Corporate Finance · Quiz 1 · Sep 2025

**1. Given:** Face value \(=5000\), price \(=4500\), maturity \(=1\) year. **2. Formula:** For a one-year zero-coupon bond, \(P=\dfrac{F}{1+y}\), so \(y=\dfrac{F}{P}-1\). **3. Substitute:** \[y=\frac{5000}{4500}-1=1.1111-1=0.1111\] **4. Conclude:** The yield is 11.11%. Answer: C — 11.11%. A: **Incorrect:** This is too low. The gain of 500 is divided by the price 4500. B: **Incorrect:** 10% would need a price of 4545.45 (5000/1.1). C: **Correct:** The gain is 500 on an investment of 4500, which is 11.11%. D: **Incorrect:** 9% would need a price of 4587.16.

**1. Given:** Rate \(r=5\%\). We need \(n\) such that money doubles. **2. Formula:** \((1.05)^n=2\). **3. Take logs:** \[n\log(1.05)=\log 2\Rightarrow n=\frac{\log 2}{\log 1.05}\approx14.2\text{ years}\] **4. Conclude:** \(n=\log(2)/\log(1.05)\). Answer: A — \(\log(2)/\log(1.05)\). A: **Correct:** Solving \(1.05^n=2\) gives \(n=\log 2/\log 1.05\). B: **Incorrect:** This is the inverse of the correct ratio and gives about 0.07 years. C: **Incorrect:** The growth factor is 1.05, not 0.05. D: **Incorrect:** The growth factor is 1.05, and this ratio is also inverted.

**1. Given:** \(P=1000\), \(r=7\%\) continuously compounded, \(t=5\). **2. Formula:** \(A=Pe^{rt}\). **3. Substitute:** \[A=1000\,e^{0.07\times5}=1000\,e^{0.35}=1000\times1.4191\] **4. Conclude:** \(A\approx1419\). Answer: C — Rs 1419. A: **Incorrect:** Rs 1350 is simple interest (1000 × 1.35), which ignores compounding. B: **Incorrect:** Rs 1402 is annual compounding (1.07^5), not continuous. C: **Correct:** \(1000e^{0.35}\approx1419\). D: **Incorrect:** Rs 1500 is too high for 7% over 5 years.

**1. Key concept:** Payback period is the time needed to recover the initial investment. A shorter payback means money returns sooner, which matters when capital is limited and interest rates are high. **2. Compare:** NPV, IRR and Profitability Index measure value or return and do not focus on how fast the money comes back. **3. Conclude:** Payback. Answer: B — Payback. A: **Incorrect:** NPV measures total value created, not speed of recovery. B: **Correct:** Payback tells how fast the invested money is recovered. C: **Incorrect:** IRR measures the rate of return, not recovery time. D: **Incorrect:** Profitability Index measures value per rupee invested, not recovery time.

**1. Concept:** Nominal GDP \(=\) prices \(\times\) quantities. Real GDP uses constant (base-year) prices, so it reflects quantities only. **2. Apply:** Real GDP unchanged means quantities are unchanged. Nominal GDP doubled, so the rise came from prices. **3. Conclude:** Only prices increased. Answer: A — Only prices increased. A: **Correct:** Real GDP is unchanged, so the whole rise in nominal GDP comes from prices. B: **Incorrect:** Unchanged real GDP means quantity did not increase. C: **Incorrect:** Quantity did not increase because real GDP is unchanged. D: **Incorrect:** Prices did increase, since nominal GDP doubled.

