Management of Financial Institutions 2078 Board Question Paper

Participants of Financial Markets

The major participants in the financial markets include:

1. Households / Individuals: Primary net suppliers of surplus funds in the economy who deposit savings and purchase securities (equities, bonds, mutual funds).
2. Business Firms / Corporations: Primary net demanders of capital that raise long-term and short-term capital by issuing equity, debentures, commercial paper, and taking bank loans.
3. Governments (Central, Provincial, Local): Borrowers that issue Treasury bills, development bonds, and citizen saving bonds to finance budgetary deficits, infrastructure projects, and public expenditures.
4. Financial Intermediaries: Institutions such as commercial banks, development banks, finance companies, insurance companies, pension funds, and mutual funds that bridge surplus and deficit economic units.
5. Foreign / International Participants: Foreign institutional investors, bilateral/multilateral agencies (e.g., ADB, World Bank), and multinational corporations engaging in cross-border capital flows and foreign exchange transactions.

Type I Liabilities

In the classification of financial institution liabilities (developed by Frank J. Fabozzi):

• Definition: A Type I Liability is an obligation where both the timing and the amount of the cash outlay are known with certainty to the financial institution.
• Characteristics:
  • Cash outflow amount is predetermined.
  • Date of cash payment is fixed.
  • Minimal uncertainty regarding the liability cash flow stream.

Example: A commercial bank issuing a 1-year Certificate of Deposit (CD) or fixed-term deposit of Rs. 100,000 at an annual interest rate of 8%.

• The bank knows with complete certainty that it must pay exactly Rs. 108,000 (Rs. 100,000 principal + Rs. 8,000 interest) precisely 12 months from the date of issuance.
• Another example is a fixed-coupon, non-callable bond issued by a corporation or bank with a scheduled maturity date.

Definition of Technology and Operational Risk

1. Technology Risk:

   • The risk that major technological investments fail to produce anticipated cost efficiencies, become obsolete prematurely, or suffer architectural failure.
   • It also encompasses core banking software malfunctions, telecommunication breakdowns, data corruption, and inability to integrate electronic banking infrastructure (e.g., connectIPS, RTGS, mobile banking).

2. Operational Risk:

   • Defined by the Basel Committee as the risk of loss resulting from inadequate or failed internal processes, people, and systems, or from external events.
   • Key drivers include human errors, internal fraud, unauthorized transactions, cyberattacks, system hacking, legal disputes, and disruptions caused by natural catastrophes.

Conditions for Issuing a Margin Call

A brokerage firm issues a margin call when the equity in an investor’s margin account falls below the regulatory or firm-specified maintenance margin requirement due to an adverse price movement in the purchased stock.

Mathematically, a margin call is triggered when:

$$\text{Actual Margin} = \frac{\text{Market Value of Securities} - \text{Loan (Debit Balance)}}{\text{Market Value of Securities}} < \text{Maintenance Margin Requirement}$$

The critical price ($P^*$) triggering a margin call is determined by:

$$P^* = \frac{P_0 \times (1 - \text{Initial Margin})}{1 - \text{Maintenance Margin}}$$

When this condition occurs, the broker demands that the client deposit additional cash or acceptable collateral into the account immediately to restore equity back to the maintenance margin level. If the investor fails to respond, the broker reserves the contractual right to liquidate the securities.

Impact on Stock Price After a Rights Offering

When a company conducts a rights offering, the stock price declines to the theoretical ex-rights price ($P_{ex}$) once the stock begins trading ex-rights:

$$P_{ex} = \frac{N \times P_{cum} + P_s}{N + 1}$$

Where:

• $P_{cum}$ = Cum-rights market price per share
• $P_s$ = Subscription (rights offer) price per share (set below $P_{cum}$)
• $N$ = Number of existing rights required to purchase one new share

Key Effects:

1. Price Drop: The market price per share falls because new shares are sold at a discount relative to the prevailing market price, diluting the per-share value.
2. Neutral Wealth Effect: The total wealth of an existing shareholder remains unchanged if they exercise their rights (or sell the rights in the market at their theoretical value $R = \frac{P_{cum} - P_s}{N + 1}$).
3. Expanded Capital Base: The firm increases its outstanding share count and total equity capital.

