Duration rule. For a small change in yield, the percentage price change is approximately proportional to modified duration:

$\frac{\Delta P}{P}\approx -D^{*}\,\Delta y$

where $D^*$ is modified duration (Macaulay duration divided by $1+y$) and $\Delta y$ is the change in yield. A rise in yield lowers the price and a fall raises it.

Error of the rule. The rule is a linear approximation to the convex price-yield curve, so it ignores convexity. A more accurate estimate is

$\frac{\Delta P}{P}\approx -D^{*}\,\Delta y+\tfrac12\,C\,(\Delta y)^2$

where $C$ is convexity. The error of the duration rule is therefore the convexity term $\tfrac12 C(\Delta y)^2$, and

$\text{Percentage error}=\frac{\text{Duration-rule estimate}-\text{Actual change}}{\text{Actual change}}\times100$

where the actual change is the true percentage change in price, found by repricing the bond at the new yield. Because $C>0$, the duration rule understates the price after a yield fall (the price gain is larger than predicted) and overstates the fall after a yield rise (the loss is smaller than predicted). The error grows with the square of the yield change, so it is small for small $\Delta y$.

Illustration (assumed values, since none are given in the question). Let $D^*=5$, $C=100$ and $\Delta y=+0.5\%$.

$\text{Duration rule: } -5(0.005)=-2.5\%$

$\text{With convexity: } -2.5\%+\tfrac12(100)(0.005)^2=-2.5\%+0.125\%=-2.375\%$

The rule overstates the fall by 0.125 percentage points, an error of about $0.125/2.375\approx5.3\%$ of the actual change.

If the question supplies the bond's actual figures, substitute them into the formulas above: first find the duration-rule prediction, then reprice the bond at the new yield and compute the percentage error.

Duration-with-convexity rule — predicted price

The duration-with-convexity (second-order Taylor) approximation for the percentage change in a bond's price is:

$\frac{\Delta P}{P} \approx -D_{\text{mod}}\,\Delta y + \tfrac{1}{2}\,C\,(\Delta y)^2$

where:

• $D_{\text{mod}}$ = modified duration,
• $C$ = convexity,
• $\Delta y$ = change in yield (in decimal).

Predicted new price:

$P_{\text{new}} \approx P_0\left[1 - D_{\text{mod}}\,\Delta y + \tfrac{1}{2}\,C\,(\Delta y)^2\right]$

Worked illustration (use your question's data in the same slots). Suppose a bond has price $P_0 = \text{Rs }1{,}000$, modified duration $D_{\text{mod}} = 8$ years, convexity $C = 120$, and yield rises by $\Delta y = +0.01$ (100 bps):

$\frac{\Delta P}{P} \approx -(8)(0.01) + \tfrac{1}{2}(120)(0.01)^2 = -0.08 + 0.006 = -0.074 = -7.4\%$

$P_{\text{new}} \approx 1{,}000\,(1 - 0.074) = \text{Rs }926$

Duration alone would have predicted $-8\%$ (Rs 920); adding the convexity term corrects the estimate upward to $-7.4\%$ (Rs 926), which is much closer to the true price.

Why the percentage changes differ under duration and convexity

1. Duration is a first-order (linear) measure. It uses the slope of the price–yield curve at the current yield: $\dfrac{\Delta P}{P} \approx -D_{\text{mod}}\,\Delta y$. It assumes price changes in a straight line with yield, so it is accurate only for very small yield changes.

2. The actual price–yield relation is convex, not linear. The true curve is bowed toward the origin. For any given yield change, the actual price is higher than the duration-predicted price — whether yields rise or fall. This asymmetry is convexity.

3. Convexity is a second-order (curvature) measure. It captures the bending of the curve through the term $\tfrac{1}{2}C(\Delta y)^2$. Since $(\Delta y)^2$ is always positive, this term is always positive, so it always adds to the duration estimate.

4. Hence the divergence grows with the size of the yield change. For small $\Delta y$, the squared term is negligible and duration is accurate. For large $\Delta y$, the convexity term becomes material, so the two measures give increasingly different predictions. The difference is also larger for bonds with greater convexity (e.g., lower-coupon, longer-maturity bonds).

