(a) Features and major participants of money market instruments

Features

1. Short maturity: instruments mature within one year (from one day up to 364/365 days), for example Treasury bills, commercial paper, certificates of deposit, call money and repos.
2. High liquidity: an active secondary market lets investors sell quickly at low cost.
3. Low default risk: issuers are the government, the central bank, commercial banks and highly rated firms.
4. Large denominations: it is largely a wholesale market with big lot sizes.
5. Discount or interest basis: T-bills are sold at a discount to face value; CDs and commercial paper may carry interest or be issued at a discount.
6. Low return: safety and liquidity mean yields are lower than on capital market securities.
7. Over-the-counter trading: trades are done through banks, dealers and brokers, not a formal exchange.
8. Auction issue: T-bills are sold by competitive and noncompetitive bidding.

Major participants

1. Government (Ministry of Finance): raises short-term public debt through T-bills.
2. Central bank (Nepal Rastra Bank): conducts the auctions as the government's agent and uses open market operations, repo and reverse repo to manage liquidity.
3. Commercial banks: issue CDs, trade T-bills and lend or borrow in the interbank call market.
4. Other financial institutions (development banks, finance companies) and primary dealers: invest surplus funds and make markets.
5. Corporations: sell commercial paper to raise funds and invest idle cash.
6. Money market mutual funds, insurance companies and pension or provident funds: invest temporary surpluses.
7. Individuals and institutional investors: buy T-bills and fund units for safe short-term returns.

(b) Treasury bill returns

Par value F = Rs 100,000; price P = Rs 98,500; t = 91 days. Discount = 100,000 - 98,500 = Rs 1,500.

Discount yield (360-day basis):

$i_d=\frac{F-P}{F}\times\frac{360}{t}=\frac{1{,}500}{100{,}000}\times\frac{360}{91}=0.0593=5.93\%$

Investor return (bond-equivalent yield, 365-day basis):

$i_{inv}=\frac{F-P}{P}\times\frac{365}{t}=\frac{1{,}500}{98{,}500}\times\frac{365}{91}=0.0611=6.11\%$

Effective annual return (compounding the 91-day holding return):

$i_{eff}=\left(1+\frac{F-P}{P}\right)^{365/91}-1=\left(\frac{100{,}000}{98{,}500}\right)^{4.011}-1=1.0625-1=6.25\%$

(c) 90-day certificate of deposit

Denomination = Rs 10,000,000; annual yield = 8%; term = 90 days (360-day year).

$\text{Interest}=10{,}000{,}000\times0.08\times\frac{90}{360}=\text{Rs }200{,}000$

$\text{Total payment at maturity}=10{,}000{,}000+200{,}000=\text{Rs }10{,}200{,}000$

The bank pays Rs 200,000 interest, and Rs 10,200,000 in total, at the end of 90 days.

Monetary Tools of the Central Bank

Introduction

The central bank (Nepal Rastra Bank in the Nepali context) is responsible for fine-tuning the money supply in the banking system by employing appropriate monetary tools. These tools are broadly classified into three types: open market operations, the discount rate, and reserve requirements. Each works through a different channel, but all aim to influence the volume of credit and the level of liquidity in the economy.

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 money supply and interest rates. Under OMO, the central bank uses four instruments:

• Repurchase Agreement (Repo): The central bank lends short-term funds to commercial banks against government securities as collateral, with an agreement to repurchase them later. It injects liquidity into the banking system.
• Reverse Repo: The opposite of a repo. The central bank absorbs liquidity from commercial banks by selling securities with an agreement to buy them back later.
• Outright Sale: The central bank sells government securities permanently (without a repurchase agreement), which permanently absorbs liquidity and reduces the money supply.
• Outright Purchase: The central bank buys government securities permanently, which permanently injects liquidity and increases the money supply.

2. Discount Rate

The discount rate is the interest rate at which the central bank lends to commercial banks, usually against eligible securities. When the central bank raises the discount rate, borrowing from the central bank becomes expensive, so commercial banks borrow less and also raise their own lending rates. This reduces credit creation and contracts the money supply. When the discount rate is lowered, borrowing becomes cheaper, banks lend more, and the money supply expands. In Nepal, this is reflected through the bank rate.

3. Reserve Requirements

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. For example, if the required reserve ratio is 10%, a bank receiving a deposit of Rs 1,000 must keep Rs 100 as reserve and can lend only Rs 900. The credit multiplier is:

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

where $r$ is the required reserve ratio. A higher $r$ means a smaller multiplier and hence a smaller expansion of deposits. In Nepal, this tool is applied through the Cash Reserve Ratio (CRR).

Conclusion

Thus, the central bank controls the money supply through open market operations (repo, reverse repo, outright sale, and outright purchase), the discount rate, and reserve requirements. By using these tools appropriately—expanding credit during recession and contracting it during inflation—the central bank maintains monetary stability in the banking system.

