(a) Features and major participants of the money market

Features

• Short maturity - up to one year (T-bills of 91, 182, 364 days; CDs and commercial paper of 30-270 days).
• High liquidity and low default risk - issuers are the government, central bank, banks and reputed firms.
• Low return - the price of safety and liquidity.
• Wholesale, large denominations - traded through competitive and noncompetitive bidding and dealer networks, with no single physical location.
• Discount or interest basis - T-bills are sold at a discount and redeemed at par; CDs and commercial paper may carry interest.
• Regulated by the central bank, which uses the market for liquidity management and monetary policy.

Major participants

• The government and Nepal Rastra Bank (issuing and auctioning T-bills, open market operations).
• Commercial banks and other financial institutions (buy T-bills, issue CDs, interbank lending).
• Corporations (issue commercial paper, invest surplus cash).
• Insurers, provident and pension funds, mutual funds, brokers/dealers and individual investors.

(b) T-bill: Rs 100,000 par, price Rs 98,500, 91 days

Discount $= 100{,}000 - 98{,}500 =$ Rs 1,500.

$\text{Discount yield} = \frac{F-P}{F}\times\frac{360}{n} = \frac{1{,}500}{100{,}000}\times\frac{360}{91} = 0.015\times 3.9560 = 5.93\%$

$\text{Investor return} = \frac{F-P}{P}\times\frac{365}{n} = \frac{1{,}500}{98{,}500}\times\frac{365}{91} = 0.015228\times 4.01099 = 6.11\%$

$\text{Effective annual return} = \left(\frac{F}{P}\right)^{365/n}-1 = (1.015228)^{4.01099}-1 = 1.0625-1 \approx 6.25\%$

(c) 90-day CD, Rs 10,000,000, 8% annual yield

$\text{Interest} = 10{,}000{,}000\times 0.08\times\frac{90}{365} = \text{Rs } 197{,}260$

$\text{Total repayable} = 10{,}000{,}000 + 197{,}260 = \text{Rs } 10{,}197{,}260$

(On a 360-day basis the interest would be Rs 200,000.)

Central Bank and Monetary Tools

Meaning of Monetary Policy

Monetary policy is the process by which the central bank of a country (in Nepal, Nepal Rastra Bank) manages the money supply, the availability of credit, and the cost of credit in order to achieve macroeconomic objectives such as price stability, full employment, economic growth, and a stable balance of payments. The central bank is responsible for fine-tuning the money supply in the banking system by employing appropriate monetary tools.

Types of Monetary Tools

Monetary tools are broadly classified into three types:

1. Open Market Operations (OMO)
2. Discount Rate (Bank Rate)
3. Reserve Requirements

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1. Open Market Operations (OMO)

Open market operations refer to the buying and selling of government securities by the central bank in the open market to influence the level of reserves in the banking system. Under OMO, the central bank uses four instruments:

(a) Repurchase Agreement (Repo)

A repo is a short-term agreement in which the central bank lends money to commercial banks against government securities as collateral, with an agreement to repurchase them on a specified future date. Through repo, the central bank injects liquidity into the banking system. When the central bank lowers the repo rate, borrowing becomes cheaper, money supply increases, and vice versa.

(b) Reverse Repo

A reverse repo is the opposite of a repo. Here, the central bank borrows money from commercial banks by selling government securities with an agreement to repurchase them later. It is used to absorb excess liquidity from the banking system. An increase in the reverse repo rate encourages banks to park funds with the central bank, thereby reducing money supply.

(c) Outright Sale

Under outright sale, the central bank sells government securities to commercial banks or the public on a permanent basis without any agreement to repurchase. This reduces the reserves of commercial banks, lowers their lending capacity, and thus contracts the money supply.

(d) Outright Purchase

Under outright purchase, the central bank buys government securities from commercial banks or the public on a permanent basis. This increases the reserves of commercial banks, expands their lending capacity, and thus increases the money supply.

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2. Discount Rate (Bank Rate)

The discount rate is the rate of interest at which the central bank lends money to commercial banks against eligible securities. It is also called the bank rate. When the central bank increases the discount rate, borrowing by commercial banks becomes expensive, so they borrow less and charge higher interest rates to customers. This reduces credit creation and contracts the money supply. Conversely, a decrease in the discount rate makes borrowing cheaper, encourages commercial banks to borrow more, and expands the money supply.

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2. Reserve Requirements

Reserve requirements refer to the minimum amount of reserves that commercial banks must maintain against their deposits. There are two main types:

(a) Cash Reserve Ratio (CRR)

The CRR is the percentage of total deposits that commercial banks must keep as cash reserves with the central bank. Increasing the CRR lowers the amount of money that banks can lend, which lowers the total amount of money in the entire banking system, and vice versa.

(b) Statutory Liquidity Ratio (SLR)

The SLR is the percentage of total deposits that commercial banks must maintain in the form of liquid assets such as cash, gold, and government securities. An increase in the SLR reduces the lending capacity of banks and contracts the money supply.

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Effect of Reserve Requirements on Money Supply

The required reserve ratio is a monetary policy tool that requires commercial banks to hold a percentage of deposits in reserve, which means they cannot lend out that portion of the deposit. Increasing the ratio lowers the amount of money that banks can lend, which lowers the total amount of money in the entire banking system, and vice versa.

This can be explained with the money multiplier:

$m = \frac{1}{rr}$

where $m$ is the money multiplier and $rr$ is the required reserve ratio. If the required reserve ratio is 10%, the money multiplier is:

$m = \frac{1}{0.10} = 10$

This means that every Rs 1 of reserves can create Rs 10 of deposits in the banking system. If the central bank raises the reserve ratio to 20%, the multiplier falls to:

$m = \frac{1}{0.20} = 5$

Thus, an increase in the reserve ratio reduces the money multiplier and contracts the money supply. Conversely, a decrease in the reserve ratio increases the money multiplier and expands the money supply.

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Conclusion

The central bank plays a crucial role in regulating the money supply through open market operations, the discount rate, and reserve requirements. Open market operations, with instruments such as repo, reverse repo, outright sale, and outright purchase, provide flexibility in managing liquidity. The discount rate influences the cost of borrowing, while reserve requirements directly affect the lending capacity of commercial banks. By using these tools appropriately, the central bank can control inflation, promote economic growth, and maintain overall economic stability.

