Fundamentals of Finance

Definition of Finance:

Finance is defined as the art and science of managing money, capital, and financial resources. It encompasses the processes, institutions, markets, and instruments involved in the transfer of funds among individuals, businesses, and governments.

At a managerial level, finance addresses three fundamental decisions:

1. Investment Decision: Determining which long-term and short-term assets the firm should acquire (capital budgeting and working capital management).
2. Financing Decision: Determining the optimal mix of debt and equity capital to fund assets (capital structure).
3. Dividend Decision: Determining what proportion of earnings to distribute to shareholders versus reinvesting for future growth.

Meaning of Treasury Bill (T-Bill):

A Treasury Bill (T-Bill) is a short-term, negotiable debt obligation issued by a sovereign government (such as Nepal Rastra Bank on behalf of the Government of Nepal) to finance short-term budgetary deficits and conduct monetary operations.

Key Features:

• Maturity: Money market instrument with maturities typically ranging from 28 days, 91 days, 182 days, up to 364 days.
• Zero-Coupon Instrument: Issued at a discount to its face value and redeemed at full face value at maturity; the return to the investor is the difference between the purchase price and face value.
• Risk-Free: Backed by the full faith and credit of the sovereign government, carrying zero default risk.

Four Core Financial Statements:

According to International Financial Reporting Standards (IFRS) and Nepal Financial Reporting Standards (NFRS), the four fundamental financial statements are:

1. Balance Sheet (Statement of Financial Position): Reports the firm’s assets, liabilities, and shareholders’ equity at a specific point in time.
2. Income Statement (Statement of Profit or Loss): Summarizes revenues, expenses, and net profit or loss generated over an accounting period.
3. Statement of Cash Flows: Details cash inflows and outflows categorized into operating, investing, and financing activities over the period.
4. Statement of Changes in Equity: Reconciles the opening and closing balances of owners’ equity, detailing contributed capital, net earnings, and dividends paid.

Meaning of Default Risk:

Default Risk (also termed credit risk) is the probability that an issuer of a debt instrument or a borrower will fail to make scheduled interest payments or principal repayments on time and in full according to the debt contract.

• Risk Premium: Investors demand a higher expected yield—termed the Default Risk Premium (DRP)—to compensate for bearing higher default risk:
  $$\text{Nominal Rate } (r) = r^* + IP + DRP + LP + MRP$$
• Assessment: Measured by independent credit rating agencies (e.g., ICRA Nepal, CARE Ratings Nepal). Sovereign government securities are deemed to have zero default risk ($DRP = 0$), whereas corporate bonds carry positive DRP depending on the borrower’s credit quality.

Difference Between Annuity and Perpetuity:

Dimension	Annuity	Perpetuity
Definition	A series of equal, periodic cash flows occurring for a fixed, finite number of periods ($n$).	A stream of equal, periodic cash flows that continues indefinitely into perpetuity ($n = \infty$).
Duration	Finite duration (e.g., 5 years, 20 years).	Infinite duration (perpetual).
Present Value Formula	$PV_A = PMT \times \left[\frac{1 - (1+r)^{-n}}{r}\right]$	$PV_P = \frac{PMT}{r}$
Future Value	Computable: $FV_A = PMT \times \left[\frac{(1+r)^n - 1}{r}\right]$	Undefined (approaches infinity as $n \to \infty$).
Typical Examples	Car loan EMIs, term mortgages, 10-year bond coupons.	Preferred stock dividends, British Consols, perpetual endowments.

Computation and Illustration of Dividend Yield:

1. Meaning and Formula: Dividend yield measures the cash income earned per share as a percentage of the stock’s current market price:

$$\text{Dividend Yield} = \frac{\text{Annual Dividend per Share } (D_1 \text{ or } D_0)}{\text{Current Market Price per Share } (P_0)} \times 100\%$$

2. Numerical Illustration:

• Suppose Nepal Telecom shares are currently trading at $P_0 = \text{Rs } 900$.
• The company announces a cash dividend of $\text{Rs } 45$ per share for the year.
  $$\text{Dividend Yield} = \frac{\text{Rs } 45}{\text{Rs } 900} \times 100\% = 5.0\%$$

This signifies that an investor earns a direct cash return of $5\%$ on the current market value of their investment, excluding capital gains.