5. Practical implication: Duration overstates price falls and understates price rises when yields change substantially; the duration-with-convexity rule captures both the slope and the curvature, giving a more accurate predicted price.

Given:

• Market expected return, $R_m = 14\%$
• Risk-free rate, $R_f = 6\%$
• Market risk premium, $R_m - R_f = 14\% - 6\% = 8\%$

CAPM equation: $R_i = R_f + \beta_i (R_m - R_f)$

---

a. Required return on each stock

Stock X: $R_X = 6\% + 1.5(8\%) = 6\% + 12\% = 18\%$

Stock Y: $R_Y = 6\% + 2.0(8\%) = 6\% + 16\% = 22\%$

Stock Z: $R_Z = 6\% + 0.5(8\%) = 6\% + 4\% = 10\%$

---

b. Undervalued, overvalued and worth investing

Compare expected return with required return:

• Undervalued stock: Z, because its expected return $(12\%)$ is greater than its required return $(10\%)$. It has positive alpha of $+2\%$.
• Overvalued stock: Y, because its expected return $(20\%)$ is less than its required return $(22\%)$. It has negative alpha of $-2\%$.
• Worth investing: Z is the best candidate for investment. X is fairly priced and may be held if it matches the investor’s required return. Y should be avoided or sold.

---

c. SML graph and location of stocks X, Y and Z

The Security Market Line equation is: $R_i = 6\% + 8\% \beta_i$

Key points on the SML:

• Risk-free asset: $\beta = 0$, return $= 6\%$
• Market portfolio: $\beta = 1$, return $= 14\%$
• Stock X: $\beta = 1.5$, required return $= 18\%$
• Stock Y: $\beta = 2.0$, required return $= 22$
• Stock Z: $\beta = 0.5$, required return $= 10\%$

Return (%)
24 |
22 |                              * Y_req (2.0, 22)
20 |                              o Y_exp (2.0, 20)
18 |                  * X (1.5, 18)
16 |
14 |          * M (1.0, 14)
12 |      o Z_exp (0.5, 12)
10 |      * Z_req (0.5, 10)
 8 |
 6 | * Rf (0, 6)
 4 |
 2 |
 0 +----|------|------|------|------|---- Beta
      0.5    1.0    1.5    2.0    2.5

Interpretation:

• The straight line is the SML, showing required return for each level of beta.
• X lies exactly on the SML, so it is fairly priced.
• Y lies below the SML, so it is overvalued.
• Z lies above the SML, so it is undervalued.

---

d. Risk premium for all stocks

The market risk premium is: $R_m - R_f = 14\% - 6\% = 8\%$

The CAPM risk premium for each stock is: $\text{Risk premium}_i = \beta_i (R_m - R_f)$

So, in CAPM terms, the required risk premiums are 12%, 16%, and 4% for X, Y, and Z respectively.
If “risk premium” means expected excess return, they are 12%, 14%, and 6%.

---

d/e. Difference between systematic and unsystematic risk

Conclusion:
Stock Z is undervalued and worth investing. Stock X is fairly valued. Stock Y is overvalued and should be avoided.

Setup. Total market value (price x shares):

Day 0 is taken as the base.

(a) Index on day 1 and day 2

(i) Value-weighted (base = 100):

$I_1=\frac{5{,}875{,}000}{5{,}400{,}000}\times100=108.80,\qquad I_2=\frac{6{,}550{,}000}{5{,}400{,}000}\times100=121.30$

(ii) Price-weighted (average of the three prices; divisor = 3):

$I_0=\frac{510}{3}=170.00,\quad I_1=\frac{535}{3}=178.33,\quad I_2=\frac{580}{3}=193.33$

(Rebased to day 0 = 100, these are 104.90 and 113.73.)

(iii) Equally weighted (equal money in each stock on day 0, so the index is the average price relative):

$I_1=\frac{1}{3}\left(\frac{135}{160}+\frac{280}{240}+\frac{120}{110}\right)\times100=\frac{0.8438+1.1667+1.0909}{3}\times100=103.38$

$I_2=\frac{1}{3}\left(\frac{150}{160}+\frac{280}{240}+\frac{150}{110}\right)\times100=\frac{0.9375+1.1667+1.3636}{3}\times100=115.59$

(b) Index on day 3 after B's 2-for-1 split

After the split B has 20,000 shares and its day-2 price falls to Rs 280/2 = Rs 140.