**1. Given:** \(D_1=20\), \(g=3\%\), \(r=10\%\), market price \(=300\). **2. Gordon growth formula:** \(P_0=\dfrac{D_1}{r-g}\). **3. Substitute:** \[P_0=\frac{20}{0.10-0.03}=\frac{20}{0.07}\approx285.71\] **4. Compare:** The market price \(300>285.71\), so the stock is overpriced. An investor should sell. **5. Conclude:** Overpriced, so sell. Answer: D — The PVC stock is overpriced, and an investor should sell PVC shares. A: **Incorrect:** The fair value 285.71 is below 300, so it is overpriced, not underpriced. B: **Incorrect:** The stock is overpriced, so buying is wrong. C: **Incorrect:** The stock is overpriced, not underpriced. D: **Correct:** Fair value is 285.71 and the market price is 300, so the stock is overpriced and should be sold.

**1. Given:** Cash flows of 200 at \(t=1\) and 200 at \(t=5\). **2. Concept:** Simple duration is the weighted average time of the cash flows, with weights equal to each payment's share of the total payments. **3. Weights:** Each payment is 200 out of 400, so each weight is \(0.5\). **4. Calculate:** \[D=0.5(1)+0.5(5)=3\text{ years}\] Answer: B — 3 years. A: **Incorrect:** 5 years is the time of the last payment only. B: **Correct:** Each payment has weight 0.5, so \(0.5(1)+0.5(5)=3\). C: **Incorrect:** 2.5 years would need weights that do not match the equal payments. D: **Incorrect:** 1 year is the time of the first payment only.

**1. Given:** 3 bonds, each with default probability 20%, and correlation \(\rho=1\). **2. Concept:** With perfect correlation, all bonds default together or none do. They behave like one bond. **3. Calculate:** \(P(\text{all three default})=P(\text{one bond defaults})=0.20\). **4. Conclude:** 0.200. (For independent bonds it would be \(0.2^3=0.008\).) Answer: C — 0.200. A: **Incorrect:** 0.008 is \(0.2^3\), which applies only to independent bonds. B: **Incorrect:** 0.128 is not the result of the perfect-correlation case. C: **Correct:** With \(\rho=1\), all bonds default together, so the probability is 0.20. D: **Incorrect:** 0.512 is \(0.8^3\), the probability that none default under independence.

**1. Formula:** Real rate \(\approx\) nominal rate \(-\) expected inflation (exactly, \(1+r_{real}=\dfrac{1+i}{1+\pi^e}\)). **2. Apply:** If nominal rate \(=\) expected inflation, then \(r_{real}=0\). **3. Conclude:** Zero. Answer: C — Zero. A: **Incorrect:** Positive would need nominal rate above expected inflation. B: **Incorrect:** Negative would need nominal rate below expected inflation. C: **Correct:** Nominal minus expected inflation is 0. D: **Incorrect:** The real rate cannot be 1 here; it equals 0.

**1. Concept:** A yield curve plots interest rates against maturity. An upward-sloping curve means longer maturities have higher rates. **2. Apply:** So short-term rates are lower than long-term rates. A recession signal is usually an *inverted* (downward-sloping) curve, not an upward-sloping one. **3. Conclude:** Short-term rates are lower than long-term rates. Answer: B — Short-term rates are lower than long-term rates. A: **Incorrect:** This describes an inverted curve, not an upward-sloping one. B: **Correct:** Upward slope means long-term rates are higher than short-term rates. C: **Incorrect:** Maturity matters; the curve shows rates varying with maturity. D: **Incorrect:** A recession signal is usually an inverted curve, not an upward-sloping one.

**1. Given:** Investment \(=10\) lakh, IRR \(=12\%\), \(n=2\) years. **2. Concept:** IRR is the rate at which the payoff's present value equals the investment, so \(10=\dfrac{X}{(1.12)^2}\). **3. Calculate:** \[X=10\times1.12^2=10\times1.2544=12.544\text{ lakh}\] Answer: C — Rs 12.544 lakh. A: **Incorrect:** 12 lakh would be a 20% return in total (about 9.5% per year). B: **Incorrect:** 12.4 lakh would use simple interest (10 × 1.24). C: **Correct:** \(10\times1.12^2=12.544\) lakh. D: **Incorrect:** 12.838 lakh would be about 13.3% per year.