Difference Between Premium Bond and Discount Bond:

Characteristic	Premium Bond	Discount Bond
Market Price vs Face Value	Market Price exceeds Par Value ($V_d > M$).	Market Price is less than Par Value ($V_d < M$).
Coupon Rate vs Required Yield	Coupon Rate > Required Yield ($C > k_d$).	Coupon Rate < Required Yield ($C < k_d$).
Current Yield vs YTM	$\text{Coupon Rate} > \text{Current Yield} > \text{YTM}$.	$\text{Coupon Rate} < \text{Current Yield} < \text{YTM}$.
Price Movement Over Time	Bond price depreciates gradually toward par value as maturity approaches.	Bond price appreciates gradually toward par value as maturity approaches.
Example	A Rs 1,000 par bond with 12% coupon selling at Rs 1,120 when market rate is 10%.	A Rs 1,000 par bond with 8% coupon selling at Rs 920 when market rate is 10%.

Assumptions of the Normal (Constant) Growth Model of DDM:

The normal growth model (Gordon Growth Model) of the Dividend Discount Model (DDM) assumes that:

1. Constant Perpetual Growth: Dividends per share grow indefinitely at a constant rate ($g$) each year:
   $$D_t = D_0(1+g)^t$$
2. Growth Less Than Required Return: The perpetual growth rate ($g$) must be strictly less than the investor’s required rate of return ($k_s > g$).
3. Constant Retention and ROE: The firm maintains a constant dividend payout ratio and earns a constant Return on Equity ($g = b \times ROE$).

Under these assumptions, the intrinsic stock price is:

$$P_0 = \frac{D_1}{k_s - g} = \frac{D_0(1+g)}{k_s - g}$$

Impact of Inventory Conversion Period on Working Capital Size:

The Inventory Conversion Period (ICP) is the average number of days required to convert raw materials into finished goods and sell them to customers:

$$\text{ICP} = \frac{360 \text{ or } 365}{\text{Inventory Turnover}} = \frac{\text{Inventory} \times 360}{\text{Cost of Goods Sold}}$$

Effect on Working Capital:

• Direct Positive Relationship: A longer ICP increases both the Operating Cycle (OC = ICP + RCP) and the Cash Conversion Cycle (CCC = OC - PDP).
• Capital Requirement: When goods sit longer in storage or processing, more cash is locked up in non-earning inventory assets. Consequently, the firm requires a larger amount of working capital and external negotiated financing to sustain daily operations.
• Conversely, shortening ICP accelerates cash generation, reduces holding costs, and minimizes working capital requirements.

Effective Annual Rate (EAR) Under Quarterly Compounding:

Given:

• Quoted nominal interest rate ($r_{nom}$) = $8\% = 0.08$
• Compounding frequency ($m$) = $4$ times per year (quarterly)

Formula:

$$\text{Effective Annual Rate (EAR)} = \left(1 + \frac{r_{nom}}{m}\right)^m - 1$$

Calculation:

$$\text{EAR} = \left(1 + \frac{0.08}{4}\right)^4 - 1$$

$$\text{EAR} = (1 + 0.02)^4 - 1 = (1.02)^4 - 1$$

$$\text{EAR} = 1.082432 - 1 = 0.082432 \text{ or } 8.24\%$$

Conclusion: The effective annual interest rate compounded quarterly is 8.24% per annum.

Financial Institutions and Depository vs. Non-Depository Institutions:

1. Concept of Financial Institutions:

Financial institutions are specialized financial intermediaries that mobilize savings from surplus economic units (households, businesses) and channel those funds to deficit economic units (investors, entrepreneurs, governments). They facilitate liquidity, reduce transaction and information search costs, provide maturity and denomination transformation, and manage financial risks.

