Corporate Finance · End Term · Jan 2026 · AN

**1. State the Fisher relation:** With real rate r, expected inflation \(\pi\) and nominal rate i, \(1+i=(1+r)(1+\pi)\). **2. Substitute the actual inputs:** Here 15.5% is the real rate, not the nominal rate. Therefore \[i=(1.155)(1.102)-1=1.27281-1=0.27281=27.281\%.\] **3. Judge the statement:** The nominal rate is about 27.28%, not 4.81%. Subtracting inflation from the given real rate would use the relation in the wrong direction. **Answer: B — Selected: False.** A: **Incorrect:** 4.81% is not the nominal rate implied by these real and inflation rates. B: **Correct:** Compounding real growth with inflation gives about 27.28%, so the statement is false.

**1. Define the graph:** A yield curve plots comparable bond yields against maturity. **2. Read a downward slope:** Longer maturities appear farther right and have lower yields. Thus long-term rates are below short-term rates. **3. Judge the statement:** Saying long-term rates are higher describes an upward slope, so the given statement reverses the correct relationship. **Answer: B — Selected: False.** A: **Incorrect:** Higher long-term rates do not describe a downward-sloping curve. B: **Correct:** A downward curve means lower long-term yields.

**1. Identify the depreciation:** A dollar becomes more expensive, rising from Rs 90 to Rs 95. Hence one rupee buys fewer dollars. **2. Link to goods:** Holding American dollar prices unchanged, a fixed rupee amount buys fewer American goods because it converts into fewer dollars. **3. Judge the whole statement:** Its depreciation claim is correct, but “buys more” is wrong. A statement containing that incorrect purchasing-power conclusion is false. **Answer: B — Selected: False.** A: **Incorrect:** The purchasing-power part is wrong even though the depreciation part is right. B: **Correct:** The rupee depreciates and buys fewer, rather than more, dollar-priced goods.

**1. Define a call:** Its holder has a right, rather than an obligation, to buy the underlying at a fixed strike price. **2. Define American exercise:** The holder may exercise on or before expiry, subject to the contract’s exercise rules. **3. Combine the definitions:** The statement correctly describes an American call. A European call has the same purchase right but can be exercised only at expiry. **Answer: A — Selected: True.** A: **Correct:** Both the purchase right and the American exercise timing are correct. B: **Incorrect:** The statement matches the definition of an American call.

**1. Define capital:** Bank capital represents the loss-absorbing funding cushion, with equity central to the simplified balance-sheet model. **2. Identify the relevant ratio:** A simplified capital ratio is equity/capital divided by assets. Regulatory capital adequacy often uses risk-weighted assets and specified eligible capital. **3. Judge the statement:** Liabilities divided by total assets measures the debt-funded share of assets, not a capital ratio under either interpretation. **Answer: B — Selected: False.** A: **Incorrect:** Liabilities are not the numerator of the stated capital-ratio definition. B: **Correct:** The proposed formula is a debt-to-assets ratio, so it is false.

**1. Explain capital requirements:** Requiring banks to hold adequate loss-absorbing capital helps them absorb unexpected losses and reduces incentives associated with extremely thin equity funding. **2. Explain asset restrictions:** Rules limiting risky or unsuitable asset exposures can reduce the probability or severity of bank distress. **3. Conclude:** Both are governance/regulatory safeguards against banking failure. They manage risk rather than eliminate it. **Answer: A — Selected: True.** A: **Correct:** Capital cushions and restrictions on asset risk are both banking-stability tools. B: **Incorrect:** The statement correctly identifies two safeguards.

**1. Write the short-put profit:** For premium p and strike K, \[\Pi=p-\max(K-S_T,0).\] The underlying stock price cannot fall below zero in the standard model. **2. Find the worst case:** At \(S_T=0\), the put writer must pay K, having collected p. **3. Calculate maximum loss:** The net loss is \(K-p\) per underlying unit, ignoring financing/costs. It is bounded, unlike the potential loss of an uncovered written call. **Answer: A — Selected: True.** A: **Correct:** The largest put obligation occurs at stock price zero and is K; subtracting the premium gives K-p. B: **Incorrect:** The stated finite maximum-loss expression is correct for a standard written put.

