:
Maximum price for DEF Co. Debentures
• The appropriate rate to use is r = 6% APR semi-annually
compounding.
• Interest Payment per half year = $3.
• Principal Payment (Year 6) = $100.
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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Valuation of corporate debt (cont)
1  1  r n 
PV  PMT
 FV (1  r )n


r


1  1  0.12 / 22*6 
100
 3.00
+

2*6
0
.
12
/
2

 1  0.12 / 2
 25.15  49.70  $74.85 per debenture
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Bond Value
Maturity and Bond Price Volatility (sensitivity)
Consider two otherwise identical bonds.
The long-maturity bond will have much more
volatility (sensitivity) with respect to changes in
the discount rate.
Par
Short Maturity Bond
Long Maturity
Bond
C
Discount Rate = yield
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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Coupon Rate and Bond Price Volatility (sensitivity)
Bond Value
Consider two otherwise identical bonds.
The low-coupon bond will have much
more volatility (sensitivity) in price with
respect to changes in the discount rate.
High Coupon Bond
Par
Low Coupon Bond
C
Discount Rate
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
September 29, 2021 China Investors brace for rough
ride as Evergrande faces coupon payment deadline
• HONG KONG, Sept 29 (Reuters) - China Evergrande Group (3333.HK) faces its next test in public markets with the
deadline for a bond coupon payment to offshore investors on Wednesday, as the cash-strapped property developer
scrambles to sell some of its assets.
• With liabilities of $305 billion, Evergrande has sparked concerns its problems could spread through China's financial
system and reverberate around the world - a worry that has eased as damage has so far been concentrated in the
property sector.
• Evergrande plans to sell a 9.99 billion yuan ($1.5 billion) stake it owns in Shengjing Bank Co Ltd (2066.HK) to a
state-owned asset management company, the developer said on Wednesday in an exchange filing.
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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Finance
(FIN200)
Stock valuation
Pierre Rostan, Ph.D.
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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Valuation of common stock (equity)
Content
• Dividend Valuation Model
• Constant Growth Model
• Multistage Growth Rate Model
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Valuing Common Stocks
• The value of a stock depends on:
(a)Future Cash Flow Pattern (Dividends) paid to shareholders
(b) Expected Return - The percentage yield that an investor
forecasts from a specific investment over a set period of time.
Sometimes called the market capitalization rate.
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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Valuing Common Stocks
One period expected return is:
Expected Return  r 
Div1  P1  P0
P0
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Valuing Common Stocks
Exercise 14 on ‘Expected Return:
• If Fledgling Electronics is selling for $100 per share today and
is expected to sell for $110 one year from now, what is the
expected return if the dividend one year from now is
forecasted to be $5.00?
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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Copyright AUAF 2022 - Pierre
Rostan, Ph.D. -
Valuing Common Stocks
Exercise 14 on‘Expected Return (solution):
If Fledgling Electronics is selling for $100 per share today and is expected to
sell for $110 one year from now, what is the expected return if the dividend
one year from now is forecasted to be $5.00?
Expected Return 
5  110  100
 .15
100
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
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Valuing Common Stocks
Expected return is a function of risk.
The riskier the company the higher should be the expected
return
•
•‘Expected
return, in this instance, can also be called that the
Required Return to the shareholder given the risk(s) of investing
in the company.
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Valuing Common Stocks: Dividend Valuation Model