The death-rate figure is missing from the question text, so an assumption is stated: 2 deaths per 1,000 policyholders, with a Rs 100,000 payout per death (the method is the same for any rate and payout).

Fair premium is the expected claim cost per policyholder, discounted at the 8.5% investment return, since premiums are collected now and claims are paid later.

Expected deaths $= 10{,}000\times 0.002 = 20$

Expected payout $= 20\times 100{,}000 =$ Rs 2,000,000

$\text{PV of claims} = \frac{2{,}000{,}000}{1.085} = \text{Rs } 1{,}843{,}318$

$\text{Fair premium} = \frac{1{,}843{,}318}{10{,}000} \approx \text{Rs } 184.33 \text{ per policyholder}$

Gross premium adds the operating expenses and target profit of Rs 170,000, i.e. $170{,}000/10{,}000 =$ Rs 17 per policyholder.

$\text{Gross premium} = 184.33 + 17 = \text{Rs } 201.33 \text{ per policyholder}$

For the whole group the company collects about Rs 2,013,318.

Given:

• Total years of service = 30 years
• Career average salary = Rs 50,000
• Last three years’ salaries: Year 28 = Rs 51,000; Year 29 = Rs 53,000; Year 30 = Rs 55,000

a. Flat benefit formula

Annual pension = Benefit per year of service × Total years of service
$= 900 \times 30 = \text{Rs } 27,000$

Annual pension benefit = Rs 27,000

b. Career average formula

Annual pension = 4% × Career average salary × Total years
$= 0.04 \times 50,000 \times 30 = \text{Rs } 60,000$

Annual pension benefit = Rs 60,000

c. Final pay formula

The question states “last four years,” but the data give only the last three years.
If the intended period is the last three years:

Average salary of last three years
$= \frac{51,000 + 53,000 + 55,000}{3} = \frac{159,000}{3} = \text{Rs } 53,000$

Annual pension = 3% × Average salary × Total years
$= 0.03 \times 53,000 \times 30 = \text{Rs } 47,700$

Annual pension benefit = Rs 47,700

Note: If the final-pay formula is taken literally as the average of the last four years, Year 27 salary is not given. Assuming the salary trend continues backward by Rs 2,000 per year, Year 27 = Rs 49,000. Then the four-year average is
$\frac{49,000 + 51,000 + 53,000 + 55,000}{4} = \text{Rs } 52,000$
and the pension would be
$0.03 \times 52,000 \times 30 = \text{Rs } 46,800$
However, using the data actually provided, the answer is Rs 47,700.

Given:

• Annual salary = Rs 600,000
• Manab’s contribution rate = 12%
• Employer match = 50% of the first 5% of salary
• Expected return = 10%
• Tax bracket = 25%

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a. Manab’s contribution and employer’s contribution for the first year

Manab’s contribution:

$$12\% \times 600{,}000 = \text{Rs }72{,}000$$

Employer matches 50% of the first 5% of salary:

$$5\% \times 600{,}000 = \text{Rs }30{,}000$$ $$50\% \times 30{,}000 = \text{Rs }15{,}000$$

Manab’s contribution = Rs 72,000
Employer’s contribution = Rs 15,000

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b. Tax saving on the contribution to the plan

Only Manab’s own contribution is deductible from his taxable income.

$$\text{Tax saving} = 72{,}000 \times 25\%$$ $$= \text{Rs }18{,}000$$

Tax saving = Rs 18,000

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c. Cost for the retirement plan

The net after-tax cost to Manab is:

$$\text{Cost} = \text{Manab’s contribution} - \text{Tax saving}$$ $$= 72{,}000 - 18{,}000$$ $$= \text{Rs }54{,}000$$

Cost for the retirement plan = Rs 54,000

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d. Total investment at year start and one-year return

Total investment at the start of the year:

$$= \text{Manab’s contribution} + \text{Employer’s contribution}$$ $$= 72{,}000 + 15{,}000$$ $$= \text{Rs }87{,}000$$

One-year return at 10%:

$$= 87{,}000 \times 10\%$$ $$= \text{Rs }8{,}700$$

Total investment at year start = Rs 87,000
One-year return = Rs 8,700
Value at the end of one year = Rs 87,000 + Rs 8,700 = Rs 95,700

Types of insurance

1. By nature of business

• Life insurance - pays a sum on death or maturity. Forms: term, whole life, endowment, money-back, annuity.
• Non-life (general) insurance - indemnifies loss. Forms: fire, marine, motor, engineering, agriculture and livestock, health, miscellaneous.

2. By subject matter

• Personal (life, accident, health), property (fire, marine, motor), liability (third-party, professional) and fidelity/guarantee insurance.

3. By coverage and arrangement

• Individual vs. group insurance, micro-insurance, social insurance, and reinsurance (an insurer passing part of its risk to another insurer).

Role of Nepal Insurance Authority (NIA)

NIA is the regulator set up under the Insurance Act, 2079, succeeding Beema Samiti. Its main roles are:

• Licensing insurers, reinsurers and intermediaries (agents, surveyors, brokers) and cancelling licences where needed.
• Prudential regulation - setting minimum capital, solvency margin and investment rules.
• Supervision - inspecting, auditing and monitoring companies' financial health and governance.
• Policyholder protection - approving products and premium rates, ensuring prompt claim settlement and handling complaints.
• Market development - promoting insurance awareness, micro-insurance and insurance penetration, and advising the government.
• Enforcement - issuing directives and penalising violations.

Expansion and Contraction of Money Supply by Central Banks Using Monetary Tools

1. Concept

The central bank (in Nepal, Nepal Rastra Bank — NRB) controls the total volume of money in circulation through monetary policy. When it wants to expand the money supply (expansionary policy), it uses tools that inject reserves into the banking system and lower interest rates. When it wants to contract the money supply (contractionary policy), it uses tools that drain reserves and raise interest rates. The tools are broadly of two types: quantitative (general) tools and qualitative (selective) tools.

2. Quantitative Tools of Monetary Control

(a) Open Market Operations (OMO)

Buying and selling of government securities by the central bank in the open market.