**1. Define put intrinsic value:** \(\max(K-S,0)\). A put is in-the-money only when the stock is below its strike. **2. Substitute:** With \(K=80\) and \(S=82\), intrinsic value is \(\max(-2,0)=0\). **3. Classify:** This put is out-of-the-money. A call with the same strike would be in-the-money, but that is a different contract. **Answer: B — Selected: False.** A: **Incorrect:** The stock price is above the put strike, so the put is not in-the-money. B: **Correct:** Its intrinsic value is zero and it is out-of-the-money.

**1. State the EMH idea:** Market prices reflect the information covered by the assumed efficiency form. An investor should not systematically earn abnormal risk-adjusted returns from information already reflected in prices. **2. Apply the comparison:** If the trader and the market share the same reflected information, merely analyzing it does not establish a persistent informational advantage. **3. Interpret the wording:** The statement expresses that intended information-efficiency principle. EMH does not rule out random outperformance, risk-related expected-return differences or every form of return predictability. “Available information” must be understood within the relevant form: public information for semi-strong efficiency, for example. **Answer: A — Selected: True.** A: **Correct:** Under the intended shared/reflected-information interpretation, this is the EMH implication. B: **Incorrect:** The statement is intended to express the absence of a systematic informational advantage over an efficient market.

**1. Identify the SML risk axis:** The Security Market Line relates expected return to beta, not standard deviation. **2. Calculate its slope:** \(E(r_M)-r_f=9\%-3\%=6\%\), or 0.06 per unit of beta. **3. Explain 0.5:** \((9\%-3\%)/12\%=0.5\) is the market Sharpe ratio and the capital-market-line slope when standard deviation is the horizontal axis. It is not the SML slope. **Answer: B — Selected: False.** A: **Incorrect:** 0.5 uses the wrong risk axis for the SML. B: **Correct:** The SML slope is the 6% market premium.

**1. State the stock-price assumption:** Standard Black-Scholes models the stock with geometric Brownian motion. **2. Describe the resulting distribution:** Conditional on today’s price, the future log price is normal. Exponentiating a normal quantity gives a lognormal stock price. **3. Conclude:** The statement is correct. The model does not assume that the stock-price level itself is normally distributed. **Answer: A — Selected: True.** A: **Correct:** Lognormal stock-price levels are the standard Black-Scholes assumption. B: **Incorrect:** The statement correctly distinguishes prices from normally distributed log changes.

**1. Define a long option position:** To be long an option means that the investor has bought/holds the option right. **2. Distinguish maturity:** The option may expire in days, months or years. “Long” in position terminology identifies the side of the contract, not a two-year minimum duration. **3. Contrast a short option:** The short side writes/sells the option and accepts the corresponding obligation. **Answer: B — Selected: False.** A: **Incorrect:** A long position is defined by being the buyer/holder, not by a two-year maturity threshold. B: **Correct:** Long means holding the option right, regardless of contract maturity.

**1. Recall the call payoff:** At expiry, \(\max(S_T-K,0)\) increases or remains unchanged as the stock price rises. **2. Use price sensitivity before expiry:** In standard non-dividend Black-Scholes, call delta is \(N(d_1)>0\). A higher stock price increases the value of the purchase right when other inputs are held constant. **3. Judge the statement:** It claims the opposite direction, so it is false. **Answer: B — Selected: False.** A: **Incorrect:** A standard call gains rather than loses value as its underlying stock price rises. B: **Correct:** The claimed negative relationship has the wrong sign.

**1. Define a long straddle:** Buy one call and one put on the same underlying with the same strike and expiration. **2. Explain why matching matters:** The combined expiry payoff is \(|S_T-K|\) only when the strikes and maturities match. Different strikes or dates produce different option combinations. **3. Judge the statement:** It specifies different strikes and different expirations, so it does not describe a long straddle. **Answer: B — Selected: False.** A: **Incorrect:** Different strikes and dates do not meet the straddle definition. B: **Correct:** A straddle requires the same strike and expiration.

**1. Locate the GMV point:** It is the least-risk point on the feasible minimum-variance boundary. **2. Compare branches:** The branch above it offers higher expected returns for a given standard deviation. A lower-branch portfolio is dominated by an upper-branch portfolio at equal risk. **3. Conclude:** The efficient frontier is the upper branch, not the portion below the GMV portfolio. **Answer: B — Selected: False.** A: **Incorrect:** The lower branch is inefficient because higher-return portfolios exist at the same risk. B: **Correct:** The statement chooses the wrong branch.

