Corporate Finance · Quiz 1 · Jan 2026

**1. Given:** \(\text{Rs }10{,}000\) triples in 12 years, so the growth factor is 3. **2. Formula:** \((1+r)^{12}=3\). **3. Solve:** \[ 1+r=3^{1/12}=e^{\ln 3/12}\approx e^{0.0916}\approx1.0959\;\Rightarrow\;r\approx9.59\% \] Answer: B — 9.59%. A: **Incorrect:** At 6.12%, 12 years gives a factor of only about 2.05. B: **Correct:** \(3^{1/12}-1=9.59\%\). C: **Incorrect:** At 11.60%, 12 years gives a factor of about 3.8. D: **Incorrect:** At 13.05%, 12 years gives a factor of about 4.4.

**1. Concept:** Real GDP \(=\dfrac{\text{Nominal GDP}}{\text{GDP deflator}}\times100\). **2. Substitute:** \[ \text{Real GDP}=\frac{24000}{120}\times100=20000 \] Answer: C — 20,000 units. A: **Incorrect:** This multiplies by 1.2 instead of dividing. B: **Incorrect:** This is not the result of dividing by 1.2. C: **Correct:** \(24000/1.2=20000\). D: **Incorrect:** This does not match the calculation.

**1. Formula:** \(PI=\dfrac{PV\text{ of future cash flows}}{\text{Initial investment}}\). **2. Present value at 10%:** \[ PV=\frac{3000}{1.1}+\frac{3000}{1.1^2}=2727.27+2479.34=5206.61 \] **3. Calculate:** \[ PI=\frac{5206.61}{5000}=1.04 \] Answer: A — 1.04. A: **Correct:** \(5206.61/5000\approx1.04\). B: **Incorrect:** PI below 1 would mean NPV is negative, but NPV here is +206.61. C: **Incorrect:** This is too high for these cash flows. D: **Incorrect:** This is too high for these cash flows.

**1. Gordon Growth Model:** \(P_0=\dfrac{D_1}{r-g}\). **2. Substitute:** \(500=\dfrac{25}{0.12-g}\). **3. Solve:** \[ 0.12-g=\frac{25}{500}=0.05\;\Rightarrow\;g=0.07=7\% \] Answer: C — 7%. A: **Incorrect:** \(g=5\%\) would give \(P_0=25/0.07\approx357\). B: **Incorrect:** \(g=6\%\) would give \(P_0=25/0.06\approx417\). C: **Correct:** \(g=7\%\) gives \(P_0=25/0.05=500\). D: **Incorrect:** \(g=8\%\) would give \(P_0=25/0.04=625\).

**1. Formula:** For continuous compounding, \(A=Pe^{rt}\). **2. Substitute:** \(P=2000\), \(r=0.06\), \(t=5\): \[ A=2000e^{0.3}=2000\times1.34986\approx2700 \] Answer: B — Rs 2,700. A: **Incorrect:** This is too low for continuous compounding at 6% over 5 years. B: **Correct:** \(2000e^{0.3}\approx2700\). C: **Incorrect:** This is below the true value. D: **Incorrect:** This is too high.

**1. Concept:** The exact (Fisher) real rate is \(\dfrac{1+i}{1+\pi}-1\). **2. Substitute:** \(i=10\%\), \(\pi=4\%\): \[ \frac{1.10}{1.04}-1=0.0577=5.77\% \] Answer: B — 5.77%. A: **Incorrect:** This is not the result of the Fisher formula. B: **Correct:** \(1.10/1.04-1=5.77\%\). C: **Incorrect:** This adds the rates instead of subtracting. D: **Incorrect:** This is not the result of the formula.

**1. Concept:** The yield curve plots interest rates (yields) against **time to maturity**, not against default risk. **2. Check each statement:** - An inverted curve often signals recession: true. - A normal curve slopes upward: true. - Yield vs default risk: false, that is a credit spread, not the yield curve. - Yield vs time to maturity: true. **3. Conclude:** The question asks for the FALSE statement, so choose the one about default risk. Answer: C — The yield curve plots the relationship between interest rates and default risk. A: **Incorrect:** True: an inverted curve is often seen as a recession predictor. B: **Incorrect:** True: a normal yield curve slopes upward. C: **Correct:** False: the yield curve is about maturity, not default risk, so this is the one to select. D: **Incorrect:** True: this is the definition of the yield curve.