Assuming the standard data for this problem:

• Number of potential policyholders, (n = 10{,}000)
• Death rate, (q = 0.002)
• Sum assured, (S = \text{Rs }1{,}00{,}000)
• Investment return, (i = 8.5% = 0.085)
• Operating expenses plus target profit (= \text{Rs }1{,}70{,}000)

1. Fair premium

Expected number of deaths:

[ nq = 10{,}000 \times 0.002 = 20 ]

Total expected death claims:

[ 20 \times 1{,}00{,}000 = \text{Rs }20{,}00{,}000 ]

Since the company can earn (8.5%) on investments, the fair premium is the present value of expected claims:

[ \text{Fair premium} = \frac{20{,}00{,}000}{1.085} ]

[ \text{Fair premium} = \text{Rs }18{,}43{,}317.97 ]

Per policy:

[ \frac{18{,}43{,}317.97}{10{,}000} = \text{Rs }184.33 ]

2. Gross premium

Expense and profit loading per policy:

[ \frac{1{,}70{,}000}{10{,}000} = \text{Rs }17 ]

Gross premium per policy:

[ 184.33 + 17 = \text{Rs }201.33 ]

Total gross premium:

[ 201.33 \times 10{,}000 = \text{Rs }20{,}13{,}317.97 ]

Answer

• Fair premium per policy = Rs 184.33
• Gross premium per policy = Rs 201.33
• Total fair premium = Rs 18,43,317.97
• Total gross premium = Rs 20,13,317.97

a. Flat benefit formula

Annual pension benefit = Benefit rate per year of service × Total years of service
= Rs 900 × 30
= Rs 27,000 per year

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b. Career average formula

Annual pension benefit = 4% × Career average salary × Total years employed
= 0.04 × Rs 50,000 × 30
= Rs 2,000 × 30
= Rs 60,000 per year

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c. Final pay formula

Annual pension benefit = 3% × Average salary of last four years × Total years employed

The last four years would be Years 27, 28, 29, and 30. The data provide salaries only for Years 28, 29, and 30:

[ \text{Year 28} = Rs,51,000,\quad \text{Year 29} = Rs,53,000,\quad \text{Year 30} = Rs,55,000 ]

The salary for Year 27 is missing. Therefore, the average salary of the last four years cannot be determined from the given data. Hence:

[ \text{Jamuna's annual pension benefit under the final pay formula} = \textbf{Cannot be determined from the given data} ]

If the question intended the last three years instead of the last four years, then:

[ \text{Average of last three years} = \frac{51,000+53,000+55,000}{3} = Rs,53,000 ]

[ \text{Annual pension benefit} = 0.03 \times 53,000 \times 30 = Rs,47,700 ]

But as written, the final pay benefit is not uniquely computable.

Given:

• Annual salary = Rs 600,000
• Manab’s contribution rate = 12% of salary
• Employer match = 50% of first 5% of salary
• Expected annual return = 10%
• Manab’s tax bracket = 25%
• Manab’s contribution is tax-deductible

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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’s contribution:

$$50\% \times 5\% \times 600{,}000 = 0.50 \times 30{,}000 = \text{Rs }15{,}000$$

Total first-year contribution:

$$72{,}000 + 15{,}000 = \text{Rs }87{,}000$$

Answer:

• 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.

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

Answer: Tax saving = Rs 18,000

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c. Cost for the retirement plan

The net cost to Manab is his own contribution minus the tax saving.

$$\text{Net cost} = 72{,}000 - 18{,}000 = \text{Rs }54{,}000$$

Answer: Cost to Manab = Rs 54,000
(The employer’s share of cost is Rs 15,000.)

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

Total investment at the start of the year:

$$72{,}000 + 15{,}000 = \text{Rs }87{,}000$$

One-year return at 10%:

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

Total value at the end of one year:

$$87{,}000 + 8{,}700 = \text{Rs }95{,}700$$

Answer:

• Total investment at year start = Rs 87,000
• One-year return = Rs 8,700
• Total at year end = Rs 95,700

Types of Insurance

Insurance is a contract (policy) under which the insurer, in return for a premium, agrees to compensate the insured for a specified loss. Insurance may be classified on the basis of nature of business, subject matter, and risk coverage.

1. On the Basis of Nature of Business

(a) Life Insurance Insurance of human life, where the sum assured is paid on death or on maturity of the policy. It is not a contract of indemnity. Major types:

• Whole Life Policy – premium payable throughout life; sum assured paid only on death.
• Endowment Policy – sum assured paid on death or on survival up to the maturity date, whichever is earlier.
• Term Insurance – protection for a fixed term only; no payment if the insured survives the term.
• Money Back Policy – periodic part-payments of the sum assured plus a lump sum at maturity.
• Annuity/Pension Policy – regular income after retirement.

(b) Non-Life (General) Insurance Insurance of property and liability, based on the principle of indemnity. Major types:

• Fire Insurance – covers loss of property by fire, lightning and allied perils.
• Marine Insurance – covers loss of cargo and hull during sea/air/land transit (hull, cargo, freight).
• Motor Insurance – covers vehicles against accident, theft and third-party liability.
• Health/Medical Insurance – covers hospitalisation and medical expenses.
• Miscellaneous Insurance – burglary, cash-in-transit, crop, livestock, aviation, engineering, personal accident, etc.

2. On the Basis of Subject Matter

• Property Insurance – buildings, plant, stock, vehicles, cargo.
• Liability Insurance – third-party motor, public liability, professional indemnity, employer's liability.
• Personal Insurance – life, health, personal accident.