Price-weighted. The divisor must change so that the split does not move the index. Day-2 index = 193.33. Sum of day-2 prices after the split = 150 + 140 + 150 = 440.

$\text{New divisor}=\frac{440}{193.33}=2.2759$

Day-3 prices: 160 + 150 + 170 = 480.

$I_3=\frac{480}{2.2759}=210.91$

Value-weighted. A split leaves total market value unchanged, so no adjustment is needed. Day-3 values: A = 160 x 5,000 = 800,000; B = 150 x 20,000 = 3,000,000; C = 170 x 20,000 = 3,400,000; total = 7,200,000.

$I_3=\frac{7{,}200{,}000}{5{,}400{,}000}\times100=133.33$

(c) Factors in constructing a market index, and its uses

Factors to consider

1. Sample (number and choice of stocks): it must represent the market, with adequate coverage of sectors (banks, hydropower, insurance, etc.) and of actively traded, liquid stocks.
2. Weighting method: price-weighted, value (market-capitalisation) weighted or equally weighted; each gives a different weight to large and small stocks.
3. Base period and base value: a stable, normal base date with a convenient base value (100 or 1,000).
4. Averaging method: arithmetic or geometric mean.
5. Adjustments: stock splits, bonus shares, rights issues, mergers and new listings must be adjusted through the divisor or base value so the index changes only because of price movement.
6. Free-float: only shares available to the public should count, not promoter holdings.
7. Periodic review: the constituents should be revised as companies are delisted or the market changes.

Uses of a market index

1. A barometer of overall market and economic condition (for example the NEPSE index).
2. A benchmark for judging the performance of portfolios and mutual funds.
3. A basis for estimating market return and beta, as in CAPM and other models.
4. The basis for index funds, index futures and other derivatives.
5. A tool for technical analysis and for forecasting market trend.
6. An indicator of investor sentiment for policy-makers, regulators and investors.

Stages of Business Cycle

A business cycle (also called a trade cycle) refers to the more or less regular fluctuations in the level of economic activity — output, employment, income and prices — over a period of time. It is a continuous and recurring process through which an economy passes. The business cycle is generally divided into four stages, though some economists also mention a fifth (the trough as a separate turning point).

1. Expansion (Boom / Upswing)

This is the phase of rising economic activity. During this stage:

• Production, employment, income and investment all increase rapidly.
• Consumer demand rises, and prices begin to move upward.
• Bank credit expands as businesses borrow to finance investment.
• Business optimism is high, and profit expectations are favourable.
• New firms enter the market and existing firms expand capacity.

The economy reaches its peak (prosperity) at the end of this stage, where activity is at its maximum. However, at the peak, costs begin to rise faster than prices, profit margins shrink, and the economy becomes vulnerable to a downturn.

2. Recession (Contraction / Downturn)

After the peak, economic activity begins to decline. During this stage:

• Demand falls, leading to a fall in production and employment.
• Investment declines as business confidence weakens.
• Prices and profits start falling; some firms incur losses.
• Bank credit contracts as borrowers are unable or unwilling to borrow.
• Inventories pile up because demand has fallen.

This stage marks the downward phase of the cycle. If the decline is severe and prolonged, it is called a depression.

3. Depression (Trough / Slump)

This is the lowest point of the business cycle. During this stage:

• Output, employment, income and investment fall to their minimum levels.
• There is large-scale unemployment and underutilisation of productive capacity.
• Prices fall sharply, and many businesses become bankrupt.
• Bank credit shrinks, and there is a general lack of confidence.
• Demand is very low, and inventories remain unsold.

The economy remains stagnant at this trough until forces of recovery begin to operate. A depression is generally shorter in duration than the expansion phase but causes severe hardship.

4. Recovery (Revival / Upswing)

From the trough, the economy begins to recover. During this stage:

• Investment and production slowly increase as confidence returns.
• Employment and income start rising.
• Prices stabilise and then begin to rise gradually.
• Bank credit expands as demand for loans increases.
• New investment opportunities emerge, and business optimism returns.