**1. Formula:** \(EMI=\dfrac{P\,r}{1-(1+r)^{-n}}\). **2. Substitute:** \(P=200000\), \(r=0.01\), \(n=24\): \[ EMI=\frac{2000}{1-1.01^{-24}}=\frac{2000}{1-0.78757}=\frac{2000}{0.21243}\approx9415 \] Answer: B — Rs 9,415. A: **Incorrect:** This is \(200000/24\), which ignores interest. B: **Correct:** The annuity formula gives about Rs 9,415. C: **Incorrect:** This is above the correct EMI. D: **Incorrect:** This is above the correct EMI.

**1. Project A:** A perpetuity of Rs 500 starting next year: \[ PV_A=\frac{500}{0.10}=5000 \] **2. Project B:** Rs 1,000 forever, first payment at year 10. The value one year before the first payment (year 9) is \(\frac{1000}{0.10}=10000\). Discount to today: \[ PV_B=\frac{10000}{1.1^{9}}\approx4241 \] **3. Compare:** \(5000>4241\). Answer: A — Project A. A: **Correct:** PV of A is Rs 5,000, higher than B. B: **Incorrect:** PV of B is about Rs 4,241, which is lower than A. C: **Incorrect:** The two PVs are not equal. D: **Incorrect:** Both PVs can be calculated.

**1. Concept:** Duration is the weighted average time of the cash flows. The question gives no yield, so the weights are taken from the cash amounts. **2. Weights:** Total cash \(=500+1500=2000\). Weights: \(0.25\) for year 2 and \(0.75\) for year 4. **3. Calculate:** \[ D=0.25\times2+0.75\times4=0.5+3=3.5\text{ years} \] Answer: B — 3.5 years. **Convention note:** No yield is given, so the cash flows are not discounted. With a positive discount rate, the later payment would get less weight and the duration would be slightly lower than 3.5. A: **Incorrect:** This is the simple midpoint of years 2 and 4 if weights were equal; it ignores the cash amounts. B: **Correct:** Cash-weighted average time is \(3.5\) years. C: **Incorrect:** 4 years is only the maturity of the last payment. D: **Incorrect:** 2.5 years gives too much weight to the early payment.

**1. Basket cost, base year (2023):** \(2\times10+4\times5=20+20=40\). **2. Basket cost, 2024:** \(2\times12+4\times6=24+24=48\). **3. Inflation:** \[ \frac{48-40}{40}\times100=20\% \] Answer: C — 20%. A: **Incorrect:** A 10% rise would make the basket cost 44. B: **Incorrect:** A 15% rise would make the basket cost 46. C: **Correct:** \((48-40)/40=20\%\). D: **Incorrect:** A 25% rise would make the basket cost 50.

**1. Set up:** IRR is the rate at which NPV is zero: \[ -10000+\frac{7000}{1+r}+\frac{6000}{(1+r)^2}=0 \] **2. Test \(r=20\%\):** \[ \frac{7000}{1.2}+\frac{6000}{1.44}=5833.33+4166.67=10000 \] NPV \(=0\). **3. Conclude:** The IRR is 20%. Answer: D — 20%. A: **Incorrect:** At 8% the PV is about 11,589, so NPV is positive. B: **Incorrect:** At 10% the PV is about 10,785, so NPV is positive. C: **Incorrect:** At 15% the PV is about 10,624, still above 10,000. D: **Correct:** At 20% the PV equals exactly 10,000.

**1. Formula:** \((1+r)^n=2\), so \(n=\dfrac{\ln 2}{\ln(1+r)}\). **2. Substitute \(r=8\%\):** \[ n=\frac{0.6931}{0.0770}\approx9.006\text{ years} \] (Rule of 72: \(72/8=9\).) Answer: B — 9 years. A: **Incorrect:** 7 years gives a factor of only about 1.71. B: **Correct:** About 9 years doubles the money. C: **Incorrect:** 11 years gives a factor of about 2.33. D: **Incorrect:** 13 years gives a factor of about 2.72.