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2. Distinguishing Between Depository and Non-Depository Institutions:

Comparative Dimension	Depository Financial Institutions	Non-Depository Financial Institutions
Core Mobilization Mechanism	Accept deposits directly from the general public which legally represent debt liabilities.	Mobilize funds through contractual premiums, policy payments, unit sales, or debt securities; do not accept regular bank deposits.
Primary Sources of Funds	Current (checking), savings, fixed, and call deposits.	Insurance premiums, pension contributions, mutual fund unit sales, debenture issuance.
Regulatory Framework (Nepal)	Regulated under the Bank and Financial Institutions Act (BAFIA) 2073 by Nepal Rastra Bank (NRB).	Regulated by specialized bodies (e.g., Nepal Insurance Authority, SEBON) according to industry acts.
Classifications in Nepal	Class ‘A’ Commercial Banks, Class ‘B’ Development Banks, Class ‘C’ Finance Companies, Class ‘D’ Microfinance.	Life/Non-life Insurance Companies, Employee Provident Fund (EPF), Citizen Investment Trust (CIT), Mutual Funds.
Liquidity & Withdrawal	High on-demand liquidity (customers can withdraw savings/current funds via ATMs and cheques anytime).	Fixed contractual maturities; funds are locked in until retirement, policy maturity, or contract terms.
Primary Use of Funds	Short-to-medium term business loans, retail consumer financing, working capital lines.	Long-term capital market investments, government bonds, corporate debentures, infrastructure equity.

Application of Cost of Capital in Financial Decision Making:

The Cost of Capital represents the minimum hurdle rate of return that a firm must earn on its investments to maintain its market value and satisfy the return expectations of its capital providers (debt holders, preferred stockholders, and equity investors).

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Key Applications in Financial Decision Making:

1. Capital Budgeting and Investment Appraisal (Hurdle Rate):

   • The Weighted Average Cost of Capital (WACC) serves as the benchmark discount rate in Net Present Value (NPV) calculations:
     $$NPV = \sum_{t=1}^n \frac{CF_t}{(1 + WACC)^t} - CF_0$$
   • A project is accepted only if its $NPV > 0$ or its Internal Rate of Return ($IRR$) exceeds the WACC ($IRR > WACC$).

2. Designing Optimal Capital Structure:

   • Management uses the cost of each individual component ($k_d, k_p, k_s$) to identify the debt-equity mix that minimizes overall WACC while maximizing the firm’s total enterprise value.

3. Working Capital Management:

   • Evaluates the carrying cost of holding short-term assets (inventories, accounts receivable). The cost of capital determines whether offering credit terms or holding safety stocks creates economic value.

4. Dividend Policy Decisions:

   • Guides the decision to retain earnings versus distributing cash dividends. If internal reinvestment yields a return exceeding the cost of equity ($ROE > k_s$), retention is wealth-maximizing.

5. Performance Evaluation (Economic Value Added - EVA):

   • Cost of capital measures true economic profitability:
     $$EVA = \text{NOPAT} - (\text{Total Invested Capital} \times WACC)$$
   • A positive EVA indicates wealth creation above capital charges.

Concept and Types of Working Capital:

1. Concept of Working Capital:

Working capital represents the funds invested in a firm’s short-term operating assets that cycle through daily business operations. It ensures that the enterprise maintains sufficient liquidity to satisfy maturing short-term obligations while supporting continuous production and sales activities.

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2. Classifications of Working Capital:

A. Based on Accounting/Balance Sheet Concept:

1. Gross Working Capital:
   • Refers to the firm’s total investment in all Current Assets (Cash, Marketable Securities, Accounts Receivable, Inventories, Prepaid Expenses).
   • Reflects the total quantum of short-term resources mobilized.
2. Net Working Capital (NWC):
   • Defined as the mathematical difference between Current Assets and Current Liabilities:
     $$NWC = \text{Current Assets} - \text{Current Liabilities}$$
   • A positive NWC indicates that current assets are partially financed by long-term funds, providing a liquidity buffer.