**1. Calculate exercise value:** The call allows purchase at Rs 64 when the stock is worth Rs 72. Its exercise payoff is \(72-64=8\) rupees. **2. Subtract the premium:** Net profit is \(8-5.50=2.50\) rupees. **3. Divide by the original investment:** \[\mathrm{HPR}=\frac{2.50}{5.50}=0.454545\approx45.45\%.\] This is the 22-day holding-period return, not an annualized return. **Answer: C — Selected: 45.45%.** A: **Incorrect:** 4.17% is not the option’s profit divided by its premium. B: **Incorrect:** 28.57% understates the calculated return. C: **Correct:** Rs 2.50 profit on Rs 5.50 invested gives 45.45%. D: **Incorrect:** 77.78% would require a different premium.

**1. Relate beta to correlation and volatility:** \[\beta=\rho_{iM}\frac{\sigma_i}{\sigma_M}.\] **2. Substitute:** \(\rho=0.5\), \(\sigma_i=18\%\), \(\sigma_M=15\%\). Thus \(\beta=0.5(18/15)=0.6\). **3. Interpret:** Despite a larger total volatility than the market, imperfect correlation yields a beta below one. Expected return inputs are not needed for this calculation. **Answer: A — Selected: 0.6.** A: **Correct:** 0.5(18/15)=0.6. B: **Incorrect:** Beta is below one for these inputs. C: **Incorrect:** 1.2 is the volatility ratio before multiplying by correlation. D: **Incorrect:** 1.5 overstates the systematic-risk exposure.

**1. Specify the appreciation quote:** Use foreign-currency units per domestic-currency unit. Under the expected interest-parity relation in the exercise, gross domestic-currency appreciation is \((1+i_f)/(1+i_d)\). **2. Calculate:** \[a=\frac{1.08}{1.05}-1=\frac{0.03}{1.05}=0.028571\approx2.86\%.\] **3. Interpret:** The lower-interest domestic currency is expected to appreciate under this parity assumption. Reversing the exchange-rate quote changes the direction and percentage; actual currency returns are not guaranteed by the model. **Answer: C — Selected: 2.86%.** A: **Incorrect:** -4.81% has both an incorrect magnitude and the wrong sign under this convention. B: **Incorrect:** -2.86% reverses the direction of domestic-currency appreciation. C: **Correct:** The specified parity calculation gives +2.86%. D: **Incorrect:** 4.81% does not use the stated 5% and 8% rates.

**1. State buyer profit:** \(\Pi=\max(S_T-78,0)-4\). **2. Find break-even:** \(78+4=82\) rupees. Profit is positive only above Rs 82. **3. Evaluate:** Rs 90 gives payoff 12 and net profit 8. Rs 80 gives payoff 2 but a net loss of 2. Rs 60 and Rs 70 give zero payoff and a loss of the full premium. **Answer: D — Selected: Rs 90.** A: **Incorrect:** At Rs 60 the buyer loses the Rs 4 premium. B: **Incorrect:** At Rs 70 the call remains out-of-the-money. C: **Incorrect:** At Rs 80 the Rs 2 payoff does not cover the Rs 4 premium. D: **Correct:** Rs 90 exceeds the Rs 82 break-even and yields an Rs 8 profit.

**1. Use call delta:** For a standard non-dividend Black-Scholes call, \(\Delta_C=N(d_1)\). **2. Substitute:** The supplied \(N(d_1)=0.5\) gives delta 0.5. Hence a Rs 1 increase in the stock implies \(\Delta C\approx0.5(1)=0.50\) rupees. **3. Interpret the approximation:** Delta is the local price sensitivity; a finite move can also involve curvature. The supplied d2 value is not needed for this sensitivity. **Data note:** The printed \(N(d_2)=0.6\) exceeds \(N(d_1)=0.5\), which is inconsistent with standard positive-volatility Black-Scholes. The intended answer uses the given d1 value only. **Answer: B — Selected: The call option price increases by Rs 0.5.** A: **Incorrect:** The given call delta is 0.5 rather than 1. B: **Correct:** Delta 0.5 predicts an approximate Rs 0.50 increase. C: **Incorrect:** A call has positive stock-price sensitivity here. D: **Incorrect:** A negative change has the wrong sign.