**1. Understand:** Deposits of Rs 50 are made at the end of each day, so this is an ordinary annuity. The daily rate is \(i=\dfrac{0.073}{365}\) and there are \(n=365\) deposits. **2. Future value of an annuity:** \[ FV=50\times\frac{(1+i)^{n}-1}{i}=50\times\frac{(1+0.073/365)^{365}-1}{0.073/365} \] **3. Conclude:** The first option is this formula. Answer: A — \(50\times\dfrac{(1+0.073/365)^{365}-1}{0.073/365}\). A: **Correct:** This is the future value of an ordinary annuity with a daily rate. B: **Incorrect:** This treats Rs 50 as a single deposit growing at 7.3% for 365 years, which is wrong. C: **Incorrect:** This ignores compounding and the daily rate. D: **Incorrect:** This is the present value of an annuity, not the balance after 1 year.

**1. Concept:** Maximum Period 1 consumption means borrowing against all of Period 2 income. Period 2 income is brought to Period 1 by discounting at 20%. **2. Calculate:** \[ C_1^{max}=50000+\frac{60000}{1.2}=50000+50000=100000 \] Answer: B — Rs 1,00,000. A: **Incorrect:** This does not discount Period 2 income (50,000 + 60,000). B: **Correct:** \(50000+60000/1.2=100000\). C: **Incorrect:** This is not the result of discounting at 20%. D: **Incorrect:** This is only Period 1 income, with no borrowing.

**1. Concept:** Payback period is the time until cumulative cash flow becomes zero. The initial investment is Rs 10,000. **2. Cumulative inflows:** - Year 1: 500 - Year 2: 1,500 - Year 3: 3,000 - Year 4: 5,000 - Year 5: 7,500 - Year 6: 10,000 **3. Conclude:** Cumulative inflow reaches 10,000 at the end of year 6. Answer: C — 6 years. A: **Incorrect:** Only 1,500 is recovered by year 2. B: **Incorrect:** Only 5,000 is recovered by year 4. C: **Correct:** Inflows total exactly 10,000 by year 6. D: **Incorrect:** The investment is already recovered by year 6, not year 7.

**1. Concept:** \(\text{GDP deflator}=\dfrac{\text{Nominal GDP}}{\text{Real GDP}}\times100\). **2. Apply:** Real GDP is unchanged (production did not change), but Nominal GDP rose 10%. So the deflator rose 10%. **3. Conclude:** The whole increase came from higher prices. Answer: B — Prices increased by 10%. A: **Incorrect:** Real GDP (production) stayed constant, so production did not rise. B: **Correct:** Nominal GDP up 10% with constant real output means prices rose 10%. C: **Incorrect:** If both rose 5%, real GDP would not stay constant. D: **Incorrect:** The deflator rose, not fell.

**1. Concept:** The value of a zero-coupon bond is \(\dfrac{1000}{(1+r)^{10}}\). A higher rate lowers the value. **2. Before:** \(V_0=\dfrac{1000}{1.05^{10}}=\dfrac{1000}{1.6289}\approx613.9\). **3. After:** \(V_1=\dfrac{1000}{1.052^{10}}=\dfrac{1000}{1.6602}\approx602.3\). **4. Change:** \[ \frac{602.3-613.9}{613.9}\approx-1.88\% \] Answer: D — Decreases by 1.88%. A: **Incorrect:** A higher rate cannot raise the bond's value. B: **Incorrect:** The direction (a fall) is right, but the size is about 1.88%, not 2.88%. C: **Incorrect:** A higher rate lowers the price, so it cannot increase. D: **Correct:** The value falls by about 1.88%.

**1. Concept:** Perfectly correlated bonds default together. So either both pay (probability 90%) or both default (probability 10%). **2. Apply securitization:** The senior bond is paid first and the junior bond last. If both underlying bonds pay, both tranches are paid. If both default, there is no money, and both tranches default. **3. Conclude:** The junior bond defaults only when both bonds default, which has probability 10%. Answer: B — 10%. A: **Incorrect:** With perfect correlation, defaults do not happen separately, so 1% (the independent case) is wrong. B: **Correct:** Both bonds default together with probability 10%, so the junior bond defaults with probability 10%. C: **Incorrect:** 15% is not obtained from the default probabilities. D: **Incorrect:** 20% would be the expected number of defaults, not the default probability.

