Corporate Finance · Quiz 1 · Jan 2025

**1. Given:** Money triples in \(n=10\) years, annual compounding. **2. Formula:** \((1+r)^{10}=3\). **3. Solve:** \[1+r=3^{1/10}\approx1.1161\Rightarrow r\approx11.61\%\] Answer: C — 11.61%. A: **Incorrect:** 5.42% gives about 1.69× in 10 years, not 3×. B: **Incorrect:** 7.60% gives about 2.08× in 10 years, not 3×. C: **Correct:** \(3^{1/10}-1\approx0.1161\). D: **Incorrect:** 20% gives about 6.19× in 10 years, which is too much.

**1. Given:** 2,000 in year 2, 4,000 in year 4, 6,000 in year 6, \(r=10\%\). **2. Formula:** \(PV=\sum \dfrac{C_t}{(1.1)^t}\). **3. Substitute:** \[PV=\frac{2000}{1.21}+\frac{4000}{1.4641}+\frac{6000}{1.7716}=1652.89+2732.05+3386.84\] **4. Add:** \(PV\approx7{,}772\). Answer: C — Rs 7,772. A: **Incorrect:** 12,000 is the undiscounted total. B: **Incorrect:** 8,196 is not the sum of the correct discounted values. C: **Correct:** The discounted values add up to about 7,772. D: **Incorrect:** 6,000 is only the last payment, undiscounted.

**1. Given:** \(P=500\), \(r=9\%\) continuous, \(t=3\). **2. Formula:** \(A=Pe^{rt}\). **3. Substitute:** \[A=500\,e^{0.27}=500\times1.3100\approx655\] Answer: D — Rs 655. A: **Incorrect:** 382 is below 500; money cannot fall at a positive rate. B: **Incorrect:** 500 is the starting value and ignores growth. C: **Incorrect:** 635 is not 500 × \(e^{0.27}\). D: **Correct:** \(500e^{0.27}\approx655\).

**1. Given:** \(C_1=800\), \(g=2\%\), \(r=10\%\). **2. Growing perpetuity formula:** \(PV=\dfrac{C_1}{r-g}\). **3. Substitute:** \[PV=\frac{800}{0.10-0.02}=\frac{800}{0.08}=10{,}000\] Answer: B — Rs 10,000. A: **Incorrect:** 40,000 is not 800 divided by (r − g). B: **Correct:** 800/0.08 = 10,000. C: **Incorrect:** 8,000 is 800/0.10, which ignores growth. D: **Incorrect:** 4,000 is not the result of the formula.

**1. Given:** Cost 100, value 50,000, \(n=40\) years. **2. Formula:** \(100(1+r)^{40}=50000\Rightarrow(1+r)^{40}=500\). **3. Solve:** \[1+r=500^{1/40}=e^{6.2146/40}=e^{0.15537}\approx1.1681\] \[r\approx16.81\%\] Answer: C — 16.81%. A: **Incorrect:** 8.32% would give only about 24× in 40 years. B: **Incorrect:** 12.5% would give about 112× in 40 years. C: **Correct:** \(500^{1/40}-1\approx0.1681\). D: **Incorrect:** 50% is far too high; it would give a huge multiple.

**1. Given:** \(D_1=50\), \(g=4\%\), \(r=10\%\), market price \(=800\). **2. Gordon growth model:** \(P_0=\dfrac{D_1}{r-g}=\dfrac{50}{0.06}\approx833.33\). **3. Compare:** Fair value \(833.33>800\), so the stock is underpriced. An investor should buy. Answer: A — The LIC stock is underpriced, and an investor should buy LIC shares. A: **Correct:** Fair value 833.33 is above the price 800, so the stock is underpriced and should be bought. B: **Incorrect:** The stock is underpriced, not overpriced. C: **Incorrect:** The stock is underpriced, so selling is wrong. D: **Incorrect:** The stock is underpriced, not overpriced.