Exercise 15: A preferred share offers a fixed dividend of $1.5 every year. The cost of equity is 10%
APR compounded annually. What is the market price of this preferred share?
It is a never ending and a constant $1.50 p.a., and the required rate of return is 0.10 (10.00%)
$1.50 $1.50 $1.50
0
1
2
3
………………………$1.50
Infinity
This is a ‘PERPETUITY’ Model. Use the PV of PERPETUITY to determine the value of
the share
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Valuing Common Stocks
Exercise 15: solution
Present Value of the share
PV of Perpetuity = $Div1 / re
Where re (or sometimes written “ke”) is the required return to equity (or cost of
equity required by shareholders)
PV of Perpetuity = $1.50 / 0.10
PV of Perpetuity = $15.00
P0 = $15.00
Where P0 = price of preferred share
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Valuing Common Stocks
•
Note that this model implicitly assumes no growth. Therefore, all earnings
must be paid out as dividends.
•
This model can also be written as below.
Perpetuity  P0 
Div1
r
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Constant Growth Model
∞
g
D1
0
1 year
P0 = ?
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The constant growth model
discounts one period…
The constant growth model
discounts one period…
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Valuing Common Stocks: Constant Growth Model
Exercise 16: A common stock will offer respectively $1.50 at the end of year one then is
expected to grow at an annual rate of 4%. What is its market price if the cost of equity if
10%?
The cash flow pattern (Dividends) is a constantly growing dividend with Div1 = $1.50 growing
4% pa forever, and the required rate of return is 0.10 (10.00%)
In this example, the $1.50 grows at 4.0% per annum forever. For example, 1.56 = 1.5*1.04.
$1.50 $1.56 $1.6224 …………………….$????
Yr 0
1
2
3
Infinity
This is a ‘constant growth’ model. Use the PV of constant growth model to
determine the value of the share
PV of Constant Growth = $Div1 /(re – g)
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Valuing Common Stocks: Constant Growth Model
Exercise 16: solution
PV of Constant Growth = $Div1 /(re – g)
PV of Constant Growth = $1.50 / (0.10 – 0.04)
PV of Constant Growth = $1.50 / 0.06
PV of Constant Growth = $25.00
P0 = $25.00
Why is this share valued at an extra $10.00 relative to the ‘Perpetuity’ model?
Because we assume a constant growth of the dividend, with the ‘Perpetuity’
model no growth.
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Valuing Common Stocks: Perpetuity Model
•
Rate of Return Observable
•
The required rate is also sometimes called the ‘Market
Capitalization’ rate.
Exercise 17: compute the cost of equity of a preferred share
having a market price of $15 and offering a fixed annual
dividend of $1.5.
It is the case of the PERPETUITY model
Perpetuity  P0 
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Div1
r
Valuing Common Stocks: Perpetuity Model
•
Rate of Return Observable
•
The required rate is also sometimes called the ‘Market Capitalization’ rate.
•
Exercise 17 (solution): compute the cost of equity of a preferred share having a
market price of $15 and offering a fixed annual dividend of $1.5.
•
It is the case of the PERPETUITY model
Div1
r
Div1
r 
P0
Capitalization Rate  P0 
$1.50
$15.00
 r  0.10
r 
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Capitalization Rate
In case of the ‘Constant Growth’ Model
Exercise 18: compute the cost of equity (capitalization rate) of a
common share having a market price of $25 and offering an annual
dividend of $1.5 next year, assumed to grow at 4% per year.
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Capitalization Rate
In case of the ‘Constant Growth’ Model
Exercise 18: solution
• Compute the cost of equity of a common share having a market price of
$25 and offering an annual dividend of $1.5 next year, assumed to grow at
4% per year.
Div
Capitalization Rate  P0 
1
rg
Div1
r
g
P0
$1.50
 0.04
$25.00
 r  0.06  0.04
 r  0.10
r
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Valuing Common Stocks: dividend discount model
• What if the Dividends and share price can be forecasted?
• In this case, the forecast the future cash flows to
shareholders:
P0 
Div1
Div2
Div H  PH