Recovery gradually turns into expansion, and the cycle repeats itself. The economy moves from recovery to boom, then to recession, then to depression, and back to recovery — and so on.

Conclusion

Thus, the business cycle passes through the four stages of expansion, recession, depression and recovery in a recurring manner. These stages are not uniform in duration or intensity; some cycles are short and mild, while others are long and severe. Understanding these stages helps the government and central bank to adopt appropriate fiscal and monetary policies to stabilise the economy.

Recent developments in the securities market of Nepal

1. Automated and online trading: NEPSE trades through a fully automated system, and investors place orders through licensed brokers using the Trade Management System (TMS), including online and mobile access.
2. Dematerialisation: the Central Depository and Clearing Services Ltd. (CDSC) holds shares in electronic form in Demat accounts, which removes the risks of forged, lost or stolen certificates. Settlement is on a T+2 cycle, and CDSC runs clearing and settlement.
3. Online IPO application: MeroShare and the ASBA (Application Supported by Blocked Amount) system let investors apply for IPOs, rights and other issues online, with the money blocked in their bank accounts until allotment.
4. Growth of the investor base: the number of Demat accounts and the number of listed companies, market capitalisation and turnover have grown considerably, reflecting wider retail participation.
5. Regulatory strengthening: the Securities Board of Nepal (SEBON), established in 1993 AD (2050 B.S.), regulates the market under the Securities Act, 2063 B.S. and its regulations. It has tightened disclosure rules, supervision of brokers and action against insider trading and price manipulation.
6. New products and institutions: mutual funds (open-end and closed-end), government bonds, corporate debentures and preference shares are listed. Merchant bankers, depository participants, credit rating agencies and market makers have been licensed. Derivatives and commodity trading have been proposed, and the legal framework for them is being developed.
7. Investor protection and education: the Investor Protection Fund, grievance handling by SEBON and investor awareness programmes support investors' confidence.
8. Institutional participation: banks, insurance companies, provident funds and mutual funds are increasingly active in the market.

Remaining challenges: shallow liquidity, concentration in banking stocks, limited product variety, speculative trading and weak investor awareness. Further reform in these areas is needed for the market to deepen.

Given: ROE = 10%, plowback b = 0.60, so payout = 0.40; beta = 1.20; E0 = Rs 12; market return = 13%; T-bill rate = 5%.

Required return (CAPM):

$k = 5\% + 1.20(13\% - 5\%) = 14.6\%$

Growth rate:

$g = b \times ROE = 0.60 \times 10\% = 6\%$

Next year's earnings and dividend:

$E_1 = 12(1.06) = \text{Rs } 12.72,\qquad D_1 = 0.40 \times 12.72 = \text{Rs } 5.088$

(a) Intrinsic value (constant-growth DDM)

$P_0=\frac{D_1}{k-g}=\frac{5.088}{0.146-0.06}=\frac{5.088}{0.086}\approx \text{Rs } 59.16$

(b) Present value of growth opportunities

Value of the firm with no growth, if it paid out all earnings:

$\frac{E_1}{k}=\frac{12.72}{0.146}=\text{Rs } 87.12$

$PVGO = P_0 - \frac{E_1}{k} = 59.16 - 87.12 = -\text{Rs } 27.96$

PVGO is negative because the firm keeps 60% of earnings and reinvests it at an ROE of 10%, which is below the required return of 14.6%. The reinvestment destroys value. The firm would be worth more if it paid out all earnings instead of plowing them back.

Behavioural Finance

Concept

Behavioural finance is a field of finance that studies how psychological factors, cognitive biases, and emotional influences affect the financial decisions of investors, managers, and markets. It emerged as a critique of traditional finance (standard finance), which assumes that investors are fully rational, have complete information, and always aim to maximise expected utility.

Behavioural finance argues that real investors are not perfectly rational; their decisions are bounded by limited information-processing capacity, emotions, and social influences. Hence, market prices often deviate from fundamental (intrinsic) values, producing anomalies that traditional theories such as the Efficient Market Hypothesis (EMH) and Modern Portfolio Theory (MPT) cannot fully explain.