**1. Given:** Cost 6,000, payoff 7,500 after 2 years. **2. IRR condition:** \(6000(1+r)^2=7500\). **3. Solve:** \[(1+r)^2=1.25\Rightarrow1+r=\sqrt{1.25}=1.1180\Rightarrow r=11.80\%\] Answer: C — 11.80%. A: **Incorrect:** 25% is the total gain over 2 years, not the annual rate. B: **Incorrect:** 17.47% is not the root of 1.25. C: **Correct:** \(\sqrt{1.25}-1\approx0.1180\). D: **Incorrect:** 8.64% is too low to grow 6,000 to 7,500 in 2 years.

**1. Given:** Cost 500; payoffs 250 at years 2, 4, 6; \(r=10\%\). **2. PV of payoffs:** \[\frac{250}{1.21}+\frac{250}{1.4641}+\frac{250}{1.7716}=206.61+170.75+141.12=518.48\] **3. Profitability index:** \(PI=\dfrac{518.48}{500}\approx1.04\). Answer: C — 1.04. A: **Incorrect:** 18.48 is the NPV figure scaled wrongly; PI is PV divided by cost. B: **Incorrect:** 4.68 is not PV divided by cost. C: **Correct:** \(518.48/500\approx1.04\). D: **Incorrect:** 0.80 would be below 1, but the PV exceeds the cost.

**1. Concept:** Payback period is the time needed for cumulative cash inflows to recover the initial cost of 5,000. **2. Project 1:** 200 per year, so it needs \(5000/200=25\) years. **3. Project 2:** Pays 8,000 only after 5 years, so payback is 5 years. **4. Project 3:** After year 1: 2,000. After year 2: \(2000+4000=6000\ge5000\). Payback is under 2 years. **5. Conclude:** Project 3 has the shortest payback. (Discounting at 4% does not change this: \(1923+3698=5621>5000\) by year 2.) Answer: D — Project 3. A: **Incorrect:** The payback periods are 25, 5 and under 2 years, so they are not equal. B: **Incorrect:** Project 1 takes 25 years, the longest. C: **Incorrect:** Project 2 takes 5 years, longer than Project 3. D: **Correct:** Project 3 recovers 5,000 in under 2 years.

**1. Given:** Total 2-year return \(30\%\), first-year return \(12\%\). **2. Formula:** \((1.12)(1+r_2)=1.30\). **3. Solve:** \[1+r_2=\frac{1.30}{1.12}=1.1607\Rightarrow r_2\approx16\%\] Answer: A — 16%. A: **Correct:** 1.30/1.12 − 1 = 16.07%, which rounds to 16%. B: **Incorrect:** 18% would give a total of 32.2%. C: **Incorrect:** 20% would give a total of 34.4%. D: **Incorrect:** 30% in year two would give a total of 45.6%.

**1. Given:** 500 grows to 800 in 8 years. **2. Formula:** \((1+r)^8=\dfrac{800}{500}=1.6\). **3. Solve:** \[1+r=1.6^{1/8}=e^{0.4700/8}\approx1.0605\Rightarrow r\approx6.05\%\] Answer: D — 6.05%. A: **Incorrect:** 60% is the total gain over 8 years, not the annual rate. B: **Incorrect:** 16% per year would give about 3.4× in 8 years. C: **Incorrect:** 8.17% would give about 1.88× in 8 years. D: **Correct:** \(1.6^{1/8}-1\approx0.0605\).

**1. Maturity:** The last payment is at year 5, so maturity \(=5\) years. **2. Duration (weighted average time):** Total payments \(=1000\). Weights are \(0.4\) at year 3 and \(0.6\) at year 5. **3. Calculate:** \[D=0.4(3)+0.6(5)=1.2+3.0=4.2\text{ years}\] Answer: A — 5 years, 4.2 years. A: **Correct:** Maturity is 5 years and duration is 4.2 years. B: **Incorrect:** The order is reversed: maturity cannot be shorter than duration. C: **Incorrect:** Duration equals maturity only for a single payment at the end. D: **Incorrect:** 3 years is the time of the first payment, not the weighted average.