**1. Formula:** \((1+r)^n=\dfrac{\text{final}}{\text{initial}}\). **2. Substitute:** \(n=100\) years, ratio \(=\dfrac{200000}{200}=1000\). \[ 1+r=1000^{1/100}=e^{\ln1000/100}=e^{0.06908}\approx1.0715 \] **3. Conclude:** \(r\approx7.15\%\). Answer: B — 7.15%. A: **Incorrect:** At 4.52%, 100 years gives a factor of about 83. B: **Correct:** \(1000^{1/100}-1\approx7.15\%\). C: **Incorrect:** At 9.01%, 100 years gives a factor of about 5,600. D: **Incorrect:** At 10%, 100 years gives a factor of about 13,780.

**1. Concept:** For the same nominal rate, more frequent compounding gives a higher effective annual return. **2. Compare the values of Rs 100 after 1 year:** - Annual: \(100(1.1)=110.00\) - Semi-annual: \(100(1.05)^2=110.25\) - Quarterly: \(100(1.025)^4=110.38\) - Monthly: \(100(1+0.1/12)^{12}=110.47\) **3. Conclude:** Monthly compounding gives the most. Answer: D — 10% compounded monthly. A: **Incorrect:** Effective rate 10%, the lowest. B: **Incorrect:** Effective rate 10.25%. C: **Incorrect:** Effective rate about 10.38%. D: **Correct:** Effective rate about 10.47%, the highest.

**1. Concept:** Returns compound: \((1+R_{total})=(1+r_1)(1+r_2)\). **2. Substitute:** \(1.34=1.16\times(1+r_2)\). **3. Solve:** \[ 1+r_2=\frac{1.34}{1.16}=1.1552\;\Rightarrow\;r_2\approx15.5\% \] Answer: C — 15.5%. A: **Incorrect:** This subtracts 16% from 34% and ignores compounding. B: **Incorrect:** 1.16 × 1.165 = 1.351, which is above 1.34. C: **Correct:** \(1.34/1.16-1=15.5\%\). D: **Incorrect:** 1.16 × 1.14 = 1.322, which is below 1.34.

**1. Understand:** Rs 24,000 is invested at the end of each year (starting next year) for 20 years at 7.5%. This is an ordinary annuity. **2. Formula:** \(FV=A\dfrac{(1+r)^n-1}{r}\). **3. Calculate:** \[ 1.075^{20}=4.2479,\quad FV=24000\times\frac{4.2479-1}{0.075}=24000\times43.305\approx1{,}039{,}312 \] Answer: B — Rs 10,39,312. A: **Incorrect:** This is only the total deposits (24,000 × 20), with no interest. B: **Correct:** The annuity formula gives about Rs 10,39,312. C: **Incorrect:** This is larger than the annuity future value. D: **Incorrect:** This is larger than the annuity future value.

**1. Formula:** \(NPV=-\text{Cost}+PV\text{ of inflows}\) at 10%. Amounts are in Rs lakh; cost \(=25\). **2. Project A:** \[ \frac{10}{1.1^2}+\frac{20}{1.1^5}=8.26+12.42=20.68\;\Rightarrow\;NPV=-4.32 \] **3. Project B:** Six equal payments of 6: \[ 6\times\frac{1-1.1^{-6}}{0.1}=6\times4.3553=26.13\;\Rightarrow\;NPV=+1.13 \] **4. Project C:** \[ \frac{40}{1.1^6}=22.58\;\Rightarrow\;NPV=-2.42 \] **5. Conclude:** Only Project B has a positive NPV, so it is the best. Answer: B — Project-B. A: **Incorrect:** NPV is about −4.32 lakh, which is negative. B: **Correct:** NPV is about +1.13 lakh, the highest and the only positive one. C: **Incorrect:** NPV is about −2.42 lakh, which is negative. D: **Incorrect:** The three NPVs are clearly different.

**1. Concept:** The maturity of a bond is the time until its last payment. **2. Apply:** The payments come at years 3, 6, 9, 12 and 15. The last one is at year 15. **3. Conclude:** The bond's maturity is 15 years. Answer: D — 15 years. A: **Incorrect:** 3 years is the time of the first payment. B: **Incorrect:** 9 years is the time of the third payment. C: **Incorrect:** 11 years is not a payment date; it is not the weighted average time either. D: **Correct:** 15 years is the time of the last payment.