Three Properties of Financial Assets

Three fundamental properties of financial assets are:

1. Moneyness: The ease and convenience with which a financial asset can be converted into or used as legal tender (cash) without delay or price sacrifice. Demand deposits exhibit maximum moneyness.
2. Liquidity: The ability to sell or liquidate the asset rapidly in the secondary market in large quantities with negligible transaction costs and minimal price discount.
3. Divisibility and Denomination: The minimum monetary size in which a financial asset can be purchased or divided into smaller units. For instance, commercial paper often has large minimum denominations, whereas mutual fund units feature high divisibility.

Features of Exchange-Traded Funds (ETFs)

Key features of Exchange-Traded Funds (ETFs) include:

1. Continuous Intraday Secondary Trading: ETFs trade on stock exchanges like ordinary equity shares at real-time market prices throughout trading hours, allowing stop-loss, limit, and short-selling orders.
2. Index Replication and Diversification: Most ETFs passively track a specific benchmark index (e.g., NEPSE Index, S&P 500, Nifty 50), providing instant broad market diversification with a single instrument.
3. In-Kind Creation and Redemption Mechanism: Authorized Participants (APs) create and redeem large blocks of ETF shares (creation units) directly with the fund sponsor using baskets of underlying securities, preventing persistent premiums or discounts relative to NAV.
4. Low Expense Ratio: Due to passive indexing, ETF management expense ratios are substantially lower than actively managed mutual funds.
5. High Portfolio Transparency: Underlying portfolio holdings and weightings are disclosed publicly on a daily basis.

Annualized Bank Discount Yield Calculation

Given:

• Face Value ($F$) = Rs. 1,000,000
• Purchase Price ($P$) = Rs. 980,000
• Days to Maturity ($t$) = 90 days
• Year base for Bank Discount = 360 days

Step 1: Compute the Dollar Discount ($D$)

$$D = F - P = 1,000,000 - 980,000 = \text{Rs. } 20,000$$

Step 2: Calculate Bank Discount Yield ($Y_{bd}$)

$$Y_{bd} = \frac{D}{F} \times \frac{360}{t}$$

$$Y_{bd} = \frac{20,000}{1,000,000} \times \frac{360}{90}$$

$$Y_{bd} = 0.02 \times 4 = 0.08 = 8.00\%$$

(Note: If evaluated on a Money Market / CD-equivalent yield basis, $Y_{mmy} = \frac{20,000}{980,000} \times \frac{360}{90} = 8.163\%$.)

Answer: The annualized yield on a bank discount basis is 8.00%.

Price-Weighted Index and New Divisor Calculation

Given:

• Stock A initial price ($P_A$) = Rs. 16
• Stock B initial price ($P_B$) = Rs. 30
• Number of stocks ($N$) = 2, Initial Divisor ($D_0$) = 2

Step 1: Calculate the Initial Price-Weighted Index ($PWI_0$)

$$PWI_0 = \frac{P_A + P_B}{D_0} = \frac{16 + 30}{2} = \frac{46}{2} = 23.00$$

Step 2: Determine New Prices After 4-for-1 Split of Stock A

• New price of Stock A:
  $$P'_A = \frac{16}{4} = \text{Rs. } 4$$
• Price of Stock B remains unchanged:
  $$P'_B = \text{Rs. } 30$$
• Sum of new prices = $4 + 30 = \text{Rs. } 34$

Step 3: Calculate the New Divisor ($D_1$) To ensure the index value remains unaffected immediately after the split:

$$\frac{\sum P'}{D_1} = PWI_0$$

$$\frac{34}{D_1} = 23 \implies D_1 = \frac{34}{23} \approx 1.4783$$

Answer:

• The initial price-weighted index is 23.00.
• The new divisor after the 4-for-1 split is 1.4783.

Real Interest Rate Calculation (Fisher Effect)

Given:

• Nominal interest rate ($i$) = 10% = 0.10
• Inflation rate ($\pi$) = 4% = 0.04

1. Exact Real Rate (Fisher’s Exact Formula):

$$1 + i = (1 + r)(1 + \pi)$$

$$1 + r = \frac{1 + i}{1 + \pi} = \frac{1 + 0.10}{1 + 0.04} = \frac{1.10}{1.04} \approx 1.05769$$

$$r = 1.05769 - 1 = 0.05769 = 5.769\% \approx 5.77\%$$

2. Approximate Real Rate:

$$r \approx i - \pi = 10\% - 4\% = 6.00\%$$

Answer: The exact real interest rate is 5.77% (or approximately 6.00%).