3. On the Basis of Risk Coverage

• Individual Insurance – policy issued to a single person or firm.
• Group Insurance – one master policy covering many persons (e.g., group life, group health).
• Social Insurance – compulsory, government-run schemes such as social security and employee deposit funds.

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Role of Nepal Insurance Authority (NIA) in Regulation of Insurance Companies in Nepal

The Nepal Insurance Authority (NIA), established under the Insurance Act, 2079 (2022) with its head office in Kathmandu, is the sole regulatory and supervisory body of the insurance sector in Nepal. Its major roles are:

1. Licensing and Registration Grants, renews, suspends or cancels licences of life and non-life insurers, reinsurers, brokers, agents, surveyors and loss assessors. No person may carry on insurance business without NIA approval.

2. Formulation of Rules, Directives and Standards Issues directives on premium rates, policy wordings, reinsurance, solvency, investment, accounting and reporting to ensure uniformity and fairness in the industry.

3. Financial and Solvency Regulation Prescribes minimum paid-up capital (e.g., Rs 5 billion for life and Rs 2.5 billion for non-life insurers as per current rules), maintains solvency margin, and monitors technical reserves so that insurers can always meet their liabilities.

4. Investment Regulation Directs the pattern of investment of insurance funds (e.g., a fixed proportion in government securities, banks, and infrastructure) to ensure safety, liquidity and profitability of policyholders' money.

5. Reinsurance Regulation Approves reinsurance programmes, fixes the compulsory retention and cession limits, and regulates foreign reinsurance so that risks are properly spread and foreign exchange outflow is controlled.

6. Market Conduct and Consumer Protection Regulates premium rates and commissions, checks unfair trade practices, and provides a grievance-handling mechanism so that policyholders are not exploited. It also runs insurance awareness and financial literacy programmes.

7. Supervision and Inspection Conducts on-site and off-site supervision, audits, and special inspections; can direct insurers to rectify weaknesses, and may take punitive action, including removal of directors or management.

8. Actuarial and Technical Oversight Approves actuarial valuation of life funds, bonus rates and premium tariffs, and ensures that technical reserves are computed on sound actuarial principles.

9. Development and Promotion of Insurance Promotes insurance penetration and density through awareness campaigns, encourages micro-insurance, crop and livestock insurance, and develops human resources through training and examinations for agents and surveyors.

10. Dispute Settlement and Coordination Settles disputes between insurers and policyholders, and coordinates with the Ministry of Finance, Nepal Rastra Bank, SEBON and other bodies on matters of common interest.

Conclusion Thus, NIA acts as the protector of policyholders, the watchdog of insurers, and the promoter of a healthy, competitive and trustworthy insurance market in Nepal. Through licensing, prudential regulation, market conduct supervision and developmental activities, it ensures the stability and growth of the insurance industry.

Central Banks and the Money Supply: Expansion and Contraction through Monetary Tools

Introduction. The central bank is the apex monetary authority responsible for controlling the volume of money and credit in an economy. In Nepal, this authority rests with Nepal Rastra Bank (NRB). The process by which the central bank increases or decreases the money supply is called monetary management, and the instruments used are called monetary tools or instruments of monetary policy. When the central bank wants to expand the money supply (expansionary policy), it uses tools that inject reserves into the banking system; when it wants to contract the money supply (contractionary policy), it uses tools that drain reserves. The tools are broadly classified into quantitative (general) and qualitative (selective) tools.

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A. Quantitative Tools

1. Open Market Operations (OMO)

OMO refers to the buying and selling of government securities (treasury bills, bonds) by the central bank in the open market.

• To expand money supply: The central bank buys government securities. It pays the sellers (banks, financial institutions, public) by crediting their accounts, which increases bank reserves. With more reserves, banks can create more credit, and the money supply expands by a multiple of the initial reserve increase (through the credit multiplier).
• To contract money supply: The central bank sells government securities. Buyers pay from their bank deposits, which reduces bank reserves. With fewer reserves, banks' lending capacity falls, and the money supply contracts.

2. Bank Rate / Discount Rate Policy

The bank rate is the rate at which the central bank lends to commercial banks against eligible securities.

• To expand: The central bank lowers the bank rate. Borrowing from the central bank becomes cheaper, so banks borrow more reserves and lend more, expanding credit and money supply. It also signals lower interest rates in the market.
• To contract: The central bank raises the bank rate. Borrowing reserves becomes costly, banks reduce borrowing and lending, and the money supply contracts.

3. Cash Reserve Ratio (CRR)

CRR is the minimum percentage of a bank's total deposits that must be kept as cash reserves with the central bank.

• To expand: A reduction in CRR leaves banks with more free reserves to lend, increasing the credit multiplier and the money supply.
• To contract: An increase in CRR locks up a larger part of deposits as reserves, reducing lendable funds and contracting the money supply.

4. Statutory Liquidity Ratio (SLR)

SLR is the minimum percentage of deposits that banks must hold in liquid assets such as cash, gold, or approved government securities.

• To expand: A cut in SLR releases funds for lending, expanding credit.
• To contract: A rise in SLR diverts more funds into liquid assets and reduces lending capacity, contracting the money supply.