...

(1  r )1 (1  r ) 2
(1  r ) H
H - Time horizon for your investment.
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Valuing Common Stocks: dividend discount model
Exercise 19: Estimated Cash Flows
Current forecasts are for XYZ Company to pay dividends of $3, $3.24, and
$3.50 over the next three years, respectively. At the end of third year, you
anticipate selling your stock at a market price of $94.48. What is the price of
the stock given a 12% expected return?
$3.00
Yr
0
1
$3.24
2
$3.50 + $94.48
3
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Valuing Common Stocks: dividend discount model
Exercise 19: solution
$3.00
$3.24
$3.50  $94 .48


(1  .12)1 (1  .12) 2
(1  .12) 3
PV  $75 .00
PV 
Po  $75 .00
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Valuing Common Stocks: dividend discount model
Exercise 20: estimated Cash Flows
Current forecasts are for XYZ Company to pay dividends of $3, $3.24, and
$3.50 over the next three years, respectively. In year 4 and onwards, it will
grow at a constant rate of 4.0% forever. What is the price of the stock given a
12% expected return?
4% ∞
$3.00
Yr
0
1
$3.24
$3.50
2
3
4
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Apply the Constant Growth Model at time 3
∞
g
D3 = 3.50
2
3 year
P2 = ?
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The constant growth model
discounts one period…
The constant growth model
discounts one period…
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CF
↓
3 ENTER
C01=3
↓
↓
3.5/(.12-.04) + 3.24 = 46.99
ENTER
C02= 46.99
NPV
I = 12
↓
CPT
NPV = 40.1387
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Multistage Growth Models
• As firms progress through their industry life cycle, earnings and
dividend growth rates (ROE) are likely to change.
• A two stage growth model:
T

(1  g1 ) t 
DT
V0  D 0 

t 
(T -1)
 t 1 (1  r)  (r  g 2 )(1  r)
• g1 = first growth rate
• g2 = second growth rate
• T = number of periods of growth at g1
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Multistage Growth Rate Model
• Exercise 21: A company has just paid a $2.00 dividend (i.e. D0 =
$2.00) to its common shareholders.
• The dividend is assumed to grow at 20% APR the next 3 years
then to grow at an expected 5% the years after.
• What is its current common stock price?
• The cost of equity is 15%.
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Multistage Growth Rate Model
• Exercise 21: solution - A company has just paid a $2.00 dividend to its common
shareholders. The dividend is assumed to grow at 20% APR the next 3 years then
to grow at an expected 5% the years after. What is its current common stock
price?
• D0 = $2.00 g1 = 20% g2 = 5%
• k = 15% T = 3
• D1 = 2.40 D2 = 2.88 D3 = 3.46
$2.40 $2.88
$3.46



1.15 1.152 (0.15  0.05)(1.15) ( 31)
$2.40 $2.88 $34.56
V0 


 30.40
1.15 1.152 (1.15) 2
V0 
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
The constant growth model
discounts one period…
The constant growth model
discounts one period…
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Copyright AUAF 2022 - Pierre
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Multistage Growth Rate Model
Exercise 22:
• A company has just paid a dividend of 15 cents per share and
that dividend is expected to grow at a rate of 20% per annum
for the next 3 years and at a rate of 5% per annum forever after
that.
• Assuming a required rate of return of 10%, calculate the
current market price of the share.
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Exercise 22: Solution
Year
Expected Dividend
1
.15 (1.2)1 = $0.180
2
.15 (1.2)2 = $0.216
3
.15 (1.2)3 = $0.259
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Exercise 16: Solution
P0 
D3
D1
D2


1  re 1 1  re 2 re  g 2 3 1  re 3

$0.180 $0.216
$0.259


1.10
1.102 0.10 - 0.05 1.102

$0.180 $0.216 $5.18


2
1.10
1.10 1.102
 $4.62
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Copyright AUAF 2022 - Pierre
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Finance
(FIN200)
More material on Bonds
Pierre Rostan, Ph.D.
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Duration: Introduction
• Objective: how to manage duration.
• Duration is a risk measure of holding a bond.
• Macaulay duration = weighted average term to maturity of the cash flows from
a bond. It measures how long on average the bondholder must wait to receive
her/his CFs.
• Modified duration = adjusted Macaulay duration
= sensitivity of the bond price to a change in interest rate.
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Duration
• Duration of a bond that provides cash flow ci at time ti is
 ci (1 y / n)nti 
D  ti 