**1. Given:** Basket: 1 clothes + 3 food. Prices: 2017 (400, 30), 2018 (380, 50). **2. Basket cost:** - 2017: \(400+3(30)=490\) - 2018: \(380+3(50)=530\) **3. CPI and inflation:** With base 2017, \(CPI_{2018}=\dfrac{530}{490}\times100=108.16\). \[\text{Inflation}=\frac{530-490}{490}\times100=8.16\%\] Answer: A — 8.16%. A: **Correct:** (530 − 490)/490 = 8.16%. B: **Incorrect:** 22.45% is not the change in the basket cost. C: **Incorrect:** The basket cost rose, so inflation is positive. D: **Incorrect:** The basket cost rose, so inflation is positive and not 22.45% in magnitude.

**1. Concept:** The intertemporal budget constraint is \(c_2=y_2+(1+r)(y_1-c_1)\). With prices equal to 1, the slope in the \((c_1,c_2)\) plane is \(-(1+r)\). **2. Substitute:** \(-(1+0.25)=-1.25\). Answer: D — -1.25. A: **Incorrect:** The slope is negative because more consumption today means less tomorrow. B: **Incorrect:** 0.80 is \(1/(1+r)\), not the slope. C: **Incorrect:** -0.80 is \(-1/(1+r)\), not the slope. D: **Correct:** The slope is \(-(1+r)=-1.25\).

**1. Given:** Nominal rate \(i=12\%\), real rate \(r=8\%\). **2. Fisher equation (exact):** \(1+i=(1+r)(1+\pi)\). **3. Solve:** \[1+\pi=\frac{1.12}{1.08}=1.0370\Rightarrow\pi\approx3.70\%\] Answer: A — 3.70%. A: **Correct:** \(1.12/1.08-1\approx3.70\%\). B: **Incorrect:** 5.42% is not given by the Fisher equation here. C: **Incorrect:** 7.60% is not given by the Fisher equation here. D: **Incorrect:** 11.61% is not given by the Fisher equation here.

**1. Given:** Two blue bonds, each default probability 15%, perfectly correlated (\(\gamma=1\)). **2. Junior bond:** It gets 0 if *any* blue bond defaults. So the junior bond defaults when at least one blue bond defaults. **3. Calculate:** With perfect correlation, both bonds default together or neither does. So \(P(\text{at least one default})=P(\text{one default})=15\%\). Answer: C — 15%. A: **Incorrect:** 30% would be the sum for independent-style addition, but perfect correlation does not add the risks. B: **Incorrect:** 22.5% is not the probability under perfect correlation. C: **Correct:** Perfect correlation makes the two defaults the same event, so the probability is 15%. D: **Incorrect:** 2.25% is \(0.15^2\), the independent chance of both defaulting.

**1. Concept:** An inverted yield curve means short-term rates are higher than long-term rates. **2. Link to recession:** It is a well-known warning sign of an impending recession. **3. Conclude:** Inverted yield curve. Answer: B — Inverted yield curve. A: **Incorrect:** An upward-sloping curve is the normal curve. B: **Correct:** An inverted curve is the classic recession signal. C: **Incorrect:** A humped curve is not the standard recession signal. D: **Incorrect:** A flat curve may be a warning, but the classic signal is inversion.

**1. Given:** \(P=5{,}00{,}000\), \(r=2\%\) per month, \(n=120\) months. **2. Formula:** \(EMI=\dfrac{P\,r}{1-(1+r)^{-n}}\). **3. Substitute:** \[(1.02)^{-120}\approx0.0930\] \[EMI=\frac{500000\times0.02}{1-0.0930}=\frac{10000}{0.9070}\approx11{,}024\] Answer: D — Rs 11,024. A: **Incorrect:** 4,167 is just principal divided by 120 months, which ignores interest. B: **Incorrect:** 5,000 is only the first month's interest. C: **Incorrect:** 9,462 is below the EMI formula result. D: **Correct:** \(10000/0.9070\approx11{,}024\).

**1. Concept:** The internal rate of return (IRR) is the discount rate at which the NPV of the cash flows equals zero. **2. Check options:** IRR is not where NPV is maximised or minimised, and it is not always above the cost of capital (a bad project has IRR below it). **3. Conclude:** The NPV is zero at the IRR. Answer: B — The IRR is the rate at which the NPV of the cashflows is zero. A: **Incorrect:** NPV is not maximised at the IRR; it is zero there. B: **Correct:** IRR is defined by NPV = 0. C: **Incorrect:** NPV is not minimised at the IRR. D: **Incorrect:** IRR can be below the cost of capital, so 'always greater' is false.