Key Premises

1. Bounded rationality — Investors are rational only within cognitive limits (Herbert Simon).
2. Investors make errors — Decisions are shaped by heuristics (rules of thumb) and biases rather than full optimisation.
3. Markets are not always efficient — Prices reflect both fundamental and psychological factors.
4. Two branches — Behavioural finance covers (a) Behavioural Microfinance (individual investor behaviour) and (b) Behavioural Macroeconomics/Finance (market-level anomalies such as bubbles and crashes).

Major Psychological Biases Studied

• Overconfidence bias — Investors overestimate their knowledge and skill, leading to excessive trading.
• Representativeness — Judging the future by recent or familiar patterns.
• Anchoring — Fixing on an initial reference point (e.g., purchase price) while deciding.
• Loss aversion — Losses hurt more than equivalent gains give pleasure (Kahneman & Tversky's Prospect Theory).
• Herding — Following the crowd rather than independent analysis.
• Mental accounting — Treating money differently depending on its source or purpose.
• Regret aversion — Avoiding decisions that may later cause regret.
• Confirmation bias — Seeking only information that supports existing beliefs.

Significance

• Explains market anomalies such as bubbles, crashes, momentum, and the January effect.
• Helps investors recognise their own biases and improve decision-making.
• Assists financial advisers, fund managers, and regulators in designing better products and policies.
• Provides a more realistic framework than traditional finance for understanding actual market behaviour.

Conclusion

Behavioural finance is the study of the psychological and emotional aspects of financial decision-making. It complements traditional finance by acknowledging that human beings are not always rational, and thereby offers a more realistic explanation of investor behaviour and market outcomes.

Given:

• Securities (assets) = Rs 750 million
• Liabilities = Rs 25 million
• Shares outstanding = 55 million
• Discount from NAV = 12%

a. Net Asset Value (NAV) per share

$\text{Net assets} = \text{Assets} - \text{Liabilities} = 750 - 25 = \text{Rs 725 million}$

$\text{NAV per share} = \frac{\text{Net assets}}{\text{Shares outstanding}} = \frac{725}{55} = \text{Rs 13.1818} \approx \text{Rs 13.18}$

NAV per share = Rs 13.18

b. Current market price per share

Since the fund trades at a 12% discount to NAV:

$\text{Market price} = \text{NAV} \times (1 - \text{Discount rate})$

$= 13.1818 \times (1 - 0.12) = 13.1818 \times 0.88 = \text{Rs 11.60}$

Current market price per share = Rs 11.60

c. Two possible reasons for trading at a discount to NAV

1. Lack of liquidity/marketability: Closed-end fund shares cannot be redeemed at NAV from the fund; investors must sell them in the secondary market. Limited buyers or low trading volume can push the market price below NAV.

2. Management fees and expenses: Investors know that the fund charges management and operating expenses, which reduce future returns. This lowers the price they are willing to pay compared to the underlying asset value.

Other acceptable reasons: poor past performance, unfavorable investor sentiment, tax liabilities on unrealized capital gains, or limited investment options in the fund.

Distinction between CAPM and APT

In short: CAPM is a single-factor general equilibrium model built on a market portfolio and beta, whereas APT is a multi-factor no-arbitrage model that prices several systematic risk factors without requiring a market portfolio or normal return distributions.

(a) Price-weighted index (Date 1 = base 100)

Sum of prices: Date 1 = 200 + 100 + 800 = 1,100; Date 2 = 250 + 110 + 800 = 1,160; Date 3 = 300 + 120 + 900 = 1,320.

Divisor for base 100: $D = 1{,}100/100 = 11$.

(If the plain average price is wanted instead: 366.67, 386.67 and 440.00.)

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

$I_2=\frac{2{,}870{,}000}{2{,}800{,}000}\times100=102.50,\qquad I_3=\frac{3{,}240{,}000}{2{,}800{,}000}\times100=115.71$

(c) Adjusting for a stock split

A split changes the price and the number of shares but not the company's value, so the index must not move because of it.

Price-weighted index: the divisor is changed so that the index stays the same just after the split. Illustration: suppose A splits 2-for-1 at Date 3, so its price falls from Rs 300 to Rs 150. Before the split, $\sum P = 1{,}320$ and the index is 120. After the split $\sum P = 150 + 120 + 900 = 1{,}170$.