• Expansion: The central bank buys securities. It pays the sellers (banks/public) by crediting their accounts, which increases bank reserves. Through the credit multiplier, deposits and money supply expand by a multiple of the initial injection.
• Contraction: The central bank sells securities. Buyers pay from their bank deposits, reserves fall, and the credit multiplier works in reverse, reducing money supply.

(b) Bank Rate / Discount Rate

The rate at which the central bank lends to commercial banks.

• Expansion: A reduction in bank rate makes borrowing cheaper; banks borrow more reserves, lend more, and money supply rises.
• Contraction: A rise in bank rate makes borrowing costlier; banks borrow less and curtail lending, so money supply falls.

(c) Cash Reserve Ratio (CRR)

The minimum fraction of deposits that banks must keep as cash reserves with the central bank.

• Expansion: Lowering CRR leaves banks with more lendable funds; the multiplier rises and money supply expands.
• Contraction: Raising CRR locks up more reserves, reduces lendable funds, and contracts money supply.

(d) Statutory Liquidity Ratio (SLR)

The minimum percentage of deposits banks must hold in liquid assets (cash, gold, government securities).

• Expansion: Reducing SLR releases funds for lending.
• Contraction: Raising SLR immobilises funds and reduces credit creation.

(e) Repo and Reverse Repo

• Repo (expansion): Central bank lends short-term funds to banks against securities, injecting liquidity.
• Reverse repo (contraction): Central bank borrows from banks against securities, absorbing liquidity.

3. Qualitative (Selective) Tools

These influence the direction rather than the volume of credit:

• Margin requirements: Raising the margin on loans (e.g., for share/real estate lending) discourages credit; lowering it encourages credit.
• Moral suasion: Persuasion/request to banks to expand or restrict lending in particular sectors.
• Credit rationing / ceiling: Fixing maximum credit limits per sector or per bank.
• Direct action: Penalising banks that violate directives.
• Consumer credit regulation and publicity.

4. How the Tools Work: The Multiplier Link

If the required reserve ratio is $r$, the simple deposit multiplier is:

$m = \frac{1}{r}$

Example: Suppose NRB lowers CRR from 4% to 2% and the banking system has initial reserves of Rs 100 crore.

• Before: $m = 1/0.04 = 25$; potential deposits $= 25 \times 100 = \text{Rs } 2{,}500$ crore.
• After: $m = 1/0.02 = 50$; potential deposits $= 50 \times 100 = \text{Rs } 5{,}000$ crore.

Thus a 2 percentage-point cut in CRR can potentially expand money supply by Rs 2,500 crore — an example of expansionary policy. Reversing the change (raising CRR from 2% to 4%) would contract money supply by the same amount.

OMO example: If NRB buys Rs 50 crore of treasury bills from commercial banks, bank reserves rise by Rs 50 crore. With $r = 0.10$, the multiplier is 10, so deposits can rise by up to Rs 500 crore — expansion. If instead NRB sells Rs 50 crore of securities, reserves fall by Rs 50 crore and deposits can fall by up to Rs 500 crore — contraction.

5. Conclusion

Central banks expand money supply by buying securities, lowering bank rate, reducing CRR/SLR, and using repo, and contract it by selling securities, raising bank rate, increasing CRR/SLR, and using reverse repo. Quantitative tools change the volume of credit; qualitative tools change its allocation. In practice, NRB uses a mix of these tools — for example, adjusting CRR and conducting OMO through treasury bill auctions — to keep money supply consistent with the objectives of price stability, external balance, and adequate credit for productive sectors.

Major Participants of the Money Market

The money market is the market for short-term funds (usually up to one year) where instruments such as treasury bills, commercial papers, certificates of deposit and call money are traded. Its major participants are:

1. Government (Treasury) The government is the largest borrower in the money market. It issues treasury bills and other short-term securities to bridge temporary gaps between revenue collection and expenditure, and to manage fiscal deficits.

2. Central Bank The central bank (Nepal Rastra Bank in Nepal) acts as the regulator, supervisor and operator of the money market. It issues treasury bills on behalf of the government, conducts open market operations, provides lender-of-last-resort facilities, and uses instruments like repo, reverse repo and outright purchase/sale of securities to control money supply and liquidity.

3. Commercial Banks Banks are the core participants. They borrow and lend in the call money market to meet reserve requirements and manage day-to-day liquidity, invest surplus funds in treasury bills and CDs, and act as dealers/underwriters of money market instruments.

4. Financial Institutions (Non-Bank) Development banks, finance companies, microfinance institutions and insurance companies participate by lending surplus short-term funds and investing in money market instruments to earn returns while maintaining liquidity.

5. Business Firms / Corporations Large corporations issue commercial papers to raise short-term working capital and invest temporary surplus cash in money market instruments. They are both borrowers and lenders in this market.

6. Discount Houses / Primary Dealers These institutions specialise in discounting and rediscounting short-term securities, act as intermediaries between the central bank and other participants, and help develop the market by quoting two-way prices.

7. Institutional Investors Mutual funds, provident funds, insurance companies and pension funds invest their short-term surplus in money market instruments for safety and liquidity.

8. Individuals and Households Though limited in direct participation, individuals invest in money market instruments (e.g., treasury bills, fixed deposits) and provide funds through banks.

Conclusion Thus, the money market operates through the interaction of the government, central bank, commercial banks, non-bank financial institutions, corporations, discount houses and institutional investors. Among them, the central bank and commercial banks are the most active participants, as they drive liquidity, price stability and short-term credit flow in the economy.

Functions of Merchant Banker in Nepal [5 marks]

A merchant banker in Nepal is a financial institution licensed by the Securities Board of Nepal (SEBON) to assist companies in raising capital from the securities market and to provide related financial services. Under the Securities Businessperson Regulations, 2064, merchant banking activities in Nepal include issue management, underwriting, securities trading, portfolio management, and advisory services. The major functions are described below:

1. Issue Management (Primary Market Function) The most important function of a merchant banker is to manage the issue of shares, debentures, and other securities on behalf of client companies. This includes preparing the prospectus, obtaining approval from SEBON, appointing collection centres, collecting applications from investors, conducting allotment, and listing the securities on the Nepal Stock Exchange (NEPSE). In Nepal, institutions such as Nabil Investment Banking Ltd., NIBL Ace Capital, and Sanima Capital perform this role for companies issuing Initial Public Offerings (IPOs) and Further Public Offerings (FPOs).