B
i1 


n
where B is its price and y is its yield (APR s.a compounded)
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Macaulay Duration
Exercise 23: A bond has a nominal value of 100 USD. It matures in 3 years. It
pays a semi-annual coupon of 10% APR semiannually compounding and has a
yield to maturity of 12% APR semiannually compounding. We represent the
diagram of cash flows of this bond below. Compute clean bond price and
Macaulay duration.
120
105
100
80
60
40
20
5
5
5
5
5
0.5
1
1.5
2
2.5
0
3
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Macaulay Duration
- Measures how long on average the bondholder must wait to receive her CF (Macaulay duration).
Exercise 23: solution
A bond has a nominal value of 100 USD. It matures in 3 years. It pays a semi-annual coupon of
10% APR semiannually compounding and has a yield to maturity of 12% APR semiannually
compounding. The duration of 2.654 year is obtained using the following calculations:
Time
Payment
Present value
Weight
Time*Weight
0.5 year
5
4.717=
0.0496=
0.0248
5/(1+0.12/2)^1
4.716 / 95.083
1
5
4.45
0.0468
0.0468
1.5
5
4.198
0.0442
0.0662
2
5
3.960
0.0417
0.0833
2.5
5
3.736
0.0393
0.0982
3
105
0.778
2.335
Total
130
74.02= 105/(1+0.12/2
)^6
95.083
1
2.654 year
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Key Duration Relationship
• When the yield y is expressed with compounding n times per year
B  
• The expression
BDy
1 y n
D
2 . 654

 2 . 504
1 y n
1  0 . 12 2
is referred to as the “modified duration”
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Macaulay Duration
An important result:  B  
 B: small variation of bond price
B : bond price
D : Macaulay duration
 y : small variation of interest rate
BD  y

1 y n
95 . 083 * 2 . 654 * 0 . 001

1  0 . 12 2
 0 . 238

NewB  95 . 083  0 .238  94 .845
120
105
100
80
60
40
20
5
5
5
5
5
0.5
1
1.5
2
2.5
0
3
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Modified duration
An upward (downward) change in interest rates leads to a fall (rise) in
the present value of a fixed rate bond, irrespective of the issuer’s
financial condition
the value of a fixed rate debt instrument
varies inversely with market rates
The modified duration of a bond measures the % change in its
price for a given change in interest rates.
It is the absolute value of the first derivative of a bond’s price with
respect to interest rates:
Modified duration 
B
1
 Macaulay duration *
y
 y
1  
 n
or Modified duration  Macaulay duration if continuous yield
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Modified duration
B = Bond Value
105
100
95
B2.504*95.083*0.012.38
90
y=
0.01
85
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
y = Yield to Maturity
The modified duration is the slope of the curve.
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Parameters influencing modified duration
Interest Rate Risk
1. 1. the bond’s maturity
the longer the maturity of a bond, the greater its sensitivity to a change in interest rates
2. 2. the bond’s coupon rate
n
 c i (1  y / n )  nt i 
the lower the coupon rate, the higher its modified duration D   t i 

B
i 1 


3. 3. market rates
the lower the level of market rates, the higher a bond’s modified duration
120
105
100
NB: modified duration is valid solely
at the point where it is calculated!
80
60
40
20
5
5
5
5
5
0.5
1
1.5
2
2.5
0
3
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Convexity
Convexity measures the relative change in a bond’s modified duration for a small
fluctuation in interest rates. It is equal to the second derivative of price with respect
to interest rates.
The convexity, C, of a bond with price P is defined as
This leads to a more accurate relationship:
P
D
1
2