**1. Given:** Cost \(=60\), current value \(=9000\), \(n=60\) years. **2. Formula:** \(60(1+r)^{60}=9000\Rightarrow(1+r)^{60}=150\). **3. Solve:** \[1+r=150^{1/60}=e^{\ln150/60}=e^{5.0106/60}=e^{0.0835}\approx1.0871\] \[r\approx8.71\%\] Answer: C — 8.71%. A: **Incorrect:** 60% is the number of years, not the rate. B: **Incorrect:** 10.87% is not the root of 150 over 60 years. C: **Correct:** \(150^{1/60}-1\approx0.0871\). D: **Incorrect:** 2.5% would give only about a 4.4× increase over 60 years.

**1. Given:** Project B pays 10 lakh each year for 6 years, cost 40 lakh, \(r=10\%\). **2. Present value of inflows:** \[PV=10\times\frac{1-1.1^{-6}}{0.10}=10\times4.3553=43.55\text{ lakh}\] **3. Profitability index:** \(PI=\dfrac{PV}{\text{cost}}=\dfrac{43.55}{40}=1.0888\approx1.09\). Answer: A — 1.09. A: **Correct:** PV of inflows 43.55 divided by cost 40 gives 1.09. B: **Incorrect:** 1.19 is not the ratio of PV to cost. C: **Incorrect:** 1.88 would need a much higher PV of inflows. D: **Incorrect:** 0.88 would be below 1, but Project B has a positive NPV.

**1. Given:** Cost \(=40\) lakh and \(r=10\%\) for each project. **2. Project A:** \[PV=\frac{30}{1.1^2}+\frac{40}{1.1^5}=24.79+24.84=49.63,\quad NPV=9.63\] **3. Project B:** \(PV=10\times4.3553=43.55\), so \(NPV=3.55\). **4. Project C:** \(PV=\dfrac{100}{1.1^{10}}=38.55\), so \(NPV=-1.45\). **5. Conclude:** Project A has the highest NPV (9.63 lakh). Answer: A — Project-A. A: **Correct:** Project A has the highest NPV, about 9.63 lakh. B: **Incorrect:** Project B has NPV about 3.55 lakh, lower than A. C: **Incorrect:** Project C has a negative NPV of about -1.45 lakh. D: **Incorrect:** Project A has a positive and the highest NPV, so one of the projects is chosen.

**1. Concept:** The intertemporal budget constraint is \(c_2=y_2+(1+r)(y_1-c_1)\). Its slope in the \((c_1,c_2)\) plane is \(-(1+r)\) (prices are equal to 1). **2. Substitute:** \(-(1+r)=-1.12\Rightarrow r=0.12\). **3. Conclude:** The interest rate is 12%. The incomes do not affect the slope. Answer: B — 12%. A: **Incorrect:** The slope \(-1.12\) gives \(1+r=1.12\), not 1.10. B: **Correct:** \(1+r=1.12\Rightarrow r=12\%\). C: **Incorrect:** 15% would give a slope of -1.15. D: **Incorrect:** The slope alone is enough, since prices are equal to 1.

**1. Given:** \(C=1000\), \(n=25\), \(r=5\%\). **2. Formula:** \(PV=C\dfrac{1-(1+r)^{-n}}{r}\). **3. Substitute:** \[1.05^{25}=3.3864,\quad 1.05^{-25}=0.2953\] \[PV=1000\times\frac{1-0.2953}{0.05}=1000\times14.094\] **4. Conclude:** \(PV\approx14{,}094\). Answer: C — Rs 14,094. A: **Incorrect:** 25,000 is the undiscounted sum of the payments. B: **Incorrect:** 18,394 is not the PV at 5%. C: **Correct:** \(1000\times14.094\approx14{,}094\). D: **Incorrect:** 12,500 is not the PV at 5%.