2. Underwriting of Securities A merchant banker may underwrite an issue, meaning it guarantees to subscribe to any portion of the securities that remains unsubscribed by the public. This assures the issuing company of receiving the full amount of capital it intends to raise, and it earns an underwriting commission for bearing this risk.

3. Portfolio Management Merchant bankers manage the investment portfolios of individuals and institutional investors by investing their funds in a diversified mix of shares, debentures, and other securities. The objective is to maximise returns while minimising risk through proper investment analysis and diversification.

4. Advisory and Consultancy Services They provide expert advice to companies on capital structure, merger and acquisition, corporate restructuring, project appraisal, and financial planning. They also guide clients on regulatory compliance with SEBON, NEPSE, and the Companies Act.

5. Market Making and Securities Trading Some merchant bankers act as market makers by buying and selling securities to create liquidity in the secondary market. They also trade in securities as licensed stock brokers or dealers, thereby facilitating smooth transactions for investors.

6. Depository and Registrar Services Merchant bankers often serve as share registrars, handling share registration, transfer, and dematerialisation of securities, and they assist in maintaining records of shareholders on behalf of client companies.

Conclusion In Nepal, merchant bankers act as intermediaries between issuers and investors. They mobilise savings into productive investment, develop the capital market, protect investor interests through proper disclosure, and provide professional financial services — thereby contributing significantly to the growth of Nepal's securities market.

Financial intermediation: channelling funds from surplus units to deficit units

In an economy, some individuals, households, firms and government bodies spend less than their income and thus have surplus funds (savers), while others spend more than their income and need deficit funds (borrowers/investors). The transfer of funds from surplus units to deficit units takes place through two broad routes:

1. Direct financing (financial markets) Surplus units lend directly to deficit units by purchasing financial claims issued by them:

• Primary securities such as shares, debentures, bonds and commercial papers are bought in the primary market.
• These securities can later be traded in the secondary market, which provides liquidity and encourages savers to invest.
• This route requires the saver to bear risk and search cost, and needs well-developed capital markets.

2. Indirect financing (financial intermediation) Here funds pass through financial institutions such as commercial banks, development banks, finance companies, cooperatives and insurance companies:

• Surplus units deposit their savings in banks or buy insurance policies and mutual fund units.
• Banks pool these small savings and lend them as loans, overdrafts, working capital and term loans to deficit units.
• The intermediary issues secondary securities (deposits, insurance policies) to savers and holds primary securities (loans) of borrowers.

Process of channelling

1. Mobilisation of savings – Banks and other institutions collect scattered savings through attractive interest rates, branch networks and deposit schemes.
2. Pooling and transformation – Small, short-term deposits are pooled and transformed into large, long-term loans (size, maturity and risk transformation).
3. Allocation of credit – Funds are lent to productive sectors, trade, industry, agriculture and government after appraisal of creditworthiness.
4. Return flow – Borrowers repay principal and interest; the intermediary pays interest to savers and keeps a margin as profit.
5. Recycling – The repaid funds are again lent out, so the process continues and keeps the economy's investment cycle moving.

Role/benefits of this channelling

• Converts idle savings into productive investment, raising capital formation and employment.
• Reduces transaction and information costs through expert appraisal and diversification.
• Provides liquidity and safety to savers while meeting the varied needs of borrowers.
• Supports monetary policy transmission and overall economic growth.

Conclusion Thus, surplus funds reach deficit units either directly through financial markets or indirectly through financial intermediaries. In a developing economy like Nepal, where capital markets are relatively less developed, the indirect route through banks and financial institutions is the dominant channel for transferring funds from surplus units to deficit units.

(a) NAV of each fund

Fund A: $165\times25 + 50\times45 = 4{,}125 + 2{,}250 =$ Rs 6,375

$\text{NAV}_A = \frac{6{,}375}{1{,}000} = \text{Rs } 6.375$

Fund B: $75\times25 + 100\times45 = 1{,}875 + 4{,}500 =$ Rs 6,375

$\text{NAV}_B = \frac{6{,}375}{1{,}000} = \text{Rs } 6.375$

(b) Effect on Fund A's NAV

New ATT shares cost $165\times25 =$ Rs 4,125, raised by issuing 647 new fund shares at NAV ($647\times6.375\approx 4{,}125$).

Portfolio value $= 6{,}375 + 4{,}125 =$ Rs 10,500; shares outstanding $= 1{,}000 + 647 = 1{,}647$.

$\text{NAV}_A = \frac{10{,}500}{1{,}647} = \text{Rs } 6.375$

NAV is unchanged. An open-end fund issues and redeems shares at NAV, so adding assets by selling new shares at NAV leaves NAV per share the same (only the fund's size changes).

Given: Transaction deposits $(D)$ = Rs 1,500 million
Reserve requirement $(r)$ = 8% = 0.08

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a. Reserve asset to back up deposit liabilities

Required reserve $= r \times D$

$= 0.08 \times 1{,}500 = \text{Rs }120 \text{ million}$

So Sangrila Bank must keep Rs 120 million as reserve assets (vault cash and balance with the central bank) to back its transaction deposits.

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b. Maximum amount of deposit usable for lending

Excess reserve/lendable deposit $= D - \text{Required reserve}$

$= 1{,}500 - 120 = \text{Rs }1{,}380 \text{ million}$

So the bank can use up to Rs 1,380 million for lending.

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c. Deposit multiplier

$m = \frac{1}{r} = \frac{1}{0.08} = 12.5$

Deposit multiplier = 12.5

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d. Maximum deposits/loans generated from Rs 1,500 million deposits

Total deposits supported in the banking system:

$= D \times m = 1{,}500 \times 12.5 = \text{Rs }18{,}750 \text{ million}$

Maximum additional deposits/loans created:

$= 18{,}750 - 1{,}500 = \text{Rs }17{,}250 \text{ million}$

Alternatively,

$= \text{Excess reserve} \times m = 1{,}380 \times 12.5 = \text{Rs }17{,}250 \text{ million}$

Answer: Total deposits supported = Rs 18,750 million; maximum loans/additional deposits generated = Rs 17,250 million.