y  C y 
y
P
2
1
n
When convexity is used for bond portfolios it allows larger shifts in the yield curve
to be considered, but the shifts still have to be parallel
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Duration application to bond portfolio management
• Since long-term bonds (10-year and +) change the most in
value for a given change in interest rate, a bond portfolio
manager holds long-term bonds when she expects lower
interest-rates: a decrease in interest-rate implies a higher
increase in portfolio value than with a portfolio of shorterterm bonds and vice versa.
• Next slide, looking at the curves: a greater modified duration
leads to a higher drop in price with higher interest-rates
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Duration
Bond Value
Exercise 24:
Consider two otherwise identical bonds:
Identify the graph of the long-term bond
Yield to Maturity
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Duration
Bond Value
Exercise 24: solution
Consider two otherwise identical bonds:
The long-term bond has a higher duration (a
steeper slope) than the short-term bond
Short-term Bond
Long-term Bond
Yield to Maturity
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Fill-up the blanks
Exercise 25:
• A bond portfolio manager may adjust her portfolio duration based on her
expectation of interest rates.
• If she expects lower interest rates, she will ………….. her duration. With a ……..
duration, her portfolio is …….. sensitive to a change in interest rates: the
portfolio will ………………… in value.
• If she expects higher interest rates, she …………. her duration. The portfolio is
……. sensitive to an increase in interest rates: its value will ………. …….. when
bond prices ………..
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Duration
Exercise 25: solution
• A bond portfolio manager may adjust her portfolio duration
based on her expectation of interest rates.
• If she expects lower interest rates, she will lenghten her
duration. With a higher duration, her portfolio is more
sensitive to a change in interest rates: the portfolio will
increase more in value.
• If she expects higher interest rates, she shortens her duration.
The portfolio is less sensitive to an increase in interest rates:
its value will decrease less when bond prices fall.
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Bond Portfolio
• The duration for a bond portfolio is the weighted average
duration of the bonds in the portfolio with weights
proportional to prices
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Exercise 26
Value
Bond
Government 2year
Government 5year
Corporate 5year
Government
10-year
Corporate 10year
Portfolio
Duration
(in millions
EUR)
80
Value x
duration
1.75
140
40
3.93
157.2
50
4.2
210
130
7.08
920.4
200
7.51
1502
500
5.8592
2929.6
• The strategy is to reallocate his portfolio by selling 10-year Corporate bonds
and buying 2-year Government bonds. What is the expectation concerning
interest rates?
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Exercise 26: solution
Value
Bond
Government 2year
Government 5year
Corporate 5year
Government
10-year
Corporate 10year
Portfolio
Duration
(in millions
EUR)
80
Value x
duration
1.75
140
40
3.93
157.2
50
4.2
210
130
7.08
920.4
200
7.51
1502
500
5.8592
2929.6
• The strategy is to reallocate his portfolio by selling 10-year Corporate bonds
and buying 2-year Government bonds.
• Expectation: interest rates will go up.
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Exercise 27
Value
Bond
Government 2year
Government 5year
Corporate 5year
Government
10-year
Corporate 10year
Portfolio
Duration
(in millions
EUR)
80
Value x
duration
1.75
140
40
3.93
157.2
50
4.2
210
130
7.08
920.4
200
7.51
1502
500
5.8592
2929.6
• Exercise: compute the number of 10-year Corporate bonds to sell in order to
buy 2-year Government bonds to reduce the duration to 5.
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Exercise 27: solution
Bond
Value
Duration
Value x duration
(in millions EUR)
Government 2-y
154.5833333
1.75
270.5208333
Government 5-y
40
3.93
157.2
Corporate 5-y
50
4.2
210
Government 10-y
130
7.08
920.4
Corporate 10-y
125.4166667
7.51
941.8791667
Portfolio
500
5
2500
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Exercise 28
Fill up the blanks:
a. The longer the maturity of a bond, the ................its sensitivity to
a change in interest rates.
b. The lower the coupon rate, the ................... its modified duration,
the ................its sensitivity to a change in interest rates.
c. The lower the level of market rates, the ..................... a bond’s
modified duration, the .....................its sensitivity to a change in