**1. Use weighted-average beta:** The exercise assigns divisional asset weights of 0.50, 0.20 and 0.30. **2. Compute contributions:** Sales contributes \(0.50(2.1)=1.05\), accounting \(0.20(0.7)=0.14\), logistics \(0.30(1.4)=0.42\). **3. Add:** \(\beta=1.05+0.14+0.42=1.61\). The company beta uses the supplied asset weights, rather than a simple unweighted average. **Answer: C — Selected: 1.61.** A: **Incorrect:** 1.15 is below the weighted sum. B: **Incorrect:** 1.41 omits part of the combined exposure. C: **Correct:** The three weighted contributions total 1.61. D: **Incorrect:** 1.81 exceeds the calculated beta.

**1. Find risk-neutral expected stock value:** The three-month rate is 4%, so \(E^Q[S_T]=25(1.04)=26\) rupees. **2. Solve for q:** \(30q+20(1-q)=26\), giving \(10q=6\). **3. Conclude:** \(q=0.60=60\%\). The risk-neutral probability is a pricing weight; it need not be the real probability of a price increase. **Answer: B — Selected: 60.0%.** A: **Incorrect:** 78.6% produces an expected price above Rs 26. B: **Correct:** 60% gives 0.6(30)+0.4(20)=26. C: **Incorrect:** 48.9% does not satisfy the required risk-neutral mean. D: **Incorrect:** 43.1% gives a mean below Rs 26.

**1. Compute the CAPM-required return:** \(4\%+1.6(12\%-4\%)=4\%+12.8\%=16.8\%\). **2. Define alpha:** It is expected return minus the CAPM benchmark for the stock’s beta. **3. Subtract:** \(\alpha=18\%-16.8\%=1.2\%\). This is a positive 1.2-percentage-point excess relative to the model benchmark. **Answer: C — Selected: 1.2%.** A: **Incorrect:** -2.4% has the wrong sign and magnitude. B: **Incorrect:** -1.2% reverses the alpha subtraction. C: **Correct:** 18%-16.8%=+1.2%. D: **Incorrect:** 2.4% is twice the calculated alpha.

**1. Rearrange Sharpe ratio:** \(S=(\mu-r_f)/\sigma\) implies \(\sigma=(\mu-r_f)/S\). **2. Calculate excess return:** \(18\%-8\%=10\%\). **3. Divide:** \(\sigma=10\%/0.75=13.3333\%\), rounded to 13.33%. The risk-free rate must be subtracted before dividing by the ratio. **Answer: A — Selected: 13.33%.** A: **Correct:** 13.33% gives the required Sharpe ratio of 0.75. B: **Incorrect:** 11.22% would imply a Sharpe ratio higher than 0.75. C: **Incorrect:** 9.35% is too small for a 10% premium and Sharpe ratio 0.75. D: **Incorrect:** 8.28% would overstate reward per unit risk.

**1. Apply two-factor APT:** \(E(r)=r_f+\beta_W\lambda_W+\beta_C\lambda_C\), where each lambda is a factor risk premium. **2. Substitute:** \(E(r)=4\%+1.2(4\%)+1.6(6\%)\). **3. Add contributions:** \(4\%+4.8\%+9.6\%=18.4\%\). The factor premiums are already excess returns; do not subtract the risk-free rate again. **Answer: D — Selected: 18.4%.** A: **Incorrect:** 7.2% omits much of the required factor compensation. B: **Incorrect:** 9.5% is below the stated weighted factor contributions plus the risk-free rate. C: **Incorrect:** 12.4% does not correctly include both factor terms. D: **Correct:** 4%+4.8%+9.6%=18.4%.

**1. Discount each dated cash flow:** The promised payments are Rs 2,000 in year 1, Rs 2,500 in year 2 and Rs 3,000 in year 3. \[PV=\frac{2000}{1.08}+\frac{2500}{1.08^2}+\frac{3000}{1.08^3}.\] **2. Evaluate:** The three present values are approximately Rs 1,851.85, Rs 2,143.35 and Rs 2,381.50. **3. Add and round:** Total value is Rs 6,376.6956, rounded to Rs 6,377. Later payments are discounted over more years. **Answer: 6377.**

**1. State European put-call parity:** \(C=P+S_0-Ke^{-rT}\) for matching options on a non-dividend-paying stock. **2. Find the strike’s present value:** \(450e^{-0.10(0.5)}=450e^{-0.05}=428.0532\) rupees. **3. Calculate call price:** \(C=30+430-428.0532=31.9468\), rounded to Rs 32. The half-year maturity must be paired with the annual continuously compounded rate. **Answer: 32.**