**1. Given:** Basket: 1 clothes, 3 food, 2 fuel. Base year 2022. **2. Cost in 2022:** \(1(200)+3(50)+2(75)=200+150+150=500\). **3. Cost in 2024:** \(1(220)+3(80)+2(100)=220+240+200=660\). **4. CPI:** \[CPI_{2024}=\frac{660}{500}\times100=132\] Answer: D — 132. A: **Incorrect:** 100 is the base-year CPI. B: **Incorrect:** The 2024 basket costs 660, which gives 132. C: **Incorrect:** 120 does not match the basket cost ratio. D: **Correct:** 660/500 × 100 = 132.

**1. Cost in 2022:** \(200+150+150=500\). **2. Cost in 2023:** \(1(180)+3(70)+2(80)=180+210+160=550\), so \(CPI_{2023}=110\). **3. Cost in 2024:** \(660\), so \(CPI_{2024}=132\). **4. Inflation 2024 over 2023:** \[\frac{132-110}{110}\times100=20\%\] Answer: C — 20%. A: **Incorrect:** 10% is the inflation from 2022 to 2023. B: **Incorrect:** 16% is not the change from 110 to 132. C: **Correct:** (132 - 110)/110 = 20%. D: **Incorrect:** 32% is the total rise from 2022 to 2024, not the annual rate.

**1. Given:** \(P=8{,}00{,}000\), monthly rate \(r=3\%\), \(n=120\) months. **2. Formula:** \(EMI=\dfrac{P\,r}{1-(1+r)^{-n}}\). **3. Substitute:** \[(1.03)^{120}\approx34.711,\quad (1.03)^{-120}\approx0.02881\] \[EMI=\frac{800000\times0.03}{1-0.02881}=\frac{24000}{0.97119}\approx24{,}711.9\] **4. Match:** The nearest listed option is Rs 24,711. **Convention note:** The exact EMI is about 24,711.93, which rounds to 24,712. The listed option is 24,711, which matches the computed value up to rounding and is the only option close to it. Answer: C — Rs 24,711. A: **Incorrect:** 12,000 is far below the EMI; it ignores the 3% monthly interest on 8,00,000, which is 24,000 in the first month. B: **Incorrect:** 22,746 is lower than the EMI formula result. C: **Correct:** This is the closest to the computed 24,711.9. D: **Incorrect:** 28,437 is higher than the EMI formula result.

**1. Given:** \(V=\dfrac{1000}{(1+r)^{20}}\), rate rises from 2.5% to 2.6%. **2. Ratio of values:** \[\frac{V_{new}}{V_{old}}=\left(\frac{1.025}{1.026}\right)^{20}=(0.999025)^{20}\approx0.98069\] **3. Change:** \(0.98069-1=-0.0193\), so the value falls by about 1.93%. **4. Conclude:** A higher rate lowers the bond price. Answer: B — The value decreases by 1.93%. A: **Incorrect:** A rate increase lowers the bond value; it cannot increase. B: **Correct:** The ratio is 0.9807, so the value falls by 1.93%. C: **Incorrect:** The value falls when rates rise, and the size is 1.93%, not 1.20%. D: **Incorrect:** The fall is 1.93% over 20 years, not 1.20%.

**1. Given:** 1-year rate \(s_1=4\%\), 2-year rate \(s_2=4.5\%\). **2. Concept:** The forward rate \(f\) satisfies \((1+s_2)^2=(1+s_1)(1+f)\). **3. Solve:** \[1+f=\frac{(1.045)^2}{1.04}=\frac{1.092025}{1.04}=1.0500\] \[f=5.00\%\] Answer: D — 5.00%. A: **Incorrect:** 4.28% is not the forward rate from the formula. B: **Incorrect:** 4.50% is the average annual 2-year rate, not the forward rate. C: **Incorrect:** 4.72% is not the forward rate from the formula. D: **Correct:** \((1.045)^2/1.04-1=0.0500\).