$\text{New divisor}=\frac{1{,}170}{120}=9.75$

The index remains $1{,}170/9.75 = 120$.

Value-weighted index: no adjustment is needed. A's shares double to 2,000 and its price halves to Rs 150, so its value stays Rs 300,000 and total value stays Rs 3,240,000. The index remains 115.71. (Adjustment of the base value is needed only for events that change total market value, such as new listings or additional share issues.)

(d) Uses of a market index

1. It shows the overall direction of the stock market and, indirectly, of the economy.
2. It is a benchmark for evaluating portfolio and mutual fund performance.
3. It helps estimate market return and beta for models such as CAPM.
4. It is the basis for index funds and for index-linked derivatives.
5. It is used in technical analysis to identify market trends.
6. It reflects investor sentiment and helps policy-makers and regulators monitor the market.

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

Step 1: Net amount invested

$1{,}000 - 2\%(1{,}000)=\text{Rs }980$

Step 2: What the savings account would give

$1{,}000(1.05)^5=\text{Rs }1{,}276.28$

Step 3: Gross return the fund must earn

The fund's net growth each year is $(1+r)(1-0.011)$, because the 1.10% fee is deducted from the year-end value of the assets. The Rs 980 must grow to Rs 1,276.28:

$980\left[(1+r)(0.989)\right]^5=1{,}276.28$

$\left[(1+r)(0.989)\right]^5=1.30233\;\Rightarrow\;(1+r)(0.989)=1.05425$

$1+r=\frac{1.05425}{0.989}=1.0660\;\Rightarrow\; r\approx 6.60\%$

The fund must earn about 6.60% a year before fees (about 6.5% if the fee is simply subtracted from the return), against 5% on the savings account. The extra return pays for the 2% load and the 1.10% annual charge.

Expected returns

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

$\bar R_p=0.40(15)+0.60(9)=6+5.4=11.4\%$

Standard deviations (population form, equally likely years)

$\sigma_A^2=\frac{(-10)^2+0^2+10^2}{3}=66.67,\quad \sigma_A=8.165\%$

$\sigma_B^2=\frac{5^2+(-1)^2+(-4)^2}{3}=14,\quad \sigma_B=3.742\%$

Covariance and correlation

$Cov_{AB}=\frac{(-10)(5)+(0)(-1)+(10)(-4)}{3}=\frac{-90}{3}=-30$

$\rho_{AB}=\frac{-30}{8.165\times3.742}=-0.982$

Portfolio variance

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

$=0.16(66.67)+0.36(14)+2(0.4)(0.6)(-30)=10.667+5.04-14.4=1.307$

$\sigma_p=\sqrt{1.307}\approx1.14\%$

Result: portfolio return = 11.4%, portfolio standard deviation = about 1.14%. The risk is far below that of either asset because the two returns move almost perfectly in opposite directions.

Arbitrage opportunity: Yes.

Step 1: Fair return for a beta of 0.6. The security market line through RF and A has slope

$\frac{12\%-6\%}{1.2-0}=5\%\text{ per unit of beta}$

$E(R)=6\%+0.6\times5\%=9\%$

(equivalently $6\% + \tfrac{0.6}{1.2}(12\%-6\%) = 9\%$).

Step 2: Compare. Portfolio E offers only 8% against the 9% required for its risk. It plots below the line, so it is overpriced.

Step 3: Mimicking portfolio. A beta of 0.6 is obtained with

$w_A=\frac{0.6}{1.2}=0.5,\qquad w_{RF}=0.5$

Its return is $0.5(12\%)+0.5(6\%)=9\%$.

Strategy: short sell Portfolio E and invest the proceeds 50% in Portfolio A and 50% in the risk-free asset.

Result: the net investment is zero and net beta is zero, yet the position earns a riskless profit of 9% - 8% = 1% of the amount shorted. As arbitrageurs short E, its price falls and its expected return rises until it reaches 9%, restoring equilibrium on the SML.