B. Based on Time and Operational Concept:

1. Permanent (Fixed) Working Capital:
   • The minimum baseline level of current assets (safety cash, minimum pipeline inventory, base customer credit) permanently required to maintain uninterrupted operations regardless of business cycle fluctuations.
   • Should ideally be financed through long-term capital (equity or long-term debt).
2. Temporary (Variable/Seasonal) Working Capital:
   • The additional working capital needed to support seasonal spikes or cyclical increases in sales volume (e.g., extra inventory build-up for Dashain/Tihar festival sales).
   • Typically financed via short-term credit (bank overdrafts, short-term commercial loans).

Future Value Calculation for Cash Flow Streams at Year 5:

Given:

• Annual interest rate ($i$) = $10\% = 0.10$
• Terminal horizon ($n$) = $5$ years

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Step-by-step Valuation:

a. Lump Sum Rs 500,000 Deposited at Present ($t = 0$):

• Compounds for the full $5$ years:
  $$FV_5(a) = PV \times (1 + i)^n = 500,000 \times (1.10)^5$$
  $$FV_5(a) = 500,000 \times 1.61051 = \text{Rs } 805,255.00$$

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b. Lump Sum Rs 800,000 Deposited at End of Year 2 ($t = 2$):

• Compounds for remaining period $(5 - 2) = 3$ years:
  $$FV_5(b) = PV \times (1 + i)^{5-2} = 800,000 \times (1.10)^3$$
  $$FV_5(b) = 800,000 \times 1.33100 = \text{Rs } 1,064,800.00$$

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c. Ordinary Annuity of Rs 100,000 Deposited at End of Each Year for 5 Years ($t = 1 \text{ to } 5$):

• Uses Future Value of an Ordinary Annuity factor:
  $$FVA_5(c) = PMT \times \left[\frac{(1 + i)^n - 1}{i}\right] = 100,000 \times \left[\frac{(1.10)^5 - 1}{0.10}\right]$$
  $$FVA_5(c) = 100,000 \times \left[\frac{1.61051 - 1}{0.10}\right] = 100,000 \times 6.1051 = \text{Rs } 610,510.00$$

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Combined Total Future Value at End of Year 5:

$$\text{Total } FV_5 = FV_5(a) + FV_5(b) + FVA_5(c)$$

$$\text{Total } FV_5 = \text{Rs } 805,255 + \text{Rs } 1,064,800 + \text{Rs } 610,510 = \mathbf{\text{Rs } 2,480,565.00}$$

Summary Table:

Component	Deposit Timing	Amount (Rs)	Compounding Periods	Future Value Factor	FV at Year 5 (Rs)
a. Present Lump Sum	$t = 0$	500,000	5 years	1.61051	805,255.00
b. Year 2 Lump Sum	$t = 2$	800,000	3 years	1.33100	1,064,800.00
c. 5-Year Annuity	$t = 1 \dots 5$	100,000/yr	5 periods	6.10510	610,510.00
Total Accumulated Value					2,480,565.00

Valuation of Bonds:

Common Parameter:

• Investor’s required rate of return ($k_d$) = $10\% = 0.10$

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a. Bond A: Rs 1,000 Par Value with 9% Coupon (Perpetual / Non-Maturity):

(Note: As no maturity period is specified, it represents a perpetual bond / consol)

• Annual Coupon Payment ($I$) = $\text{Rs } 1,000 \times 9\% = \text{Rs } 90$
  $$V_d = \frac{I}{k_d} = \frac{\text{Rs } 90}{0.10} = \mathbf{\text{Rs } 900.00}$$
  (If treated as a 1-year holding bond: $V_d = \frac{90 + 1000}{1.10} = \text{Rs } 990.91$. The perpetual formulation of Rs 900 is standard TU practice).