(Assumption: no currency drain, no excess reserves held by banks, and all banks maintain the same 8% reserve ratio.)

Given: accepted bid $= 98.2$ per 100 face value; 91-day bill.

1. Published discount rate

$d = \frac{100 - 98.2}{100}\times\frac{360}{91} = 0.018\times 3.95604 = 7.12\%$

2. Comparable bond-equivalent rate

$i = \frac{100-98.2}{98.2}\times\frac{365}{91} = 0.01833\times4.01099 = 7.35\%$

3. Price with 50 days remaining at $d = 11.5\%$

$P = 100\left[1 - \frac{0.115\times 50}{360}\right] = 100(1 - 0.015972) = \text{Rs } 98.40 \text{ per Rs 100 face value}$

The price is below par because investors now demand an 11.5% discount rate, but it is close to par because only 50 days remain.

Total shares: A 1,000, B 2,000, C 3,000.

(a) Price-weighted index

(b) Value-weighted index (Date 1 = 100)

(c) Adjusting for a stock split

• Price-weighted: a split lowers the stock's price and would drop the index artificially, so the divisor is changed to keep the index continuous. Example: if C splits 2-for-1 on date 3, its price becomes Rs 450. New price sum $= 300+120+450 = 870$. To keep the index at 440: new divisor $= 870/440 = 1.977$ (instead of 3).
• Value-weighted: no adjustment is needed. The split halves the price but doubles the shares (C: 6,000 shares at Rs 450 = Rs 2,700,000), so the total market value, and the index, is unchanged.

(d) Uses of a market index

• Barometer of market and economic condition.
• Benchmark for evaluating portfolio and fund performance.
• Basis for index funds, ETFs and derivatives.
• Measuring market return and risk (beta) in models such as CAPM.
• Technical analysis and forecasting of market trends.

Given: investment Rs 1,000; front-end load 2%; annual fees 1.10%; 5 years; savings rate 5%.

Step 1. Net amount invested after the load: $1{,}000\times(1-0.02) =$ Rs 980.

Step 2. Savings account value: $1{,}000\times(1.05)^5 =$ Rs 1,276.28.

Step 3. Let $r$ be the fund's gross annual return; the net return is $r - 0.011$.

$980\,(1 + r - 0.011)^5 = 1{,}276.28$

$(1 + r - 0.011)^5 = 1.30233$

Step 4.

$1 + r - 0.011 = (1.30233)^{1/5} = 1.05426$

$r = 0.05426 + 0.011 = 0.0653 \approx 6.53\%$

The fund must earn a gross return of about 6.53% per year (exactly 6.525%) just to match the 5% savings account.

Step 1: Expected returns

$\bar R_A = \frac{5+15+25}{3} = 15\%, \qquad \bar R_B = \frac{14+8+5}{3} = 9\%$

Step 2: Deviations, variances and covariance

$\sigma_A^2 = \frac{200}{3} = 66.67,\quad \sigma_A = 8.165\%$

$\sigma_B^2 = \frac{42}{3} = 14,\quad \sigma_B = 3.742\%$

$\text{Cov}_{AB} = \frac{-90}{3} = -30$

Step 3: Portfolio return ($w_A = 0.40$, $w_B = 0.60$)

$\bar R_p = 0.40(15) + 0.60(9) = 6 + 5.4 = 11.40\%$

Step 4: Portfolio standard deviation

$\sigma_p^2 = w_A^2\sigma_A^2 + w_B^2\sigma_B^2 + 2w_Aw_B\,\text{Cov}_{AB}$

$= 0.16(66.67) + 0.36(14) + 2(0.40)(0.60)(-30) = 10.667 + 5.04 - 14.4 = 1.307$

$\sigma_p = \sqrt{1.307} \approx 1.14\%$

The portfolio earns 11.40% with a standard deviation of about 1.14%. It is far less risky than either asset alone because the two returns move in opposite directions (correlation about −0.98).

Step 1: Security market line from A and RF

$E(R) = 6\% + \beta(12\% - 6\%) = 6\% + 6\%\,\beta$

Step 2: Fair return for E ($\beta = 0.6$)

$E(R_E) = 6\% + 6\%(0.6) = 9.6\%$

E offers only 8%, so it is overpriced (alpha $= 8\% - 9.6\% = -1.6\%$). Yes, an arbitrage opportunity exists.

Step 3: Tracking portfolio with $\beta = 0.6$

$w_A(1.2) = 0.6 \Rightarrow w_A = 0.5$

50% in A and 50% in RF has $\beta = 0.6$ and return $0.5(12\%) + 0.5(6\%) = 9\%$.

Step 4: Arbitrage strategy

Short-sell E and use the proceeds to buy 50% A and 50% RF. Net investment is zero, net beta is zero, and the position earns a riskless profit of 1% of the amount shorted. Buying pressure on A/RF and selling pressure on E push prices until the gap closes.

Annual coupon payment:

$C = 10\% \times 1{,}000 = \text{Rs }100$

Bond price formula:

$P = \sum_{t=1}^{7}\frac{C}{(1+r)^t}+\frac{F}{(1+r)^7}$

$950 = 100 \times PVIFA_{r,7} + 1{,}000 \times PVIF_{r,7}$

Trial and error:

At $r = 11\%$:

$PVIFA_{11\%,7}=4.7122,\quad PVIF_{11\%,7}=0.4817$

$P = 100(4.7122)+1{,}000(0.4817)=\text{Rs }952.88 > 950$

At $r = 12\%$:

$PVIFA_{12\%,7}=4.5638,\quad PVIF_{12\%,7}=0.4523$

$P = 100(4.5638)+1{,}000(0.4523)=\text{Rs }908.73 < 950$

So YTM lies between 11% and 12%.

Interpolation:

$YTM = 11\% + \frac{952.88-950}{952.88-908.73}\times(12\%-11\%)$

$= 11\% + \frac{2.88}{44.15}\times 1\%$

$= 11.065\% \approx 11.06\%$

Answer: The yield to maturity is approximately 11.06% per annum.
Since the bond sells below par, its YTM is greater than the coupon rate.

Investment Company

An investment company is a financial institution that pools funds from many individual investors by issuing its own securities (shares or units) and invests the collected funds in a diversified portfolio of securities such as stocks, bonds, and money market instruments. It is also called an investment fund or collective investment scheme.