5. Repo and Reverse Repo

• Repo (repurchase agreement): The central bank lends short-term funds to banks against securities, injecting liquidity — used to expand.
• Reverse repo: The central bank borrows from banks against securities, absorbing liquidity — used to contract.

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B. Qualitative / Selective Tools

These influence the direction and use of credit rather than its total volume:

• Margin requirements: Raising the margin reduces credit for speculative activities; lowering it encourages credit.
• Moral suasion: The central bank persuades banks to follow a desired lending policy.
• Credit rationing / selective credit control: Fixing credit ceilings for particular sectors.
• Direct action: Penalising banks that violate directives.
• Publicity and direct appeal: Publishing policy intentions to guide bank behaviour.

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C. How the Tools Work Together: The Money Multiplier Link

The central bank controls high-powered money (reserve money) = currency with the public + reserves of banks. The total money supply is:

$M = m \times H$

where (M) = money supply, (m) = money multiplier, and (H) = high-powered money. Since

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

((c) = currency–deposit ratio, (r) = reserve–deposit ratio), the central bank can change (M) either by changing (H) (through OMO, bank rate, repo) or by changing (r) (through CRR and SLR).

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D. Appropriate Example: Nepal Rastra Bank

Expansionary case: Suppose Nepal is in a recession with low credit growth. NRB:

1. Buys Rs 10 billion of treasury bills through OMO → bank reserves rise by Rs 10 billion.
2. Lowers the bank rate from 6.5% to 5.5% → banks borrow more reserves.
3. Reduces CRR from 4% to 3% → releases additional lendable funds.

If the money multiplier is 4, the initial Rs 10 billion reserve injection can raise the money supply by up to Rs 40 billion. Lower interest rates encourage investment and consumption, stimulating output and employment.

Contractionary case: Suppose inflation rises to 8% due to excess demand. NRB:

1. Sells Rs 10 billion of treasury bills → absorbs reserves, reducing bank lending.
2. Raises the bank rate to 7.5% → borrowing becomes expensive.
3. Increases CRR from 4% to 5% → locks up more deposits as reserves.

The money supply contracts, market interest rates rise, credit demand falls, aggregate demand cools, and inflationary pressure is controlled.

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E. Limitations of Monetary Tools

• Commercial banks may hold excess reserves and not lend, weakening the multiplier effect.
• In a deep recession, even low interest rates may not stimulate borrowing (liquidity trap).
• The unorganised/informal sector may remain outside the reach of monetary policy.
• Time lags and conflicting objectives (e.g., price stability vs. growth) reduce effectiveness.
• In developing economies like Nepal, a large informal economy and underdeveloped money market weaken transmission.

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Conclusion

The central bank expands the money supply by buying securities, lowering the bank rate, and reducing CRR/SLR, and contracts it by selling securities, raising the bank rate, and increasing CRR/SLR. Through these tools, it regulates credit, controls inflation, and promotes economic stability. In Nepal, NRB uses OMO, CRR, SLR, bank rate, and repo/reverse repo as its principal instruments. However, their effectiveness depends on the development of the financial system, the behaviour of commercial banks, and the overall economic environment.

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 (Ministry of Finance / 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.

2. Central Bank (Nepal Rastra Bank) The central bank acts as the regulator, supervisor, and operator of the money market. It issues treasury bills on behalf of the government, conducts open market operations, and uses instruments such as repo, reverse repo, and outright purchase or sale to control money supply and liquidity.

3. Commercial Banks Commercial banks are dominant participants. They borrow and lend short-term funds among themselves through the call money market to meet reserve requirements and manage liquidity. They also deal in treasury bills, certificates of deposit, and commercial papers.

4. Non-Bank Financial Institutions (Development Banks, Finance Companies, Microfinance Institutions) These institutions participate in the call money market and invest in short-term instruments to manage their day-to-day liquidity positions.

5. Insurance Companies and Mutual Funds They have temporary surplus funds and invest them in money market instruments to earn a return while keeping funds safe and liquid.

6. Corporates and Business Firms Large firms with surplus cash invest in commercial papers and other short-term instruments, while firms facing temporary cash shortages raise funds by issuing commercial papers or borrowing from banks.

7. Discount Houses / Primary Dealers These specialized institutions act as intermediaries between the central bank and other participants. They underwrite and discount short-term securities and provide a ready market for them.

8. Foreign Institutional Investors and Non-Resident Entities In an open economy, they participate through short-term instruments and foreign currency deposits, adding depth to the market.

9. Individuals and Households Through deposits and participation in mutual fund schemes, individuals indirectly supply short-term funds to the money market.

Conclusion Thus, the money market brings together the government, central bank, banks, non-bank financial institutions, corporates, and individual investors. The central bank and commercial banks are the most active participants, while the others provide funds, demand funds, or act as intermediaries, making the market liquid and efficient.

Functions of Merchant Banker in Nepal (5 marks)

A merchant banker in Nepal is a financial institution licensed by SEBON (Securities Board of Nepal) to assist companies in raising capital and managing securities-related activities. Its major functions are:

1. Issue Management (Underwriting and Capital Raising): Merchant bankers act as issue managers for Initial Public Offerings (IPOs), Further Public Offerings (FPOs), rights issues and debenture issues. They advise the company on the size, price and timing of the issue, prepare and file the prospectus with SEBON, and may underwrite the shares by guaranteeing to buy any unsubscribed portion.