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b. Bond B: Rs 1,000 Par Value Zero Coupon Bond with 7 Years Maturity:

• Par Value ($M$) = $\text{Rs } 1,000$, Maturity ($n$) = $7$ years, Annual Coupon ($I$) = $\text{Rs } 0$
  $$V_d = \frac{M}{(1 + k_d)^n} = M \times PVIF(10\%, 7)$$
  $$PVIF(10\%, 7) = \frac{1}{(1.10)^7} = \frac{1}{1.948717} \approx 0.513158$$
  $$V_d = 1,000 \times 0.513158 = \mathbf{\text{Rs } 513.16}$$

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c. Bond C: Rs 1,000 Par Value, 12% Coupon Bond with 10 Years Maturity:

• Par Value ($M$) = $\text{Rs } 1,000$, Coupon ($I$) = $1,000 \times 12\% = \text{Rs } 120$, Maturity ($n$) = $10$ years
  $$V_d = I \times PVIFA(k_d, n) + M \times PVIF(k_d, n)$$

Factors at 10% for 10 Years:

• $PVIF(10\%, 10) = \frac{1}{(1.10)^{10}} = 0.385543$
• $PVIFA(10\%, 10) = \frac{1 - 0.385543}{0.10} = 6.144567$

Calculation:

$$V_d = (120 \times 6.144567) + (1,000 \times 0.385543)$$

$$V_d = \text{Rs } 737.35 + \text{Rs } 385.54 = \mathbf{\text{Rs } 1,122.89}$$

(Because coupon rate 12% exceeds required yield 10%, Bond C sells at a premium above par).

Required Rate of Return and Expected Stock Price for Paiyukhola Fabric:

Given:

• Current market price per share ($P_0$) = $\text{Rs } 210$
• Recently paid dividend ($D_0$) = $\text{Rs } 20$ per share
• Expected constant growth rate in earnings, dividends, and price ($g$) = $5\% = 0.05$

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1. Calculation of Expected Dividend Next Year ($D_1$):

$$D_1 = D_0 \times (1 + g) = \text{Rs } 20 \times (1 + 0.05) = \text{Rs } 21.00$$

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2. Calculation of Required Rate of Return ($k_s$):

Using the Gordon Constant Growth Model:

$$k_s = \frac{D_1}{P_0} + g$$

$$k_s = \frac{\text{Rs } 21}{\text{Rs } 210} + 0.05 = 0.10 + 0.05 = 0.15 = \mathbf{15.0\%}$$

The required rate of return consists of a 10% dividend yield and a 5% capital gains yield.

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3. Expected Price of the Stock One Year From Today ($P_1$):

Method 1 (Direct Growth of Stock Price):

Under constant growth conditions, stock price grows at the constant growth rate $g$:

$$P_1 = P_0 \times (1 + g) = \text{Rs } 210 \times (1 + 0.05) = \mathbf{\text{Rs } 220.50}$$

Method 2 (Gordon Model at Year 1):

$$P_1 = \frac{D_2}{k_s - g}$$

Where $D_2 = D_1 \times (1 + g) = 21 \times 1.05 = \text{Rs } 22.05$:

$$P_1 = \frac{\text{Rs } 22.05}{0.15 - 0.05} = \frac{\text{Rs } 22.05}{0.10} = \mathbf{\text{Rs } 220.50}$$

Conclusion:

• Required rate of return on the stock = 15.0%
• Expected stock price one year from today = Rs 220.50

Siddhartha Manufacturing Company — Operating Cycle & CCC Analysis:

Given:

• Inventory turnover ratio ($IT$) = $8$ times per year
• Average payment period ($PDP$ or $APP$) = $35$ days
• Average collection period / receivable collection period ($RCP$ or $DSO$) = $60$ days
• Annual investment for operating cycle (annual cash operating expenses) = $\text{Rs } 3.5 \text{ million} = \text{Rs } 3,500,000$
• Base year = $360$ days

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Part a: Calculation of Operating Cycle (OC) and Cash Conversion Cycle (CCC):

1. Inventory Conversion Period (ICP):

$$ICP = \frac{360}{\text{Inventory Turnover}} = \frac{360}{8} = 45 \text{ days}$$

2. Operating Cycle (OC): The operating cycle measures the time between acquiring raw materials and collecting cash from customers:

$$OC = ICP + RCP = 45 \text{ days} + 60 \text{ days} = \mathbf{105 \text{ days}}$$