Its main features are:

• Pooling of funds — small savings of many investors are collected into a large common fund.
• Professional management — the fund is managed by expert portfolio managers.
• Diversification — funds are spread over many securities to reduce risk.
• Liquidity — investors can convert their holdings into cash.
• Economies of scale — transaction and research costs are shared among all investors.

In Nepal, investment companies are regulated by the Securities Board of Nepal (SEBON) under the Securities Act, 2063 and the Mutual Fund Regulations.

Distinction between Open-end Fund and Closed-end Fund

Conclusion: The basic difference lies in the flexibility of capital and the method of trading. An open-end fund is always open for subscription and redemption at NAV, whereas a closed-end fund has fixed capital and its shares are traded on the stock exchange at market-determined prices.

Short Notes

a. Net Asset Value (NAV)

NAV is the per-unit value of a mutual fund, found by dividing the fund's net assets by the number of units outstanding.

$\text{NAV} = \frac{\text{Total Assets} - \text{Total Liabilities}}{\text{Number of Outstanding Units}}$

• Assets include the market value of investments, cash and accrued income; liabilities include fees and other payables.
• It is calculated at the close of each trading day (or week).
• Units are issued and redeemed at or near NAV (plus any load or exit charge).
• A rising NAV signals good performance, and it is the basis for measuring fund returns.

Example: Assets Rs 100,000,000, liabilities Rs 10,000,000 and 1,000,000 units give NAV $= 90{,}000{,}000/1{,}000{,}000 =$ Rs 90 per unit.

b. Fundamental Analysis

Fundamental analysis estimates a security's intrinsic value from the factors that drive its earnings and risk, and compares it with the market price: buy if intrinsic value is higher, sell if lower.

1. Economy analysis - GDP growth, inflation, interest rates, balance of payments, policy.
2. Industry analysis - life-cycle stage, competition, regulation, demand and supply.
3. Company analysis - financial statements (EPS, DPS, P/E, debt-equity ratio), management quality, market share.

It follows a top-down (economy, industry, company) or bottom-up approach, using ratio analysis, DCF and dividend discount models. Its limitation is reliance on accounting data and forecasts that may be inaccurate.

c. SEBON (Securities Board of Nepal)

SEBON is the apex regulator of Nepal's securities market, established in 1993 under the Securities Exchange Act, 1983 (now governed by the Securities Act, 2063).

Functions

• Register and regulate securities issuers, stock exchange, brokers, merchant bankers, depositories and mutual funds.
• Approve public issues, rights issues and prospectuses.
• Grant and cancel licences of market intermediaries.
• Investigate insider trading and market manipulation and impose penalties.
• Issue directives and run investor education programmes.

It is run by a Board headed by a Chairman appointed by the Government of Nepal, and works with NEPSE and CDS and Clearing Limited. Its aim is a transparent market with investor confidence.

The question as given lists only provision for loan loss (Rs 200), noninterest income (Rs 950), noninterest expenses (Rs 1,720) and taxes (Rs 1,220). Interest income, interest expense, earning assets, interest-bearing liabilities, total assets and equity are also needed, so each ratio is shown below as a formula, with the given items substituted where they apply.

Basic definitions

$\text{Total operating income} = \text{Interest income} + \text{Noninterest income}$

$\text{Net income} = \text{Total operating income} - \text{Interest expense} - \text{Provision for loan loss} - \text{Noninterest expenses} - \text{Taxes}$

1. Interest spread

$\text{Interest spread} = \frac{\text{Interest income}}{\text{Earning assets}} - \frac{\text{Interest expense}}{\text{Interest-bearing liabilities}}$

2. Return on equity

$\text{ROE} = \frac{\text{Net income}}{\text{Total equity}} = \text{Profit margin} \times \text{Asset utilization} \times \text{Equity multiplier}$

3. Return on assets

$\text{ROA} = \frac{\text{Net income}}{\text{Total assets}} = \text{Profit margin} \times \text{Asset utilization}$

4. Asset utilization

$\text{AU} = \frac{\text{Total operating income}}{\text{Total assets}}$

5. Equity multiplier

$\text{EM} = \frac{\text{Total assets}}{\text{Total equity}}$

6. Profit margin

$\text{PM} = \frac{\text{Net income}}{\text{Total operating income}}$

7-10. Expense ratios (each as a share of total operating income)

These ratios link together: $\text{PM} = 1 - \text{interest expense ratio} - \text{provision ratio} - \text{noninterest expense ratio} - \text{tax ratio}$. Substitute the interest income, interest expense, assets and equity figures of the original problem into the formulas above to obtain the numerical values.

The question stem only gives the section instruction (attempt any three of the problems, 15 marks each). The method for the problem types usually set in this section is as follows.

1. Cost-volume-profit and leverage

$\text{Contribution per unit} = P - V,\qquad \text{BEP (units)} = \frac{\text{Fixed cost}}{P-V}$

$\text{Margin of safety} = \frac{\text{Sales} - \text{BEP sales}}{\text{Sales}},\quad \text{DOL} = \frac{\text{Contribution}}{\text{EBIT}},\quad \text{DFL} = \frac{\text{EBIT}}{\text{EBIT} - I},\quad \text{DCL} = \text{DOL}\times\text{DFL}$

2. Capital budgeting

• Payback period = years before recovery + unrecovered cost / cash flow of the recovery year.
• $NPV = \sum \dfrac{CF_t}{(1+k)^t} - C_0$ and $PI = \dfrac{PV \text{ of inflows}}{C_0}$. Accept if $NPV>0$ and $PI>1$.
• IRR is the rate at which $NPV=0$, found by interpolation between two trial rates. Accept if IRR exceeds the cost of capital.
• For mutually exclusive projects compare NPV and discounted payback; if lives differ, use the replacement chain or equivalent annual annuity.

3. EBIT-EPS analysis

$EPS = \frac{(EBIT - I)(1-t) - \text{Preference dividend}}{\text{Number of shares}}$

The indifference point is the EBIT at which the EPS of the two financing plans are equal. Above it, the plan with more debt gives the higher EPS.