Types of Insurance and Their Detailed Explanation

Insurance is a contractual risk-transfer mechanism wherein an individual or entity transfers the financial risk of potential loss to an insurer in exchange for a consideration called premium.

                         Types of Insurance
           ┌─────────────────────┴─────────────────────┐
     Life Insurance                            Non-Life (General) Insurance
  ┌────────┼────────┐                       ┌───────┼────────┬───────┐
Term     Whole   Endowment                Fire   Marine   Motor   Liability
Life     Life                                             & Eng.

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1. Life Insurance

Protects against financial hardship caused by premature death or provides income security in retirement.

1. Term Life Insurance:
   • Provides pure risk protection for a designated period (e.g., 10, 20, 30 years).
   • If the insured dies during the term, the face amount is paid to beneficiaries.
   • If the insured survives the term, no benefit is paid. Carries the lowest premium.
2. Whole Life Insurance:
   • Provides permanent lifetime protection up to age 100.
   • Accumulates cash value on a tax-deferred basis, against which policyholders can borrow.
3. Endowment Life Insurance:
   • Combines life coverage with forced savings.
   • The sum assured is payable either on the death of the insured during the term or upon survival to maturity.
   • Very popular in Nepal for funding children’s education and marriage.
4. Unit-Linked Insurance Plans (ULIPs):
   • Integrates insurance protection with equity/debt market investment, where the policyholder bears the investment risk.

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2. Non-Life (General / Property & Casualty) Insurance

Covers losses to tangible assets, property, and legal liabilities.

1. Fire Insurance:
   • Covers property (factories, warehouses, dwellings, inventories) against direct damage caused by fire, lightning, explosion, and allied perils (floods, earthquakes, strikes).
2. Marine Insurance:
   • Marine Cargo: Protects goods during transit by sea, air, rail, or road against damage, piracy, and sinking. Vital for landlocked Nepal’s foreign trade via Kolkata/Visakhapatnam ports.
   • Marine Hull: Protects the vessel, machinery, and equipment.
3. Motor Insurance:
   • Mandatory Third-Party Liability Insurance covers bodily injury, disability, and death caused to third parties by motor vehicles.
   • Comprehensive Motor Insurance covers both third-party liability and accidental damage to the owner’s vehicle.
4. Engineering and Construction Insurance:
   • Contractors All Risks (CAR) and Erection All Risks (EAR) protecting hydropower, road, and bridge infrastructure projects in Nepal.
5. Aviation Insurance:
   • Covers aircraft hulls, passenger liabilities, and cargo for domestic and international airlines.
6. Micro-Insurance:
   • Low-premium policies tailored for low-income rural households, covering livestock, crops, and micro-health.

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Regulatory Context in Nepal

In Nepal, all insurance business is regulated by the Nepal Insurance Authority (Nepal Beema Pradhikaran) under the Insurance Act, 2079 (2022), enforcing solvency margins, compulsory micro-insurance quotas, and statutory capital requirements.

Corporate Senior Securities and Their Types

1. Concept of Corporate Senior Securities

Senior securities are financial claims issued by a corporation that have priority of claim over common equity on the firm’s earnings and assets. In the event of liquidation or bankruptcy, senior security holders must be satisfied in full before any residual cash is distributed to common shareholders.

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2. Hierarchy of Corporate Claims

   1. Senior Secured Debt (Mortgage Bonds, Equipment Trust Certificates)
   2. Senior Unsecured Debt (Debentures)
   3. Subordinated (Junior) Debt
   4. Preferred Stock
   5. Common Equity (Residual Claimant)

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3. Types of Corporate Senior Securities

A. Senior Secured Debt

These obligations are backed by specific pledged physical or financial collateral:

1. Mortgage Bonds: Secured by a direct lien on specified real property, land, or manufacturing plants. If default occurs, bondholders can foreclose on the real estate.
2. Equipment Trust Certificates (ETCs): Secured by tangible movable equipment (such as aircraft, locomotives, or shipping containers). Legal title remains with a trustee until the debt is fully amortized.
3. Collateral Trust Bonds: Backed by a portfolio of financial assets, such as stocks or bonds of subsidiaries or other companies, held in trust.

B. Senior Unsecured Debt (Debentures)

• Backed solely by the general creditworthiness and earning power of the issuing corporation, without a specific lien on collateral.
• Include protective covenants (e.g., negative pledge clause, dividend restrictions, minimum debt-service coverage ratio) to safeguard investors.