interest rates.
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Exercise 28: solution
Fill up the blanks:
a. The longer the maturity of a bond, the HIGHER its sensitivity to a
change in interest rates.
b. The lower the coupon rate, the HIGHER its modified duration, the
HIGHER its sensitivity to a change in interest rates.
c. The lower the level of market rates, the HIGHER a bond’s
modified duration, the HIGHER its sensitivity to a change in interest
rates.
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Research paper and conference presentation:
•Rostan, P., Alami, S.N., Shahab, E., Rahmani, M.A., Azizi, S. 2021.
Challenges of Islamic Banking in Least Developed Countries: the case
of Afghanistan, Journal of Emerging Economies & Policy, vol. 6:2, pp.
5-19, https://dergipark.org.tr/tr/download/article-file/1774224
•Rostan, P., Alami, S.N., Shahab, E., Rahmani, M.A., Azizi, S. 2021.
Challenges of Islamic Banking in Least Developed Countries: the case
of Afghanistan, Symposium on Islamic Economics, Finance and
Banking, Tekirdağ, Turkey.
https://www.youtube.com/watch?v=YrQhRYEiwCA
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Islamic Banking in the world
• The last four decades have witnessed an exceptional growth in Islamic financial
institutions. The global Islamic financial services industry was equal to about 10%
of the Global financial services industry in 2018 (= about 20 trillions USD in 2018)
Source: https://www.ifsb.org
• The number of Islamic financial institutions has increased worldwide from 85 in 1996 to
200 in 2000 and then to 300 in 2008 and to 430 in 2010 across over 75 countries due to
an increased demand across the world. In 2019, the number of Islamic banks was 526
of which 428 were commercial, 57 investment, 22 wholesale (*) and 19 specialized**.
• Sources: Rostan, P., Alami, S.N., Shahab, E., Rahmani, M.A., Azizi, S. 2021. Challenges of Islamic Banking
in Least Developed Countries: the case of Afghanistan, Journal of Emerging Economies & Policy, vol. 6:2,
pp. 5-19, https://dergipark.org.tr/tr/download/article-file/1774224
• Rostan, P., Alami, S.N., Shahab, E., Rahmani, M.A., Azizi, S. 2021. Challenges of Islamic Banking in Least
Developed Countries: the case of Afghanistan, Symposium on Islamic Economics, Finance and Banking,
Tekirdağ, Turkey. https://www.youtube.com/watch?v=YrQhRYEiwCA
• (*) Wholesale banking refers to banking services sold to large clients, such as other banks, other
financial institutions, government agencies
• (**) Specialized banks are banks with banking operations that serve a specific type of economic activity,
such as industrial activity or agricultural or real estate, under the resolutions of their establishment.
source: https://www.statista.com/statistics/1090895/worldwide-number-of-islamic-banks-by-type/
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Top 11 Islamic Banking Countries by Assets
in Billions USD in 2018
Iraq (25 banks), 6.9
Jordan (4 banks), 10.8
Oman (2 banks), 3.3
Algeria (2 banks), 2.4
Egypt (4 banks), 10.9
Sudan (38 banks), 25.1
Bahrain (23 banks), 32.3
Saudi Arabia (4
banks), 157.2
Kuwait (6 banks),
95.2
UAE (8 banks), 146.6
Qatar (5 banks), 97.1
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Islamic Banking in Least Developed Countries
• Among 42 Least Developed Countries, only 5 countries had an Islamic Banking
Share in Total Banking Assets based on the third quarter of 2019 (IFSB, 2020) by
order of importance:
• Sudan (100% of Islamic Banking Share),
• Bangladesh (20%),
• Djibouti (18%),
• Afghanistan (10%) and
• Senegal (5%).
• The 2019 Total Islamic Bank Assets estimate in Billions (USD) of these 5 countries is
equal to $39.02B, which represented the Islamic banking market share of the Least
Developed Countries or about 2% of the global Islamic banking segment in 2019.
Copyright AUAF 2022 - Pierre Rostan, Ph.D. -
Islamic Banking in Least Developed Countries
• Benchmarking the development of conventional and Islamic banking
sectors of Afghanistan compare to Sudan, Bangladesh, Djibouti and
Senegal in 2019
Country
2019 Islamic
Bank Assets
estimate in
Billions (USD)
Percent of
Islamic
Banking
Share
3Q2019
(IFSB)
Bank Assets
estimate in
Billions (USD)
Bank assets,
percent of GDP
2017 (theglobal
economy.com)
People with bank
Nominal GDP
GDP per
accounts, percent of the
ATMs per
2019
capita 2019
population over 14
100,000 adults
estimate in
in Current
years of age in 2018
in 2018 (World
billion USD USD (World
(the global
Bank)
(World Bank)
Bank)
economy.com)
Sudan
3.6189
100%
3.6189
12%
15% (2014)
6.42
30.5135
441.5
Bangladesh
34.717
20%
173.585
57%
41%
8.86
302.571
1855.7
Djibouti
0.19204