**1. Compute option payoffs:** The call pays \(75-70=5\) in the up state and zero in the down state at 55. **2. Compute delta:** \[\Delta=\frac{5-0}{75-55}=0.25.\] One option therefore provides the two-state stock exposure of one quarter of a share. **3. Hedge the long shares:** Short \(50/0.25=200\) calls against 50 purchased shares. The terminal portfolio is \(50(75)-200(5)=2750\) in the up state and \(50(55)=2750\) in the down state. **Price note:** The stated Rs 4 option quote differs from the model’s zero-rate value \(0.25(5)=1.25\). That pricing inconsistency does not alter the terminal-payoff hedge quantity. **Answer: 200.**

**1. Use the Gordon Growth model:** \(P_0=D_1/(k-g)\), with next year’s dividend \(D_1=20\), current price 400 and growth \(g=0.02\). **2. Rearrange:** \(k=D_1/P_0+g\). **3. Substitute:** \(k=20/400+0.02=0.05+0.02=0.07\). Thus the cost of capital is 7% and the requested x is 7. The required return exceeds the growth rate, as the model requires. **Answer: 7.**

**1. Choose the stated annual contribution convention:** Treat Rs 100 as paid at each year-end for 30 years. This is an ordinary annuity earning 7% annually. **2. Accumulate the payments:** \[FV=100\frac{(1.07)^{30}-1}{0.07}.\] The expression sums the different numbers of years for which each contribution earns interest. **3. Calculate and round:** \((1.07)^{30}\approx7.612255\), giving \(FV=9{,}446.0786\). The retirement account contains Rs 9,446. Beginning-of-year contributions would give an annuity-due value and are a different timing assumption. **Answer: 9446.**

**1. Find call payoffs:** With strike Rs 45, the up-state stock price Rs 50 gives payoff 5; the down-state price Rs 35 gives zero. **2. Calculate the pricing probability:** \[q=\frac{40(1.05)-35}{50-35}=\frac{7}{15}.\] **3. Price 100 calls:** One call costs \((7/15)(5)/1.05=2.222222\) rupees. One hundred cost Rs 222.2222, rounded to Rs 222. The 5% rate already covers the six-month period. **Answer: 222.**

**1. Calculate the initial premium:** Two calls at Rs 4 and one put at Rs 6 cost \(2(4)+6=14\) rupees. **2. Calculate expiry payoff:** At stock price 96 with strike 80, each call pays 16 and the put pays zero. Total payoff is \(2(16)=32\). **3. Subtract cost:** Net profit is \(32-14=18\) rupees. No shares were bought, so the initial share price does not enter the strategy’s cash outlay. This uses the usual premium-subtracted profit without financing costs. **Answer: 18.**

**1. Express portfolio moments:** Let w be the risky allocation. Its expected return is \(\mu=0.04+0.08w\); its variance is \(\sigma^2=(0.18w)^2=0.0324w^2\). **2. Maximize the source utility:** With \(U=\mu-5\sigma^2\), \[U(w)=0.04+0.08w-0.162w^2.\] The derivative is \(0.08-0.324w\). Setting it to zero gives \(w=0.08/0.324=0.2469136\); the negative second derivative confirms a maximum. **3. Calculate final wealth:** Expected return is \(0.04+0.08(0.2469136)=0.0597531\). Thus expected wealth is \(100(1.0597531)=105.97531\), rounded to 106 units. **Answer: 106.**

**1. Add premiums:** The call costs Rs 8 and two puts cost \(2(4)=8\), so total initial cost is Rs 16. **2. Minimize expiry payoff:** \[V_T=\max(S_T-65,0)+2\max(65-S_T,0).\] The payoff is nonnegative everywhere and reaches zero when \(S_T=65\). **3. Find maximum loss:** Under the usual payoff-minus-premium convention, the worst outcome is loss of the full Rs 16. **Convention note:** If loss were measured at maturity including the premium’s foregone 4% return, the economic loss would be \(16(1.04)=16.64\), rounded to 17. The source key uses the unfinanced premium-loss convention. **Answer: 16.**

**1. Calculate the CAPM-required return:** \[k=0.04+1.5(0.08-0.04)=0.04+0.06=0.10.\] **2. Discount the one-year payoff:** \(PV=4000/1.10=3{,}636.3636\) rupees. **3. Round:** The price is Rs 3,636 to the nearest integer. The 1.5 beta applies to the 4% market premium. **Answer: 3636.**