C. Subordinated (Junior) Debt

• Unsecured debt that ranks below senior debt in liquidation. In bankruptcy, subordinated debenture holders receive payment only after senior lenders and bank lines of credit have been paid in full.
• Yields are correspondingly higher to compensate for elevated credit risk.

D. Preferred Stock

Preferred stock is a hybrid security positioned between debt and common equity:

1. Cumulative Preferred Stock: Any skipped dividend payments accumulate as arrearages that must be fully cleared before common shareholders receive dividends.
2. Convertible Preferred Stock: Grants the holder the right to convert preferred shares into a predetermined number of common shares.
3. Callable Preferred Stock: Gives the issuer the contractual right to retire the shares at a designated call price after a call-protection window.
4. Participating Preferred Stock: Allows holders to receive additional dividends beyond the fixed rate if common dividends exceed a designated threshold.

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4. Importance to Issuers and Investors

• For Issuers: Senior securities enable raising long-term capital without diluting voting control or equity ownership, and interest payments on debt are tax-deductible.
• For Investors: Offers predictable income streams, lower default risk, and superior recovery rates relative to common equities.

Capital Adequacy and Risk-Weighted Assets (RWA) Calculation

Given Data for ABC Commercial Bank:

• Assets with risk weight 0.0 = Rs. 20 million
• Assets with risk weight 0.2 = Rs. 250 million
• Assets with risk weight 0.5 = Rs. 870 million
• Assets with risk weight 1.0 = Rs. 950 million
• Tier 1 Capital (Core Capital) = Rs. 250 million
• Tier 2 Capital (Supplementary Capital) = Rs. 80 million

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a. Total Risk-Weighted Assets (RWA)

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

$$\begin{aligned} \text{RWA}_1 &= 20 \times 0.0 = \text{Rs. } 0 \text{ million} \\ \text{RWA}_2 &= 250 \times 0.20 = \text{Rs. } 50 \text{ million} \\ \text{RWA}_3 &= 870 \times 0.50 = \text{Rs. } 435 \text{ million} \\ \text{RWA}_4 &= 950 \times 1.00 = \text{Rs. } 950 \text{ million} \\[6pt] \mathbf{\text{Total RWA}} &= 0 + 50 + 435 + 950 = \mathbf{\text{Rs. } 1,435 \text{ million}} \end{aligned}$$

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b. Tier-One (Core) Capital Ratio

$$\text{Tier-1 Capital Ratio} = \frac{\text{Tier 1 Capital}}{\text{Total RWA}} \times 100$$

$$\text{Tier-1 Capital Ratio} = \frac{250}{1,435} \times 100 = \mathbf{17.42\%}$$

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c. Tier-Two (Supplementary) Capital Ratio

$$\text{Tier-2 Capital Ratio} = \frac{\text{Tier 2 Capital}}{\text{Total RWA}} \times 100$$

$$\text{Tier-2 Capital Ratio} = \frac{80}{1,435} \times 100 = \mathbf{5.57\%}$$

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d. Total Capital Ratio (Capital Adequacy Ratio - CAR)

$$\text{Total Capital Fund} = \text{Tier 1 Capital} + \text{Tier 2 Capital} = 250 + 80 = \text{Rs. } 330 \text{ million}$$

$$\text{Total Capital Ratio} = \frac{\text{Total Capital Fund}}{\text{Total RWA}} \times 100$$

$$\text{Total Capital Ratio} = \frac{330}{1,435} \times 100 = \mathbf{23.00\%}$$

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e. Compliance Assessment Under NRB Directives

Under the Capital Adequacy Framework mandated by Nepal Rastra Bank (Basel III framework for commercial banks):

1. Minimum Tier 1 Capital Ratio: Mandated at 6.0% (or 8.5% including the 2.5% Capital Conservation Buffer).
   • ABC Bank’s Tier 1 ratio = 17.42%, well above the regulatory threshold.
2. Minimum Total Capital Ratio (CAR): Mandated at 11.0% (8.5% minimum total capital + 2.5% Capital Conservation Buffer).
   • ABC Bank’s CAR = 23.00%, exceeding the 11.0% minimum by 12.00 percentage points.
3. Tier 2 Capital Ceiling: Tier 2 capital cannot exceed 100% of Tier 1 capital.
   • Tier 2 (Rs. 80M) is well within Tier 1 (Rs. 250M).