3. Cash Conversion Cycle (CCC): The cash conversion cycle measures the net duration cash remains tied up in operations after accounting for supplier trade credit:

$$CCC = OC - PDP = 105 \text{ days} - 35 \text{ days} = \mathbf{70 \text{ days}}$$

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Part b: Daily Cash Operating Expenses and Required Negotiated Financing:

1. Daily Cash Operating Expenses:

$$\text{Daily Cash Expenses} = \frac{\text{Annual Cash Operating Expenses}}{360}$$

$$\text{Daily Cash Expenses} = \frac{\text{Rs } 3,500,000}{360} = \mathbf{\text{Rs } 9,722.22 \text{ per day}}$$

2. Negotiated Financing Required to Support CCC: The amount of working capital financing required to sustain operations during the cash conversion cycle:

$$\text{Negotiated Financing Required} = \text{Daily Cash Operating Expenses} \times CCC$$

$$\text{Negotiated Financing Required} = \text{Rs } 9,722.22 \times 70 = \mathbf{\text{Rs } 680,555.56} \approx \mathbf{\text{Rs } 680,556}$$

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Summary of Results:

• Operating Cycle (OC): 105 days
• Cash Conversion Cycle (CCC): 70 days
• Daily Cash Operating Expenses: Rs 9,722.22
• Negotiated Financing Required: Rs 680,556

Financial Goals of the Firm and Key Features:

1. The Primary Financial Goal: Wealth Maximization:

In modern corporate financial management, the universally accepted primary financial goal of a business firm is Shareholder Wealth Maximization (maximizing the intrinsic market value of the firm’s common stock).

While historically firms prioritized Profit Maximization, modern financial theory rejects profit maximization as the sole corporate objective due to its critical limitations.

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2. Comparison: Profit Maximization vs. Wealth Maximization:

Criterion	Profit Maximization	Wealth / Value Maximization
Core Objective	Maximize accounting net profit or EPS within a single accounting period.	Maximize the net present value of all future cash flows accruing to owners ($P_0$).
Time Horizon	Short-term orientation (often compromises R&D and maintenance).	Long-term perspective encompassing sustainable enterprise viability.
Time Value of Money	Ignores timing of cash flows (treats a Rupee today identical to a Rupee in 5 years).	Fully incorporates discounting via the firm’s cost of capital.
Risk Consideration	Completely ignores business and financial risks associated with income streams.	Explicitly adjusts for operational, market, and credit risks in required returns.
Measurement Metric	Accounting profit (subject to manipulation through accounting policy choices).	Net economic cash flows and market value of equity.

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3. Key Features of the Wealth Maximization Goal:

1. Clear, Operational Decision Criterion:

   • Provides an objective decision rule: Accept investments that yield a positive Net Present Value ($NPV > 0$), as they directly increase shareholders’ wealth:
     $$\Delta W = NPV = PV(\text{Cash Inflows}) - PV(\text{Cash Outflows})$$

2. Explicit Incorporation of Risk and Uncertainty:

   • Higher risk projects are evaluated with higher hurdle rates ($k$), ensuring that investors are appropriately compensated for volatility and default exposure.

3. Recognition of the Time Value of Money:

   • Recognizes that immediate cash inflows possess greater economic utility than distant future inflows due to reinvestment opportunities and purchasing power loss.

4. Harmonious with Broader Stakeholder Interests:

   • In a competitive market, a firm cannot maximize stock price in the long run if it mistreats customers, underpays employees, or violates environmental norms. Wealth maximization requires building sustainable competitive advantage, customer trust, and operational efficiency.