2. Advisory Services: They provide financial and corporate advisory services such as corporate restructuring, merger and acquisition advice, capital structure planning, project appraisal and feasibility studies, and valuation of shares and businesses.

3. Portfolio Management: Licensed merchant bankers manage investment portfolios of individuals and institutions by investing their funds in shares, debentures and other securities, aiming to maximise return at a given level of risk.

4. Market Making and Trading Support: They help create a market for securities by acting as market makers, providing liquidity, and assisting in the buying and selling of shares and debentures.

5. Other Services: They undertake registrar and share transfer functions, act as trustee for debenture holders, provide loan syndication and consortium lending support, and offer depository participant (DP) services and investor education.

In Nepal, institutions such as Nabil Investment Banking Ltd., NIBL Ace Capital, Civil Capital Market Ltd. and Sanima Capital Ltd. perform these merchant banking functions under SEBON's licensing and regulation.

Answer (5 marks)

In every economy, some units spend less than their income and thus have surplus funds (households, savers, some firms), while others spend more than their income and need deficit funds (businesses, government, borrowers). The financial system channels savings from surplus units to deficit units through two routes:

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

• Primary securities — shares, debentures, bonds, and commercial papers issued by firms and government.
• Financial markets — the money market (short-term instruments like Treasury bills, commercial papers) and the capital market (long-term instruments like shares and bonds through the primary market, and their resale in the secondary market).
• Investment bankers underwrite and help issue new securities, so savings flow straight from savers to users.

2. Indirect financing (financial intermediaries) Surplus units deposit their savings in banks and financial institutions (commercial banks, development banks, finance companies, cooperatives, insurance companies, mutual funds). These institutions pool the small savings and lend them as loans and advances to deficit units. Here the intermediary creates secondary securities (deposits, insurance policies, mutual fund units) for savers and holds primary securities (loans) against borrowers. The intermediary bears the risk, performs maturity transformation (short-term deposits into long-term loans), and earns the interest spread.

Role of the central bank: Nepal Rastra Bank regulates and supervises these institutions, controls money supply, and directs credit, making the flow smooth and safe.

Conclusion: Thus, through financial markets and financial intermediaries, the savings of surplus units are mobilised into productive investment by deficit units, which raises capital formation, employment, and economic growth.

(a) NAV of each fund

$NAV=\frac{\text{Market value of assets}}{\text{Shares outstanding}}$

(b) Effect of adding 165 shares of ATT to Fund A

The new ATT shares cost 165 x 25 = Rs 4,125, financed by selling 647 new fund shares at the current NAV of Rs 6.375 (647 x 6.375 = Rs 4,124.6, about Rs 4,125).

• New total assets = 6,375 + 4,125 = Rs 10,500
• New shares outstanding = 1,000 + 647 = 1,647

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

The NAV is unchanged. New shares were sold at NAV and the proceeds were invested at unchanged prices, so assets and shares increased in the same proportion. Only the size of the fund changes, not the value per share.

Given:
Transaction deposits (D = \text{Rs } 1{,}500) million
Reserve requirement (r = 8% = 0.08)

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a. Reserve asset to back up deposit liabilities

The bank must hold required reserves as vault cash and balances with the central bank.

[ \text{Required reserve} = r \times D = 0.08 \times 1{,}500 = \text{Rs } 120 \text{ million} ]

Answer: Rs 120 million

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b. Maximum amount the bank can use for lending

The lendable amount is the excess reserve:

[ \text{Excess reserve} = D - \text{Required reserve} ]

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

Answer: Rs 1,380 million

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c. Deposit multiplier

[ \text{Deposit multiplier} = \frac{1}{r} = \frac{1}{0.08} = 12.5 ]

Answer: 12.5

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

Total deposit creation in the banking system:

[ \text{Total deposits} = D \times \text{Deposit multiplier} ]

[ = 1{,}500 \times 12.5 = \text{Rs } 18{,}750 \text{ million} ]

Additional deposits/loans generated beyond the initial deposit:

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

Alternatively,

[ \text{Additional deposits/loans} = \text{Excess reserve} \times \text{Multiplier} ]

[ = 1{,}380 \times 12.5 = \text{Rs } 17{,}250 \text{ million} ]

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

Given: bid price = 98.2 per 100 face value; a 91-day T-bill.

1. Published discount rate

$d=\frac{F-P}{F}\times\frac{360}{n}=\frac{100-98.2}{100}\times\frac{360}{91}=0.018\times3.956=7.12\%$

2. Annual interest rate comparable to bond yields (bond-equivalent yield, 365-day basis)

$i=\frac{F-P}{P}\times\frac{365}{n}=\frac{1.8}{98.2}\times\frac{365}{91}=0.01833\times4.011=7.35\%$

3. Price with 50 days remaining at a discount rate of 11.5%

$P=F\left[1-\frac{d\times n}{360}\right]=100\left[1-\frac{0.115\times50}{360}\right]=100(1-0.01597)=\text{Rs }98.40$

The bill would sell at about Rs 98.40 per Rs 100 of face value.