Conclusion: Yes, ABC Commercial Bank has a highly adequate capital ratio as demanded by Nepal Rastra Bank. It maintains substantial surplus capital buffers, indicating high solvency and strong shock-absorption capacity.

Deposit Multiplier and Money Creation Calculation

Given Data:

• Additional Excess Reserve ($\Delta ER$) = Rs. 200,000
• Required Reserve Ratio ($r_d$) = 5% = 0.05
• Depository institutions continually make loans with excess reserves and there is no currency drain.

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a. Transaction Deposit Multiplier ($m$)

The transaction deposit multiplier reflects the multiple by which total deposits expand per rupee of new reserves:

$$m = \frac{1}{r_d} = \frac{1}{0.05} = \mathbf{20}$$

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b. Maximum Amount of New Deposits (Loans) Created

1. Maximum Expansion in Total Deposits ($\Delta D$):

   $$\Delta D = \Delta ER \times m = 200,000 \times 20 = \mathbf{\text{Rs. } 4,000,000}$$

2. Maximum Amount of New Loans Created:

   $$\Delta L = \Delta D - \Delta ER = 4,000,000 - 200,000 = \mathbf{\text{Rs. } 3,800,000}$$
   (Note: Depository institutions can create up to Rs. 4,000,000 in total new deposits, backed by Rs. 3,800,000 in loans and Rs. 200,000 in required reserves).

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c. Impact if Excess Reserves Decline to Rs. 150,000

If excess reserves fall from Rs. 200,000 to Rs. 150,000:

• New Deposit Creation Potential:

  $$\Delta D_{new} = 150,000 \times 20 = \text{Rs. } 3,000,000$$

• Contraction in Deposit Creation:

  $$\text{Reduction in Deposits} = 4,000,000 - 3,000,000 = \mathbf{\text{Rs. } 1,000,000}$$

Alternatively, the decline in reserves is $\Delta ER' = 150,000 - 200,000 = -\text{Rs. } 50,000$.

$$\text{Change in Deposits} = -50,000 \times 20 = -\mathbf{\text{Rs. } 1,000,000}$$

Conclusion: Total potential transaction deposits in the banking system will decrease by Rs. 1,000,000 (from Rs. 4,000,000 to Rs. 3,000,000).

Treasury Inflation-Protected Securities (TIPS) Cash Flow Calculation

Given Data:

• Par Value (Principal on Jan 1) = Rs. 100,000
• Annual Coupon Rate = 3.5% (Semi-annual coupon rate = $3.5\% / 2 = 1.75\%$)
• Inflation rate for first 6-month period = 3%
• Inflation rate for second 6-month period = 1%
• Inflation adjustments occur semi-annually.

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a. Inflation-Adjusted Principal at End of First 6 Months

$$\text{Adjusted Principal}_1 = \text{Initial Principal} \times (1 + \text{Inflation Rate}_1)$$

$$\text{Adjusted Principal}_1 = 100,000 \times (1 + 0.03) = \mathbf{\text{Rs. } 103,000}$$

(Note: If the 3% stated is annual inflation applied semi-annually at 1.5%, adjusted principal would be $100,000 \times 1.015 = \text{Rs. } 101,500$. In TU conventions, the stated period rate of 3% is standardly applied as the 6-month inflation rate: Rs. 103,000).

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b. Coupon Amount for the First 6-Month Period

The semi-annual coupon is computed on the inflation-adjusted principal:

$$\text{Coupon Payment}_1 = \text{Adjusted Principal}_1 \times \left(\frac{\text{Annual Coupon Rate}}{2}\right)$$

$$\text{Coupon Payment}_1 = 103,000 \times \left(\frac{0.035}{2}\right) = 103,000 \times 0.0175 = \mathbf{\text{Rs. } 1,802.50}$$

(If 1.5% semi-annual inflation: $101,500 \times 0.0175 = \text{Rs. } 1,776.25$.)

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c. Inflation-Adjusted Principal at End of Second 6 Months

Using the second-period inflation rate of 1%:

$$\text{Adjusted Principal}_2 = \text{Adjusted Principal}_1 \times (1 + \text{Inflation Rate}_2)$$

$$\text{Adjusted Principal}_2 = 103,000 \times (1 + 0.01) = 103,000 \times 1.01 = \mathbf{\text{Rs. } 104,030}$$

(If using 1.5% and 1%: $101,500 \times 1.01 = \text{Rs. } 102,515$.)