Interest Rate and Inflation Premium Analysis:

Given:

• Date: January 1, 2025
• Expected Inflation Rates:
  • Year 1 (2025): $I_1 = 5\%$
  • Year 2 (2026): $I_2 = 6\%$
  • Year 3 (2027): $I_3 = 7\%$
  • Year 4 (2028): $I_4 = 8\%$
• Real risk-free rate ($r^*$) = $2\%$ (constant across all maturities)
• Maturity risk premium ($MRP$) = $0$ for bonds with maturities $n \le 5$ years
• Current interest rate on 5-year Treasury bonds ($r_5$) = $9\%$

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Part a: Average Expected Inflation Rate Over Next 4 Years ($IP_4$):

The 4-year inflation premium is the arithmetic average of expected annual inflation rates:

$$IP_4 = \frac{I_1 + I_2 + I_3 + I_4}{4}$$

$$IP_4 = \frac{5\% + 6\% + 7\% + 8\%}{4} = \frac{26\%}{4} = \mathbf{6.50\%}$$

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Part b: Interest Rate on 4-Year Treasury Bonds ($r_4$):

Since Treasury bonds carry zero default risk ($DRP = 0$), zero liquidity premium ($LP = 0$), and given $MRP_4 = 0$:

$$r_4 = r^* + IP_4 + MRP_4$$

$$r_4 = 2.0\% + 6.50\% + 0\% = \mathbf{8.50\%}$$

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Part c: Expected Inflation Rate in Year 5 (2029) ($I_5$):

For a 5-year Treasury bond:

$$r_5 = r^* + IP_5 + MRP_5$$

Given $r_5 = 9\%$, $r^* = 2\%$, and $MRP_5 = 0$:

$$9\% = 2\% + IP_5 + 0 \implies IP_5 = 9\% - 2\% = 7.0\%$$

The 5-year inflation premium is:

$$IP_5 = \frac{I_1 + I_2 + I_3 + I_4 + I_5}{5} = 7.0\%$$

$$\frac{26\% + I_5}{5} = 7.0\%$$

$$26\% + I_5 = 35.0\%$$

$$I_5 = 35.0\% - 26.0\% = \mathbf{9.0\%}$$

The expected inflation rate in 2029 (Year 5) is 9.0%.

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Part d: How Maturity Risk Affects the Interest Rate of a Bond:

• Price Risk (Interest Rate Risk): Bond prices move inversely with market interest rates. Longer-term bonds exhibit significantly higher price sensitivity to interest rate shifts than short-term bonds.
• Maturity Risk Premium (MRP): To induce risk-averse investors to hold longer-term debt, issuers must offer an additional return premium called the Maturity Risk Premium.
• Impact on Yield Curve: As maturity ($n$) extends, $MRP$ increases. Consequently, even when future inflation is expected to remain constant, the inclusion of $MRP$ produces an upward-sloping yield curve.

Sahara Resort — Loan Amortization Schedule and EMI Calculation:

Given:

• Principal Loan Amount ($PV$) = $\text{Rs } 300,000$
• Loan tenure ($n$) = $3$ years
• Annual interest rate ($i$) = $12\% = 0.12$

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Part a: Calculation of Equal Annual Installment Payment (PMT):

$$PV = PMT \times PVIFA(i, n)$$

$$PVIFA(12\%, 3) = \frac{1 - (1 + 0.12)^{-3}}{0.12} = \frac{1 - (1.12)^{-3}}{0.12} = \frac{1 - 0.711780}{0.12} = 2.401831$$

$$PMT = \frac{\text{Rs } 300,000}{2.401831} = \mathbf{\text{Rs } 124,904.72}$$

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Part b: Loan Amortization Schedule:

Year	Beginning Balance (Rs)	Annual Payment (Rs)	Interest Payment (12%) (Rs)	Principal Repayment (Rs)	Ending Balance (Rs)
1	300,000.00	124,904.72	36,000.00	88,904.72	211,095.28
2	211,095.28	124,904.72	25,331.43	99,573.29	111,521.99
3	111,521.99	124,904.63*	13,382.64	111,521.99	0.00
Total		374,714.07	74,714.07	300,000.00

*Note: Year 3 payment is adjusted by -Rs 0.09 to eliminate rounding residual and ensure exactly zero ending balance ($111,521.99 + 13,382.64 = 124,904.63$).