TU MBS — Fourth Semester

Financial Statement Analysis: Computation of Key Bank Ratios

Note: The question paper normally supplies the bank's income statement and balance sheet. Since the figures are not reproduced here, the following illustrative figures are used to demonstrate the full method. Substitute your question paper's figures in the same formulas.

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Given Data

Income Statement for the year ended (Rs '000)

Balance Sheet (Rs '000)

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Formulas and Computations

1. Interest Spread

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

$= \frac{12{,}000}{90{,}000} - \frac{7{,}000}{80{,}000} = 0.1333 - 0.0875 = 0.0458$

Interest spread = 4.58%

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2. Return on Equity (ROE)

$\text{ROE} = \frac{\text{NPAT}}{\text{Shareholders' equity}} = \frac{3{,}000}{15{,}000} = 0.20$

ROE = 20%

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3. Return on Assets (ROA)

$\text{ROA} = \frac{\text{NPAT}}{\text{Total assets}} = \frac{3{,}000}{100{,}000} = 0.03$

ROA = 3%

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4. Asset Utilization

$\text{Asset utilization} = \frac{\text{Total operating income}}{\text{Total assets}} = \frac{14{,}000}{100{,}000} = 0.14$

Asset utilization = 14%

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5. Equity Multiplier (EM)

$\text{EM} = \frac{\text{Total assets}}{\text{Shareholders' equity}} = \frac{100{,}000}{15{,}000} = 6.67$

Equity multiplier = 6.67 times

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6. Profit Margin

$\text{Profit margin} = \frac{\text{NPAT}}{\text{Total operating income}} = \frac{3{,}000}{14{,}000} = 0.2143$

Profit margin = 21.43%

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7. Interest Expense Ratio

$\text{Interest expense ratio} = \frac{\text{Interest expense}}{\text{Total operating income}} = \frac{7{,}000}{14{,}000} = 0.50$

Interest expense ratio = 50%

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8. Provision for Loan Loss Ratio

$\text{Provision for loan loss ratio} = \frac{\text{Provision for loan losses}}{\text{Total operating income}} = \frac{600}{14{,}000} = 0.0429$

Provision for loan loss ratio = 4.29%

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9. Non-interest Expense Ratio

$\text{Non-interest expense ratio} = \frac{\text{Non-interest expenses}}{\text{Total operating income}} = \frac{2{,}400}{14{,}000} = 0.1714$

Non-interest expense ratio = 17.14%

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10. Tax Ratio

$\text{Tax ratio} = \frac{\text{Tax}}{\text{Total operating income}} = \frac{1{,}000}{14{,}000} = 0.0714$

Tax ratio = 7.14%

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Summary of Results

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Verification (DuPont Identity)

$\text{ROA} = \text{Profit margin} \times \text{Asset utilization} = 0.2143 \times 0.14 = 0.03 = 3\% \checkmark$

$\text{ROE} = \text{ROA} \times \text{Equity multiplier} = 0.03 \times 6.67 = 0.20 = 20\% \checkmark$

$\therefore \text{ROE} = \text{Profit margin} \times \text{Asset utilization} \times \text{Equity multiplier}$

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Interpretation

• Interest spread of 4.58% shows the bank earns more on its earning assets than it pays on its interest-bearing liabilities — a healthy positive spread.
• ROE of 20% indicates strong returns to shareholders, generated mainly through a high equity multiplier (6.67 times), i.e., leverage, rather than a high profit margin alone.
• Profit margin of 21.43% means 21 paisa of net profit per rupee of operating income, after absorbing interest cost (50%), provisions (4.29%), operating expenses (17.14%) and tax (7.14%).
• Asset utilization of 14% reflects the bank's ability to generate revenue from its asset base; a higher ratio would further strengthen ROA.
• The interest expense ratio (50%) is the largest cost component, so the bank's profitability is most sensitive to its cost of funds.

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 major 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 guarantees to buy any unsold portion, thereby bearing the risk of the issue not being fully subscribed. It advises the firm on the type, price and timing of the issue.

b. Corporate advisory services. They advise on mergers and acquisitions (M&A), takeovers, divestitures, restructuring, joint ventures and valuation of businesses. They identify targets, negotiate terms and arrange the financing of the deal.

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, and provide portfolio advisory and private banking services.

e. Research and other services. They publish research reports on companies and industries, provide project finance, syndicated loans, IPO (initial public offering) management, risk management through derivatives, and act as intermediaries in the money market.

In short, investment banks bridge the gap between those who need funds (corporations and governments) and those who have surplus funds (investors), while earning fees, commissions and trading gains.

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. Acting as an agent. It executes buy and sell orders of investors on the stock exchange in the client's name and for the client's account, and charges a commission (brokerage fee) for this service.

b. Providing market access. It gives investors access to the exchange, which an individual cannot enter directly. It maintains trading terminals, online trading platforms and mobile apps for order placement.

c. Advisory and information services. It supplies market information, price quotations, research reports and investment advice, and helps clients decide what, when and how much to buy or sell.

d. Account and settlement services. It opens and maintains client accounts (Demat/trading accounts), keeps records of transactions, arranges settlement of trades, and assists in the transfer and delivery of securities.

e. Margin financing and other services. Many brokers provide margin (loan) facilities to clients for buying shares, offer portfolio management services, and assist in primary market applications and IPO allotment.

f. Market making and liquidity. By continuously trading, brokers add liquidity and depth to the market and help in price discovery.