**1. Given:** Deposit \(C=100\) at the end of each day, \(r=3.65\%\), daily rate \(i=0.0365/365=0.0001\), \(n=730\) days. **2. Future value of an ordinary annuity:** \(FV=C\dfrac{(1+i)^n-1}{i}\). **3. Substitute:** \[(1.0001)^{730}\approx1.07574\] \[FV=100\times\frac{0.07574}{0.0001}\approx75{,}727\] Answer: B — Rs 75,727. A: **Incorrect:** 73,000 is just the total deposits, with no interest. B: **Correct:** The annuity formula gives about 75,727. C: **Incorrect:** 81,234 is too high for such a low rate. D: **Incorrect:** 85,000 is too high for such a low rate.

**1. Formula:** GDP deflator \(=\dfrac{\text{Nominal GDP}}{\text{Real GDP}}\times100\). **2. Rearrange:** Real GDP \(=\dfrac{14000}{112}\times100=12{,}500\). Answer: C — 12,500 units. A: **Incorrect:** 15,680 comes from multiplying instead of dividing. B: **Incorrect:** 14,000 would need a deflator of 100. C: **Correct:** \(14000/1.12=12{,}500\). D: **Incorrect:** 10,000 would need a deflator of 140.

**1. Given:** 10,000 grows to 20,000 in 5 years. **2. Formula:** \((1+r)^5=2\). **3. Solve:** \[1+r=2^{1/5}\approx1.1487\Rightarrow r\approx14.87\%\] Answer: A — 14.87%. A: **Correct:** \(2^{0.2}-1\approx0.1487\). B: **Incorrect:** 11.61% is the rate for tripling in 10 years. C: **Incorrect:** 7.18% is the rate for doubling in 10 years. D: **Incorrect:** 20% is the average simple gain per year (100%/5), not the compound rate.

**1. Option A:** Stocks pay variable dividends, so they are not fixed income securities. False. **2. Option B:** A bond's price falls when market interest rates rise. The statement is not correct in the usual sense. False. **3. Option C:** Shares have no maturity. False. **4. Option D:** A zero-coupon bond pays only at maturity, with no interim coupons. True. **Convention note:** Option B is read in the usual course sense: when the interest rate (yield) rises, the bond price falls. If 'interest rate offered' meant the coupon rate, B could look true, but D is clearly true and matches the source key. Answer: D — A zero-coupon bond pays only at maturity. There are no interim payments. A: **Incorrect:** Stocks do not give fixed payments, so they are not fixed income. B: **Incorrect:** Bond prices fall, not rise, when the prevailing interest rate (yield) rises. C: **Incorrect:** Shares have no fixed maturity. D: **Correct:** This is the definition of a zero-coupon bond.

**1. Given:** \(r=5\%\). Compare NPVs. **2. Project A:** \[NPV_A=-12000+\frac{5000}{1.05}+\frac{10000}{1.05^2}=-12000+4761.90+9070.29\approx1{,}832\] **3. Project B:** \[NPV_B=-10000+\frac{5000}{1.05}+\frac{4000}{1.05^2}+\frac{3000}{1.05^3}+\frac{2000}{1.05^4}\approx2{,}627\] **4. Conclude:** \(NPV_B>NPV_A>0\), so prefer Project B. Answer: A — Sahitya Inc. should prefer Project B as it has a higher net present value than Project A. A: **Correct:** NPV of B (about 2,627) is higher than NPV of A (about 1,832). B: **Incorrect:** A has the lower NPV. C: **Incorrect:** The NPVs are different. D: **Incorrect:** Both NPVs are positive.

**1. Concept:** Credit rating agencies rate the creditworthiness of borrowers: Standard & Poor's, Moody's and Fitch. **2. Apply:** Standard Chartered is a bank, not a rating agency. Answer: B — Standard Chartered. A: **Incorrect:** S&P is a major credit rating agency. B: **Correct:** Standard Chartered is a bank, not a rating agency. C: **Incorrect:** Moody's is a major credit rating agency. D: **Incorrect:** Fitch is a major credit rating agency.