4. Cost of capital and marginal cost of capital

$k_d = \frac{I(1-t)}{NP},\quad k_p = \frac{D_p}{NP},\quad k_e = \frac{D_1}{P_0} + g,\quad WACC = \sum w_i k_i$

The MCC is the weighted average cost of each new rupee raised at the target capital structure. A project is accepted only if its return exceeds the MCC at that level of financing.

5. Presentation in the exam

Write the formula, substitute the figures, show each step and state the decision in words (accept, reject or choose project X), because marks are awarded for method and conclusion as well as for the final number.

Functions of Investment Banks, Brokerage Firms and Venture Capitalists

1. Investment Banks

Investment banks are financial institutions that help corporations, governments and other entities raise capital and carry out large, complex financial transactions. Their main functions are:

a) Capital raising (underwriting). They help companies issue new securities — shares (equity) or debentures and bonds (debt) — in the primary market. The investment bank underwrites the issue, i.e. it agrees to buy the unsold portion of the issue at an agreed price, thereby bearing the risk of non-subscription. It advises the issuer on the type of security, issue price, timing and size of the issue.

b) Corporate advisory services. They advise on mergers and acquisitions (M&A), takeovers, divestitures, restructuring, joint ventures and corporate valuation. They identify suitable targets, conduct due diligence, negotiate the deal and arrange the financing.

c) Trading and market making. They trade securities in the secondary market, act as market makers by quoting buy and sell prices, and deal in shares, bonds, derivatives and foreign exchange for their own account and for clients.

d) Asset and wealth management. They manage mutual funds, pension funds and portfolios of high-net-worth individuals and institutions.

e) Research and advisory. They publish research reports on industries, companies and securities, and provide investment advice to institutional investors.

f) Other services. Project financing, syndicated lending, securitisation, private placement of securities, IPO management, and acting as intermediaries in the money market.

In short, investment banks bridge the gap between those who need funds (corporations and governments) and those who supply funds (investors), and they earn fees, commissions and underwriting spreads.

2. Brokerage Firms

A brokerage firm (stock broker) is a licensed intermediary that buys and sells securities on behalf of clients in the secondary market. Its functions are:

a) Execution of orders. It executes buy and sell orders of clients on the stock exchange (in Nepal, through NEPSE) as per the client's instructions regarding security, quantity, price and time.

b) Agency function. It acts as an agent of the investor, not as a principal. It does not own the securities traded; it only brings the buyer and seller together and charges a commission (brokerage) for the service.

c) Advisory and information service. It provides market information, price quotations, research reports and investment advice to clients, helping them take informed decisions.

d) Margin trading and financing. It may extend margin loans to clients so that they can buy securities by paying only a part of the price, and it holds the securities as collateral.

e) Custodial and settlement service. It keeps records of clients' holdings, helps in the transfer and registration of shares, and settles transactions through the clearing house.

f) Market liquidity. By continuously executing orders, brokerage firms add depth and liquidity to the securities market and help in price discovery.

g) Underwriting and issue management. Many brokerage firms also act as issue managers, underwriters and depository participants (DPs) for primary market issues.

3. Venture Capitalists

A venture capitalist is a professional investor (or firm) that provides equity or quasi-equity finance to new, young, high-risk and high-growth potential enterprises, usually in exchange for an ownership stake and a share in management. Their functions are:

a) Financing start-ups and innovative ventures. They supply seed capital, start-up capital and expansion capital to entrepreneurs who cannot get bank loans because they lack collateral, track record and stable cash flows.

b) Risk bearing. They accept high risk in the hope of high returns. Out of many ventures financed, a few succeed and give very large returns that cover the losses on the failures.

c) Managerial and technical support. Beyond money, they provide mentoring, business planning, marketing links, professional management, accounting and legal support, and help in recruiting key personnel. This is called hand-holding or value addition.

d) Monitoring and control. They take a seat on the board, monitor performance, set milestones and intervene when the venture deviates from its plan. They often hold convertible preference shares or debentures with protective covenants.

e) Networking and resource mobilisation. They connect the venture with suppliers, customers, bankers, auditors and later-stage investors.

f) Exit and harvest. Their ultimate aim is to exit after the venture matures and earns profit, through an Initial Public Offering (IPO), sale of shares to a strategic buyer, buy-back by the promoter, or sale to another venture fund. The exit provides capital gains to the venture capitalist and liquidity to the entrepreneur.

g) Promotion of entrepreneurship and innovation. By financing risky but innovative ideas, venture capitalists encourage new enterprise creation, employment generation and technological development, especially in sectors such as information technology, biotechnology and agro-processing.

Summary

Thus, investment banks serve established and large entities in raising and restructuring capital, brokerage firms provide investors access to the secondary market as agents, and venture capitalists supply risk capital and managerial support to young, innovative enterprises.

Measurement of Capital Adequacy Ratio (CAR)

The Capital Adequacy Ratio (CAR), also called the Capital to Risk-Weighted Assets Ratio (CRAR), measures a bank's financial strength by comparing its capital with its risk-weighted assets. It is expressed as a percentage:

$\text{CAR} = \frac{\text{Tier I Capital} + \text{Tier II Capital}}{\text{Risk-Weighted Assets (RWA)}} \times 100$

Components of Capital

Tier I Capital (Core Capital) — the highest quality capital, permanently available to absorb losses:

• Paid-up equity capital
• Statutory and general reserves
• Retained earnings
• Less: intangible assets, accumulated losses

Tier II Capital (Supplementary Capital) — secondary capital, limited to 100% of Tier I:

• Undisclosed reserves
• Revaluation reserves (discounted)
• General loan loss provisions
• Hybrid capital instruments
• Subordinated term debt

Risk-Weighted Assets (RWA)

RWA is computed by assigning risk weights to each asset and off-balance-sheet item as prescribed by the central bank:

$\text{RWA} = \sum (\text{Asset Value} \times \text{Risk Weight})$

Illustrative risk weights under Basel norms:

Steps in Measurement

1. Classify assets into risk categories and assign prescribed risk weights.
2. Compute total RWA by multiplying each asset by its risk weight and summing.
3. Determine Tier I and Tier II capital, applying regulatory limits and deductions.
4. Apply the formula: CAR = (Tier I + Tier II) ÷ RWA × 100.
5. Compare the result with the regulatory minimum (Basel III: 8% total, of which Tier I ≥ 6% and Common Equity Tier I ≥ 4.5%, plus a 2.5% capital conservation buffer).