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d. Coupon Amount for the Second 6-Month Period

$$\text{Coupon Payment}_2 = \text{Adjusted Principal}_2 \times \left(\frac{\text{Annual Coupon Rate}}{2}\right)$$

$$\text{Coupon Payment}_2 = 104,030 \times 0.0175 = \mathbf{\text{Rs. } 1,820.525} \approx \mathbf{\text{Rs. } 1,820.53}$$

(If using 1.5% and 1%: $102,515 \times 0.0175 = \text{Rs. } 1,794.01$.)

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Summary Table

Mutual Fund NAV and Investment Yield Calculation

Given Data:

• Stock (current market value) = Rs. 20,000,000
• Bonds (current market value) = Rs. 10,000,000
• Cash = Rs. 500,000
• Total Liabilities = Rs. 300,000
• Number of outstanding shares = 10 million (10,000,000 shares)

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a. Initial Net Asset Value (NAV)

1. Calculate Total Assets:

   $$\text{Total Assets} = 20,000,000 + 10,000,000 + 500,000 = \text{Rs. } 30,500,000$$

2. Calculate Net Worth (Net Assets):

   $$\text{Net Assets} = \text{Total Assets} - \text{Liabilities} = 30,500,000 - 300,000 = \text{Rs. } 30,200,000$$

3. Calculate NAV:

   $$\text{NAV}_a = \frac{\text{Net Assets}}{\text{Number of Shares}} = \frac{30,200,000}{10,000,000} = \mathbf{\text{Rs. } 3.02 \text{ per share}}$$

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b. Revised Net Asset Value After Portfolio Changes

• Revised Stock Value: Rises by 10%
  $$\text{Stock} = 20,000,000 \times (1 + 0.10) = \text{Rs. } 22,000,000$$
• Revised Bond Value: Falls by 2%
  $$\text{Bonds} = 10,000,000 \times (1 - 0.02) = \text{Rs. } 9,800,000$$
• Cash: Unchanged = Rs. 500,000
• Liabilities: Unchanged = Rs. 300,000

1. New Total Assets:

   $$\text{Total Assets}_{new} = 22,000,000 + 9,800,000 + 500,000 = \text{Rs. } 32,300,000$$

2. New Net Assets:

   $$\text{Net Assets}_{new} = 32,300,000 - 300,000 = \text{Rs. } 32,000,000$$

3. New NAV:

   $$\text{NAV}_b = \frac{32,000,000}{10,000,000} = \mathbf{\text{Rs. } 3.20 \text{ per share}}$$

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c. Yield on Investment

If units are purchased at $\text{NAV}_a$ and sold at $\text{NAV}_b$:

$$\text{Yield} = \frac{\text{NAV}_b - \text{NAV}_a}{\text{NAV}_a} \times 100$$

$$\text{Yield} = \frac{3.20 - 3.02}{3.02} \times 100 = \frac{0.18}{3.02} \times 100 = \mathbf{5.96\%}$$

Answer:

• Initial NAV = Rs. 3.02
• Revised NAV = Rs. 3.20
• Investor Yield = 5.96%

Financial Innovation: Categories and Motivations

Financial innovation refers to the development and popularization of new financial instruments, technologies, institutions, and market mechanisms that improve the efficiency of capital allocation and risk sharing.

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1. Categories of Financial Innovation

According to economic classifications (Llewellyn, Silber, and Merton):

1. Product / Instrument Innovation:
   • Creation of novel securities tailored to specific investor appetites and issuer requirements.
   • Examples: Collateralized Debt Obligations (CDOs), Credit Default Swaps (CDS), Exchange Traded Funds (ETFs), floating rate notes (FRNs), hybrid equity-debt instruments.
2. Process / Operational Innovation:
   • Introduction of new delivery channels, back-office automation, and clearing systems that lower transaction costs and boost transaction velocity.
   • Examples: Core Banking Solutions (CBS), Real-Time Gross Settlement (RTGS), mobile payment wallets (eSewa, Khalti), QR payment interoperability, and automated clearing houses (NCHL).
3. Market Innovation:
   • Establishing new organized trading platforms, auction venues, and secondary market structures.
   • Examples: Electronic trading systems (NEPSE NOTS), dark pools, derivatives exchanges, and cross-border currency trading platforms.
4. Institutional / Organizational Innovation:
   • Emergence of specialized financial entities filling market niches.
   • Examples: Microfinance institutions (MFIs), peer-to-peer (P2P) lending platforms, venture capital funds, private equity firms, and credit rating agencies (ICRA Nepal, Care Ratings Nepal).