Thus, brokerage firms are the connecting link between investors and the stock exchange, and they earn income mainly through commissions and margin interest.

3. Venture Capitalists

Venture capitalists (VCs) are specialized investors who provide equity or quasi-equity finance to new, young, high-risk and high-growth potential enterprises, usually in exchange for part ownership and a share in management. Their functions are:

a. Financing start-ups and risky ventures. They supply seed capital, start-up capital and expansion capital to entrepreneurs who cannot obtain bank loans because they lack collateral, track record or stable cash flow.

b. Risk sharing and risk bearing. By investing equity, the VC shares the business risk with the entrepreneur instead of demanding fixed interest, and diversifies risk across a portfolio of ventures.

c. Managerial and technical support. Beyond money, VCs provide "smart capital": business planning, marketing, accounting, recruitment of key personnel, networking and strategic guidance. They often sit on the board and monitor performance.

d. Screening and evaluation. They carefully evaluate business plans, management quality, market size and technology before investing, and carry out due diligence — thereby channeling scarce capital to the most promising ventures.

e. Value addition and exit. They help the venture grow to a stage where it can be sold or listed, and then exit through IPO, sale to a strategic buyer or buyback, earning capital gains. This exit route also encourages innovation and entrepreneurship in the economy.

f. Promotion of innovation and employment. By funding technology-based and innovative enterprises, VCs promote research, new products, employment generation and overall economic development.

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Conclusion: Investment banks serve large corporations and governments in raising capital and advisory work; brokerage firms serve investors by executing trades and providing market access and advice; venture capitalists serve new, risky enterprises by supplying equity finance, managerial support and an exit mechanism. Together they form an important part of the financial system by mobilizing savings and allocating them to productive uses.

Measurement of Capital Adequacy Ratio (CAR)

The Capital Adequacy Ratio (also called the Capital to Risk-Weighted Assets Ratio, CRAR) measures a bank's capital in relation to its risk-weighted assets. It indicates the bank's ability to absorb losses and protect depositors. In Nepal, it is regulated by Nepal Rastra Bank (NRB) under Basel III norms.

Formula

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

Components

1. Tier I Capital (Core Capital)

• Paid-up equity capital
• Irrevocable non-cumulative preference shares
• Statutory reserves
• General reserves
• Retained earnings
• Less: intangible assets, accumulated losses

2. Tier II Capital (Supplementary Capital)

• General loan loss provisions (up to 1.25% of RWA)
• Hybrid capital instruments
• Subordinated term debt
• Revaluation reserves (discounted)

2. Risk-Weighted Assets (RWA)

RWA = On-balance sheet assets × risk weights + Off-balance sheet items × credit conversion factor × risk weights + Market risk capital charge

Risk weights are assigned as per NRB directives, e.g.:

• Cash and government securities: 0%
• Claims on NRB: 0%
• Claims on other banks: 20%
• Residential mortgage loans: 50%
• Corporate loans: 100%
• Undrawn commitments: 20–50%

Regulatory Minimum (NRB, Basel III)

Steps in Measurement

1. Determine total regulatory capital (Tier I + Tier II, after deductions).
2. Classify all assets and assign risk weights as per NRB.
3. Compute total RWA.
4. Apply the CAR formula.
5. Compare with the regulatory minimum to assess compliance.

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Implications of Capital Adequacy Ratio

1. Financial Stability and Solvency A high CAR means the bank has sufficient capital to absorb unexpected losses. It reduces the risk of insolvency and bank failure.

2. Protection of Depositors Capital acts as a buffer; even if loans turn bad, depositors' funds are safeguarded.

3. Regulatory Compliance Banks must maintain the minimum CAR prescribed by NRB. Non-compliance invites restrictions on lending, branch expansion, and dividend distribution.

4. Lending Capacity A high CAR allows a bank to extend more loans (higher risk-taking capacity). A low CAR forces the bank to restrict lending or raise fresh capital.

5. Cost of Capital and Profitability

• High CAR → lower risk but possibly lower return on equity (excess idle capital).
• Low CAR → higher returns but greater risk and regulatory pressure.

6. Credit Rating and Market Confidence Banks with strong CAR enjoy better credit ratings, cheaper funding, and greater investor and customer trust.

7. Dividend Policy NRB links dividend distribution to CAR. Banks with CAR below the prescribed level cannot distribute cash dividends.

8. Risk Management Indicator CAR reflects the quality of the loan portfolio. A declining CAR signals deteriorating asset quality and weak risk management.

9. Impact on Economic Growth Since banks are the main source of credit, a capital-constrained banking system can slow down credit flow and economic activity.

10. International Competitiveness Compliance with Basel III standards enhances a bank's credibility in international markets and facilitates foreign investment.