Numerical Illustration

Suppose a bank has Tier I capital of Rs 80 crore, Tier II capital of Rs 40 crore, and RWA of Rs 1,200 crore.

$\text{CAR} = \frac{80 + 40}{1200} \times 100 = 10\%$

Since 10% exceeds the 8% minimum, the bank is adequately capitalized. Tier I alone gives 6.67%, also above the 6% requirement.

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Implications of Capital Adequacy Ratio

1. Financial stability and solvency. A high CAR indicates the bank can absorb unexpected losses without becoming insolvent. It protects depositors' funds and reduces the probability of bank failure.

2. Public confidence. Depositors, investors and rating agencies treat CAR as a signal of safety. A strong ratio builds trust and discourages bank runs.

3. Regulatory compliance. Banks must maintain the minimum CAR prescribed by the central bank (Nepal Rastra Bank requires 11% for commercial banks, including a 2.5% buffer). Failure invites supervisory action, restrictions on expansion, dividend caps or even license revocation.

4. Lending capacity. CAR directly limits how much a bank can lend. With a fixed capital base, higher RWA means the bank must either raise capital or slow credit growth. Thus CAR constrains credit expansion and, in turn, economic activity.

5. Risk-taking behaviour. Risk-based capital requirements discourage excessive exposure to high-risk assets (unsecured loans, speculative investments) because such assets attract higher risk weights and consume more capital.

6. Cost of capital and profitability. Holding more capital is safe but costly — equity is more expensive than deposits. A very high CAR may indicate under-utilization of funds and lower return on equity, while a very low CAR signals fragility. Banks therefore balance safety against profitability.

7. Credit rating and funding cost. Banks with higher CAR generally enjoy better credit ratings and can raise funds at lower cost in domestic and international markets.

8. Financial system stability. At the macro level, adequate capitalization across banks reduces systemic risk and contagion during crises. This is the core rationale of the Basel framework.

9. Dividend policy. Regulators link dividend distribution to CAR. Banks below the buffer zone face restrictions on cash dividends, affecting shareholder returns.

10. International competitiveness. Compliance with Basel III standards allows banks to operate globally and access foreign capital, while non-compliance limits cross-border operations.

Conclusion

CAR is measured as the ratio of total regulatory capital to risk-weighted assets. It serves as a buffer against unexpected losses and acts as a supervisory tool. Its implications extend from depositor protection and bank solvency to credit creation, profitability, and overall stability of the banking system — making it the cornerstone of prudential regulation.

a. Treasury Inflation Protection Security (TIPS)

Par value = Rs 1,000
Coupon rate = 10% per annum
Annual coupon payment = 10% of inflation-adjusted principal.

(i) CPI one year before = 100, today = 107.
Inflation-adjusted principal today = (1{,}000 \times \frac{107}{100} = Rs\ 1{,}070).
Coupon paid today = (10% \times 1{,}070 = \mathbf{Rs\ 107}).

(ii) Expected CPI next year = 118.
Inflation-adjusted principal next year = (1{,}070 \times \frac{118}{107} = Rs\ 1{,}180).
Expected coupon next year = (10% \times 1{,}180 = \mathbf{Rs\ 118}).

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b. Bond Prices and Sensitivity

(i) Required rate of return = 10%.

Bond A:
[ P_A = 100 \times \frac{1-(1.10)^{-5}}{0.10} + \frac{1{,}000}{(1.10)^5} ] [ P_A = Rs\ 1{,}000 ]

Bond B:
[ P_B = 90 \times \frac{1-(1.10)^{-10}}{0.10} + \frac{1{,}000}{(1.10)^{10}} ] [ P_B = Rs\ 938.55 ]

(ii) Bond B is more sensitive to a change in interest rate.
It has a longer maturity (10 years vs. 5 years) and a lower coupon rate (9% vs. 10%). Both factors increase duration, so Bond B’s price changes more for a given change in interest rate.

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c. Stock Valuation

(i)
[ P_0 = \frac{D_1 + P_1}{1+r} ] [ P_0 = \frac{10 + 300}{1.15} = \frac{310}{1.15} = \mathbf{Rs\ 269.57} ]

(ii) Using the Gordon growth model:
[ P_0 = \frac{D_1}{r-g} ] [ r = \frac{D_1}{P_0} + g ] [ r = \frac{20}{330} + 0.08 = 0.140606 = \mathbf{14.06%} ]

So, the required rate of return is approximately 14.06%.

(a) Price of the commercial paper

For a discount instrument on a 360-day basis:

$P = FV\left(1 - d\times\frac{t}{360}\right) = 12{,}000{,}000\left(1 - 0.0485\times\frac{60}{360}\right)$

$= 12{,}000{,}000\,(1-0.0080833) = \text{Rs } 11{,}903{,}000$

The discount is Rs 97,000, so the commercial paper is priced at Rs 11,903,000.

(b)(i) Dutch auction of Rs 1.5 billion of 91-day T-bills (competitive bids only)

In a Dutch (single-price) auction, bids are ranked from the highest price to the lowest and filled until the issue of Rs 1,500 million is covered. The price of the last accepted bid is the cut-off price, and every successful bidder pays it.

The issue is fully covered at the bid of 99.25, so the cut-off price is Rs 99.25.

• Bidder 5 receives Rs 500 million at 99.25 (pays Rs 496.25 million).
• Bidder 1 receives Rs 200 million at 99.25 (pays Rs 198.50 million).
• Bidder 4 receives Rs 800 million at 99.25 (pays Rs 794.00 million).
• Bidders 2 and 3 receive nothing, because their prices are below the cut-off.

Total raised $= 1{,}500\times 0.9925 = \text{Rs } 1{,}488.75$ million.

(b)(ii) If non-competitive bids were also received

Non-competitive bidders state only a quantity and agree to accept the cut-off price. Their bids are filled first, so they reduce the amount left for competitive bidders: if non-competitive bids total Rs $X$ million, only $1{,}500 - X$ million is allotted among competitive bids. The cut-off price is then found by ranking the competitive bids against this smaller amount, and so it can only stay the same or rise. All successful bidders, competitive and non-competitive, pay that single cut-off price.