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2. Motivations for Financial Innovation

A. Increased Macroeconomic Volatility

• Fluctuations in interest rates, inflation, and foreign exchange rates generate immense financial exposure for firms.
• Innovations such as interest rate swaps, currency futures, and adjustable-rate mortgages (ARMs) were developed directly to hedge against volatile macroeconomic environments.

B. Regulatory Arbitrage and Circumvention

• Regulatory constraints (reserve requirements, capital adequacy ratios, interest rate ceilings such as Regulation Q) often incentivize institutions to engineer loopholes.
• Examples: Eurodollar markets emerged to bypass US reserve requirements; off-balance sheet securitization allowed banks to manage regulatory capital ratios under Basel accords.

C. Advances in Computer and Information Technology

• Exponential growth in computing power and algorithmic models reduced the cost of processing vast amounts of data and executing transactions.
• Facilitated high-frequency trading (HFT), automated credit underwriting, and real-time mobile banking.

D. Changing Customer Needs and Demographic Shifts

• Aging populations demanded retirement products (annuities, reverse mortgages), while younger generations demand instantaneous digital payments and fractional share investments.

E. Globalization and Market Integration

• International trade and cross-border investment require instruments that overcome currency restrictions, withholding taxes, and legal differences (e.g., American Depository Receipts - ADRs, Global Depository Receipts - GDRs).

F. Agency Costs and Asymmetric Information

• Financial contracts (convertible bonds, venture capital earn-outs) are structured innovatively to align manager incentives with shareholder interests and reduce moral hazard.

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Conclusion

Financial innovation expands market completeness and liquidity, though excessive complexity without proper macroprudential regulation can create systemic vulnerability, as evidenced by the 2007-2008 global financial crisis.

Mortgage Loan Amortization Analysis

Given Data:

• Purchase Price of House = Rs. 175,000
• Down Payment = 20% of purchase price = $0.20 \times 175,000 = \text{Rs. } 35,000$
• Loan Amount ($PV$) = $175,000 - 35,000 = \text{Rs. } 140,000$
• Loan Term = 15 years $\implies n = 15 \times 12 = 180$ months
• Annual Interest Rate = 7.75%
• Monthly Interest Rate ($i$) = $\frac{0.0775}{12} = 0.006458333$

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a. Monthly Payment ($PMT$)

$$PMT = \frac{PV \times i}{1 - (1 + i)^{-n}}$$

$$\begin{aligned} (1 + i)^{-n} &= (1.006458333)^{-180} = 0.313885 \\[4pt] 1 - (1 + i)^{-n} &= 1 - 0.313885 = 0.686115 \\[4pt] PMT &= \frac{140,000 \times 0.006458333}{0.686115} = \frac{904.1667}{0.686115} = \mathbf{\text{Rs. } 1,317.81} \end{aligned}$$

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b. Interest and Principal Paid in the $180^{\text{th}}$ Payment

In the final ($180^{\text{th}}$) month, the beginning balance equals the present value of 1 remaining payment ($PMT$):

$$B_{179} = \frac{PMT}{1 + i} = \frac{1,317.81}{1.006458333} = \text{Rs. } 1,309.35$$

• Interest in Month 180:

  $$I_{180} = B_{179} \times i = 1,309.35 \times 0.006458333 = \mathbf{\text{Rs. } 8.46}$$

• Principal in Month 180:

  $$PR_{180} = PMT - I_{180} = 1,317.81 - 8.46 = \mathbf{\text{Rs. } 1,309.35}$$
  (The principal fully liquidates the remaining balance $B_{179}$, bringing the final balance to Rs. 0.00).