18%
1.06687
32%
12%
12.33
3.32463
3414.9
Afghanistan
0.06617
10%
0.66168
3%
16%
1.61
19.2911
507.1
Senegal
0.4283
5%
8.56592
36%
20%
6.1
23.5781
1446.8
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Islamic Banking in Afghanistan
• The Islamic Bank Assets in Billions (USD) of Afghanistan represents a very small
amount ($0.06617B) even compare to the remaining countries, Djibouti
($0.19204B) and Senegal ($0.4283B).
• In terms of percentage of banks users, Afghanistan compares to Sudan (16% in
2018 in Afghanistan versus 15% in 2014 in Sudan) which had a comparable GDP
per capita ($507.10 in Afghanistan versus $441.5 in Sudan).
• In terms of development of ATM machines, Afghanistan is also lagging behind the
4 countries (1.61 ATMs per 100,000 adults).
• In conclusion, Afghanistan is a weak economy with one tiny GDP per capita,
ranked 207th out of 213 countries in 2019, Sudan being ranked 210th.
• This sluggish state of the economy may explain the underdeveloped banking
sector.
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Islamic Banking in Afghanistan
• Afghanistan’s banking sector is small where, out of 12 banks in total, seven are Islamic
windows in conventional banks and one is a full-fledged Islamic bank (i.e. the Islamic
Bank of Afghanistan, IBA).
• According to Vizcaino (2018), the bulk of Islamic financing in Afghanistan is offered via
only two types of sharia-compliant structures, Murabaha (a cost-plus-profit
arrangement) and Ijarah (a leasing-based contract).
• At the end of Q2 2018, IBA and the seven Islamic windows held a combined 27.8
billion afghani ($365.5 million), versus to 9.7 billion afghani ($127.5 million) at the end
of 2014, data being compiled by the IFSB (Vizcaino, 2018).
• Out of $365.5 million, about 60% of the Islamic assets were held by the seven Islamic
windows and 40% by IBA.
• Comparing $365.5 million to $2.4 billion, which was the size of the Islamic banking
assets of Algeria in 2018, the 11th largest Islamic banking country, confirms the very
small size of Islamic banking assets in Afghanistan.
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The Islamic Bank of Afghanistan (IBA)
• IBA was previously known as Bakhtar Bank and has operated under a conventional
banking license.
• Da Afghanistan Bank awarded the license to IBA as a first full-fledged Islamic bank in
2018 after IBA completed the conversion of its balance sheet.
• IBA agreed to adhere to religious principles that include bans on gambling, alcohol, and
interest-bearing debt, among others, as part of its transition. It delivers services across
a network of 62 branches – reportedly the second largest branch network in
Afghanistan – inherited from the Bakhtar Bank.
• IBA’s website offers a variety of Shariah-compliant products such as Mudaraba savings
account, a form of investment management partnership, Murabaha, a cost-plus-profit
arrangement (with different types such as Purchase Order, Spot, Deferred payment,
Letter of Credit), as well as financing products based on Ijarah, an installment-based
leasing contract, Musharakah, joint partnership arrangement, Istisna, contract to
construct, build or manufacture an asset and Salam, advance payment for deferred
delivery. What is the reality of the use of these products by IBA?
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The Islamic Bank of Afghanistan (IBA)
• What is the reality of the use of these products by IBA?
• Referring to the IBA’s Financial Statements for the first 9 months of 2020, the revenue
from the Bank share as Mudarib was representing 14% (AFN 113,635,000 = USD
1,463,290) of the Total Bank Revenue/Operating Income (AFN 836,787,000 = USD
10,775,400), the Net fee and commission income 9% (AFN 72,643,000 = USD 935,434),
the Foreign Exchange gain 49% (AFN 411,378,000 = USD 5,297,370), Capital gain 16%
(AFN 130,926,000 = USD 1,685,950) and Other non-operating income 13% (AFN
108,205,000 = USD 1,393,370).
• Under the item Bank share as Mudarib, the bank acts as the agent (Mudarib) on behalf
of depositors who invested in a partnership equity-based trust financing (Mudaraba)
with the bank.
• IBA offers two types of Mudaraba accounts to its clients, Saving account and Fixed
Term account.
• Under the bank share as Mudarib, the bank invested in two main Islamic products
during the first 9 months of 2020, Murabaha who represented 10% (AFN 80,008,000 =
USD 1,030,270) of the Total Bank Revenue and Diminishing Musharakah 0.4% (AFN
3,504,000 = USD 45,121).
• In addition, the bank invested in Corporate and Sovereign Islamic bonds (Sukuk) under
the Bank share as Mudarib.
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