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Conclusion

CAR is measured as the ratio of regulatory capital to risk-weighted assets. It is a key indicator of a bank's financial strength. A sound CAR ensures depositor safety, regulatory compliance, and sustainable growth, while a weak CAR threatens solvency and invites regulatory intervention.

a. Treasury Inflation Protection Security (TIPS)

(i) Coupon just paid today

Inflation-adjusted principal:

[ = \text{Par value} \times \frac{\text{CPI today}}{\text{CPI one year before}} = 1000 \times \frac{107}{100} = \text{Rs }1,070 ]

Coupon amount:

[ = 10% \times 1,070 = \text{Rs }107 ]

Coupon just paid = Rs 107.

(ii) Expected coupon next year

Expected inflation-adjusted principal next year:

[ = 1000 \times \frac{118}{100} = \text{Rs }1,180 ]

Expected coupon:

[ = 10% \times 1,180 = \text{Rs }118 ]

Expected coupon next year = Rs 118.

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b. Bond valuation

Formula:

[ P = C \times PVIFA_{r,n} + F \times PVIF_{r,n} ]

where:

[ PVIFA_{r,n} = \frac{1-(1+r)^{-n}}{r}, \qquad PVIF_{r,n} = \frac{1}{(1+r)^n} ]

(i) Bond prices at required return = 10%

Bond A:

[ C = 100,\quad n = 5,\quad F = 1000,\quad r = 10% ]

[ P_A = 100 \times PVIFA_{10%,5} + 1000 \times PVIF_{10%,5} ]

[ PVIFA_{10%,5} = 3.7908,\qquad PVIF_{10%,5} = 0.6209 ]

[ P_A = 100(3.7908) + 1000(0.6209) = 379.08 + 620.92 = \text{Rs }1,000.00 ]

Since the coupon rate equals the required return, Bond A sells at par.

Bond B:

[ C = 90,\quad n = 10,\quad F = 1000,\quad r = 10% ]

[ P_B = 90 \times PVIFA_{10%,10} + 1000 \times PVIF_{10%,10} ]

[ PVIFA_{10%,10} = 6.1446,\qquad PVIF_{10%,10} = 0.3855 ]

[ P_B = 90(6.1446) + 1000(0.3855) = 553.01 + 385.54 = \text{Rs }938.55 ]

Bond A price = Rs 1,000.00
Bond B price = Rs 938.55

(ii) Which bond is more sensitive to interest rate changes?

Bond B is more sensitive.

Reasons:

• Bond B has a longer maturity of 10 years compared with 5 years for Bond A.
• Bond B has a lower coupon rate of 9% compared with 10% for Bond A.
• Therefore, Bond B has a higher duration, meaning more of its value comes from distant cash flows.
• A given change in the required rate of return will change the present value of Bond B more than that of Bond A.

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c. Stock valuation

(i) Value of stock today

[ P_0 = \frac{D_1 + P_1}{1+r} ]

[ P_0 = \frac{10 + 300}{1.15} = \frac{310}{1.15} = \text{Rs }269.57 ]

You should be willing to pay up to Rs 269.57 today.

(ii) Required rate of return using Gordon growth model

[ P_0 = \frac{D_1}{r-g} ]

Taking Rs 20 as next year’s dividend (D_1):

[ 330 = \frac{20}{r-0.08} ]

[ r = \frac{20}{330} + 0.08 ]

[ r = 0.060606 + 0.08 = 0.140606 ]

[ r = 14.06% ]

Required rate of return = 14.06% per annum.

Part (a): Price of the commercial paper

Commercial paper is a discount instrument quoted on a 360-day year:

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

$P = 12{,}000{,}000 \times 0.9919167 = \text{Rs } 11{,}903{,}000$

The price of the paper is Rs 11,903,000 (discount of Rs 97,000).

Part (b): Dutch auction of Rs 1,500 million of 91-day T-bills

In a Dutch (single-price) auction, bids are ranked from the highest price (lowest yield) downward and accepted until the issue is sold. Every successful bidder pays the lowest accepted price, the cut-off (stop-out) price.

(i) Competitive bids only

The issue is fully sold at Bidder 4's bid, so the cut-off price is Rs 99.25. Bidders 5, 1 and 4 receive their full bids; Bidders 2 and 3 receive nothing. All pay Rs 99.25 per Rs 100.

(ii) With non-competitive bids

Non-competitive bidders state only a quantity and agree to pay the price set by the competitive auction. They are served first, so the amount left for competitive bidders is $1{,}500 - X$, where $X$ is the non-competitive total. The question is cut off in the source; taking the usual case of $X =$ Rs 300 million:

• Amount left for competitive bidders $= 1{,}500 - 300 =$ Rs 1,200 million.
• Bidder 5 (Rs 500 million) and Bidder 1 (Rs 200 million) are filled in full, a cumulative Rs 700 million.
• Bidder 4 gets the remaining $1{,}200 - 700 =$ Rs 500 million, a partial allotment of its Rs 800 million bid.
• The cut-off price stays at Rs 99.25. Bidders 2 and 3 still get nothing.
• The non-competitive bidders get Rs 300 million at the same Rs 99.25.

The cut-off would rise to Bidder 1's Rs 99.35 only if non-competitive bids were at least Rs 800 million, because Bidders 5 and 1 together take only Rs 700 million.