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c. Remaining Mortgage Balance at the End of $60^{\text{th}}$ Month ($B_{60}$)

At month 60, there are $180 - 60 = 120$ payments remaining.

$$B_{60} = PMT \times \left[ \frac{1 - (1 + i)^{-120}}{i} \right]$$

$$\begin{aligned} (1 + i)^{-120} &= (1.006458333)^{-120} = 0.461933 \\[4pt] 1 - (1 + i)^{-120} &= 0.538067 \\[4pt] \text{PVIFA}_{0.006458333, 120} &= \frac{0.538067}{0.006458333} = 83.3136 \\[4pt] B_{60} &= 1,317.81 \times 83.3136 = \mathbf{\text{Rs. } 109,791.22} \end{aligned}$$

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d. Amortization Schedule for the First Five Months

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e. Total Interest Paid Over the Life of the Mortgage

$$\begin{aligned} \text{Total Payments} &= n \times PMT = 180 \times 1,317.81 = \text{Rs. } 237,205.80 \\[4pt] \text{Total Principal Repaid} &= \text{Rs. } 140,000.00 \\[4pt] \mathbf{\text{Total Interest Paid}} &= 237,205.80 - 140,000.00 = \mathbf{\text{Rs. } 97,205.80} \end{aligned}$$

Comprehensive Bond Valuation Analysis

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(a) Percentage Change in Bond Price and Convexity

Given:

• Base Price ($P_0$) = Rs. 677.57 at Yield $Y_0 = 9.0\%$
• Case 1: Yield increases by 50 bps (+0.50%) to 9.5%: Price $P_1 = \text{Rs. } 647.73$
• Case 2: Yield decreases by 50 bps (-0.50%) to 8.5%: Price $P_2 = \text{Rs. } 709.35$

1. Percentage Price Change When Yield Increases by 50 bps:

$$\% \Delta P_{\text{increase}} = \frac{P_1 - P_0}{P_0} \times 100 = \frac{647.73 - 677.57}{677.57} \times 100 = \frac{-29.84}{677.57} \times 100 = \mathbf{-4.40\%}$$

2. Percentage Price Change When Yield Decreases by 50 bps:

$$\% \Delta P_{\text{decrease}} = \frac{P_2 - P_0}{P_0} \times 100 = \frac{709.35 - 677.57}{677.57} \times 100 = \frac{+31.78}{677.57} \times 100 = \mathbf{+4.69\%}$$

Convexity Observation: The percentage price appreciation for a 50 bps decline in yield (+4.69%) is greater in magnitude than the percentage price depreciation for an identical 50 bps increase in yield (-4.40%). This asymmetric property illustrates positive convexity of option-free bonds.

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(b) Cash Flows and Price of a 6% Coupon Bond

Given:

• Par Value ($M$) = Rs. 1,000
• Coupon Rate = 6% per annum $\implies I = 1,000 \times 0.06 = \text{Rs. } 60$
• Maturity ($n$) = 7 years
• Required Discount Rate ($k_d$) = 8%

1. Cash Flow Schedule:

• Years 1 to 6: Annual coupon payment of Rs. 60 each year.
• Year 7: Annual coupon plus principal repayment = $60 + 1,000 = \mathbf{\text{Rs. } 1,060}$.

2. Bond Price Calculation:

$$P_0 = I \times \left[ \frac{1 - (1 + k_d)^{-n}}{k_d} \right] + \frac{M}{(1 + k_d)^n}$$

$$\text{PVIFA}_{8\%, 7} = \frac{1 - (1.08)^{-7}}{0.08} = \frac{1 - 0.583490}{0.08} = 5.20637$$

$$\text{PVIF}_{8\%, 7} = (1.08)^{-7} = 0.583490$$

$$P_0 = (60 \times 5.20637) + (1,000 \times 0.583490) = 312.38 + 583.49 = \mathbf{\text{Rs. } 895.87}$$

(Because the coupon rate 6% is below the market yield 8%, the bond sells at a discount).

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(c) Valuation of a Callable Bond

Given:

• Annual Coupon Payment ($I$) = Rs. 75
• Call Horizon ($n$) = 2 years
• Call Price ($CP$) = Rs. 1,050 at $t = 2$
• Required Discount Rate ($k_d$) = 9%

Bond Price Formula:

$$P_0 = \frac{I}{(1 + k_d)^1} + \frac{I + CP}{(1 + k_d)^2}$$

$$\begin{aligned} P_0 &= \frac{75}{1.09} + \frac{75 + 1,050}{(1.09)^2} \\[6pt] &= \frac{75}{1.09} + \frac{1,125}{1.1881} \\[6pt] &= 68.81 + 946.89 = \mathbf{\text{Rs. } 1,015.70} \end{aligned}$$

Answer: The current market price of the callable bond is Rs. 1,015.70.