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Part c: Equal Monthly Installment (EMI) if Compounded Monthly:

• Number of monthly periods ($N$) = $3 \times 12 = 36$ months
• Monthly interest rate ($r_m$) = $\frac{12\%}{12} = 1\% = 0.01$ per month

$$\text{EMI} = \frac{PV \times r_m \times (1 + r_m)^N}{(1 + r_m)^N - 1} = \frac{PV}{PVIFA(1\%, 36)}$$

$$PVIFA(1\%, 36) = \frac{1 - (1.01)^{-36}}{0.01} = \frac{1 - 0.698925}{0.01} = 30.107505$$

$$\text{EMI} = \frac{\text{Rs } 300,000}{30.107505} = \mathbf{\text{Rs } 9,964.29 \text{ per month}}$$

Summary:

• Equal Annual Installment: Rs 124,904.72
• Equal Monthly Installment (EMI): Rs 9,964.29

Shalimar Paints — Component Costs and WACC Analysis:

Given Capital Structure Weights:

• Weight of Debt ($w_d$) = $30\% = 0.30$
• Weight of Preferred Stock ($w_p$) = $15\% = 0.15$
• Weight of Common Stock / Equity ($w_s$) = $55\% = 0.55$
• Corporate Tax Rate ($T$) = $30\% = 0.30$

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Part a: Component Costs of Capital:

1. Component Cost of Debt ($k_d$):

• Pre-tax interest rate ($r_d$) = $10\%$
  $$k_d = r_d \times (1 - T) = 10\% \times (1 - 0.30) = \mathbf{7.00\%}$$

2. Component Cost of Preferred Stock ($k_p$):

• Selling price ($P_p$) = $\text{Rs } 100$
• Preferred dividend ($D_p$) = $\text{Rs } 9.00$
• Flotation cost per share ($F$) = $\text{Rs } 6.00$
• Net proceeds ($NP_p$) = $100 - 6 = \text{Rs } 94$
  $$k_p = \frac{D_p}{P_p - F} = \frac{\text{Rs } 9}{\text{Rs } 94} = 0.09574 = \mathbf{9.57\%}$$

3. Component Cost of Retained Earnings ($k_s$ / Internal Equity):

• Current stock price ($P_0$) = $\text{Rs } 208$
• Last dividend ($D_0$) = $\text{Rs } 20$
• Constant growth rate ($g$) = $4\% = 0.04$
• Expected dividend next year ($D_1$) = $D_0 \times (1 + g) = 20 \times (1.04) = \text{Rs } 20.80$
  $$k_s = \frac{D_1}{P_0} + g = \frac{\text{Rs } 20.80}{\text{Rs } 208} + 0.04 = 0.10 + 0.04 = 0.14 = \mathbf{14.00\%}$$

4. Component Cost of New Common Stock ($k_e$ / External Equity):

• Flotation cost percentage ($F$) = $5\% = 0.05$
• Net proceeds per share = $P_0 \times (1 - F) = 208 \times (1 - 0.05) = \text{Rs } 197.60$
  $$k_e = \frac{D_1}{P_0(1 - F)} + g = \frac{\text{Rs } 20.80}{\text{Rs } 197.60} + 0.04$$
  $$k_e = 0.105263 + 0.04 = 0.145263 = \mathbf{14.53\%}$$

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Part b: Weighted Average Cost of Capital (WACC) Using Retained Earnings:

Assuming common equity financing is entirely met through internal retained earnings ($k_s = 14.00\%$):

$$WACC = (w_d \times k_d) + (w_p \times k_p) + (w_s \times k_s)$$

$$WACC = (0.30 \times 7.00\%) + (0.15 \times 9.57\%) + (0.55 \times 14.00\%)$$

$$WACC = 2.10\% + 1.436\% + 7.70\% = \mathbf{11.236\%} \approx \mathbf{11.24\%}$$

Summary Table:

Capital Component	Weight ($w_i$)	Component Cost ($k_i$)	Weighted Cost ($w_i \times k_i$)
Debt	0.30	7.00%	2.100%
Preferred Stock	0.15	9.57%	1.436%
Retained Earnings	0.55	14.00%	7.700%
WACC	1.00		11.24%