Annual coupon payment:

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

Bond price formula:

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

Given:

$P = 950,\quad C = 100,\quad F = 1{,}000,\quad n = 7$

So,

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

Trial and error:

• At $r = 11\%$:

$P = 100(4.7122) + 1{,}000(0.4817) = 471.22 + 481.66 = \text{Rs }952.88$

This is greater than Rs 950.

• At $r = 11.1\%$:

$P = 100(4.6970) + 1{,}000(0.4786) = 469.70 + 478.63 = \text{Rs }948.33$

This is less than Rs 950.

Interpolation:

$r = 11\% + \frac{952.88 - 950}{952.88 - 948.33} \times 0.1\%$

$r = 11\% + \frac{2.88}{4.55} \times 0.1\% = 11.063\%$

Therefore, the yield to maturity is approximately:

$\boxed{r = 11.06\% \text{ per annum}}$

Since the bond is selling at a discount, its YTM is greater than the coupon rate of 10%.

Investment Company

An investment company is a financial institution that pools the savings of many individual and institutional investors and invests those pooled funds in a diversified portfolio of securities such as shares, debentures, bonds and money-market instruments. It issues its own securities (shares or units) to investors and manages the collected fund professionally through a team of experts, so that small investors can earn returns while enjoying the benefits of diversification, liquidity and professional management. In Nepal, such companies are regulated by the Securities Board of Nepal (SEBON) under the Securities Act, 2063 and are commonly known as mutual funds.

Distinction between Open-End Fund and Closed-End Fund

In short, an open-end fund has a flexible corpus and offers ready redemption at NAV, whereas a closed-end fund has a fixed corpus and its units are traded in the market at prices fixed by demand and supply.

Short notes (any two)

a. Net Asset Value (NAV)

Net Asset Value is the per-unit value of a mutual fund scheme's assets after deducting all liabilities. It shows what each unit of the fund is actually worth on a given date.

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

• Total assets include market value of shares, bonds, debentures, cash, and accrued income.
• Liabilities include management fees, operating expenses, and other payables.
• NAV is calculated daily (in Nepal, generally at the close of each trading day) and published by the fund manager.
• If NAV rises above the unit's issue price, unit-holders gain; if it falls, they lose. Units are bought and sold (redeemed) at NAV, sometimes with a small premium or discount.
• It is the key measure of a mutual fund's performance and is used to compare different schemes.

b. Fundamental analysis

Fundamental analysis is the method of evaluating a security's intrinsic value by examining the underlying economic, industry, and company fundamentals. It assumes that the market price may deviate from true value in the short run but moves toward it in the long run.

It is studied at three levels:

• Economy analysis: GDP growth, inflation, interest rate, balance of payments, government policy, and political stability.
• Industry analysis: stage of the industry life cycle, competition, government regulation, demand-supply conditions, and cost structure.
• Company analysis: financial statements — EPS, DPS, P/E ratio, debt-equity ratio, profitability, liquidity, management quality, and future earnings prospects.

Tools used include ratio analysis, trend analysis, common-size and comparative statements, and discounted cash flow or dividend discount models. If intrinsic value exceeds the market price, the share is undervalued and should be bought; if it is lower, the share is overvalued and should be sold. Its limitation is that it is time-consuming and relies on accounting data that may not reflect current conditions.

c. SEBON (Securities Board of Nepal)

SEBON is the apex regulatory body of the Nepalese securities market, established in 1993 AD (2050 B.S.) under the Securities Exchange Act, 2040 B.S. (as amended), and is now governed by the Securities Act, 2063 B.S.. It is the sole authority to regulate, develop, and supervise the securities market in Nepal.

Functions:

• Regulatory: licenses and regulates stock brokers, dealers, merchant bankers, mutual funds, and depository institutions; approves the issue of shares, debentures, and other securities.
• Supervisory: monitors the activities of the Nepal Stock Exchange (NEPSE), CDSC, and listed companies to protect investor interests.
• Developmental: formulates policies and rules for the orderly growth of the capital market and promotes investor education.
• Quasi-judicial: hears and settles disputes, and can impose penalties, suspend or cancel the license of market intermediaries.

Its main objectives are to protect the interests of investors, ensure a fair and transparent market, and promote capital market development. It is headed by a chairman and a board of directors appointed by the Government of Nepal.