Corporate Finance · Quiz 1 · Sep 2024

**1. Given:** The model predicted 120 semantic roles, and 100 of them were correct. **2. Formula:** \(\text{Precision}=\dfrac{\text{correct predictions}}{\text{total predictions}}\). **3. Substitute:** \[\text{Precision}=\frac{100}{120}=0.8333\approx0.83\] **Review note:** The export has no answer key for this question (the PDF shows an accepted range of 0.8 to 0.85). The calculated value 0.83 lies inside that range. Answer: \(0.83\).

**1. Maturity:** The last payment is at year 10, so maturity \(=10\) years. **2. Duration:** Total payments \(=500+1000=1500\). Weights: \(\tfrac{500}{1500}=\tfrac13\) at year 5 and \(\tfrac{1000}{1500}=\tfrac23\) at year 10. **3. Calculate:** \[D=\tfrac13(5)+\tfrac23(10)=1.67+6.67=8.33\text{ years}\] Answer: C — 10 years, 8.33 years. A: **Incorrect:** Duration equals maturity only for a single payment at the end. B: **Incorrect:** The maturity is the last payment date (10 years), not 5. C: **Correct:** Maturity is 10 years and duration is the weighted average time, 8.33 years. D: **Incorrect:** Maturity is 10 years, not 5.

**1. Given:** Basket: 2 clothes + 3 burgers. 2017: cloth 400, burger 30. 2018: cloth 300, burger 50. **2. Basket cost:** - 2017: \(2(400)+3(30)=890\) - 2018: \(2(300)+3(50)=750\) **3. Inflation (CPI-based):** \[\frac{750-890}{890}\times100=-15.73\%\] The basket became cheaper, so the rate is negative. Answer: A — -15.73%. A: **Correct:** (750 − 890)/890 = −15.73%. B: **Incorrect:** −18.67% is not the change in the basket cost. C: **Incorrect:** The basket cost fell, so inflation is negative. D: **Incorrect:** The basket cost fell, so inflation is negative, and 18.67% is not the change.

**1. Concept:** The intertemporal budget constraint has slope \(-(1+r)\) in the \((c_1,c_2)\) plane when both prices equal 1. **2. Substitute:** \(-(1+0.10)=-1.10\). Answer: D — -1.10. A: **Incorrect:** The slope is negative: more consumption today means less tomorrow. B: **Incorrect:** 0.91 is \(1/(1+r)\), not the slope. C: **Incorrect:** −0.91 is \(-1/(1+r)\), not the slope. D: **Correct:** The slope is \(-(1+r)=-1.10\).

**1. Given:** Price level now \(=80\), expected next period \(=90\), nominal rate \(=10\%\). **2. Expected inflation:** \[\pi^e=\frac{90-80}{80}=12.5\%\] **3. Real rate (approximate):** \(r\approx i-\pi^e=10\%-12.5\%=-2.5\%\). Answer: C — -2.5%. A: **Incorrect:** 8.89% is not nominal rate minus expected inflation. B: **Incorrect:** 12.5% is the expected inflation, not the real rate. C: **Correct:** \(10\%-12.5\%=-2.5\%\). D: **Incorrect:** −1.11% is not the approximate real rate here.

**1. Concept:** A AAA rating means very low default risk. Lower risk means investors demand a lower return. **2. Apply:** So a AAA company pays a *lower* interest rate than a BBB company, not a higher one. The statement is false. Answer: B — False. A: **Incorrect:** The statement reverses the risk–return link. B: **Correct:** AAA bonds are safer and therefore pay lower interest rates than BBB bonds.

**1. Given:** Two blue bonds, each \(p_b=20\%\), perfectly correlated (\(\gamma=1\)). **2. Senior bond:** It pays 100 unless *both* blue bonds default. So it defaults only when both default. **3. Calculate:** With perfect correlation, both default together or neither does. So \(P(\text{both default})=P(\text{one defaults})=20\%\). Answer: B — 20%. A: **Incorrect:** 25% is not related to the given default probability. B: **Correct:** Perfect correlation makes both defaults the same event, so the probability is 20%. C: **Incorrect:** 16% is not the result under perfect correlation. D: **Incorrect:** 4% is \(0.2^2\), the chance of both defaulting if they were independent.

**1. Given:** The junior bond pays 100 if no blue bond defaults and 0 otherwise. With perfect correlation, \(P(\text{any default})=20\%\). **2. Expected payoff:** \[E=0.8\times100+0.2\times0=80\text{ units}\] Answer: C — 80 units. A: **Incorrect:** 20 units is the expected loss, not the payoff. B: **Incorrect:** 64 units is \(0.8^2\times100\), which assumes independence. C: **Correct:** \(0.8\times100=80\). D: **Incorrect:** 96 units is \(0.96\times100\), which assumes independence.

**1. Definition:** 1 basis point \(=0.01\%\) \(=\) one-hundredth of one percent. Answer: C — One-hundredth of one percent. A: **Incorrect:** One percent is 100 basis points. B: **Incorrect:** One-tenth of one percent is 10 basis points. C: **Correct:** One basis point is 0.01%. D: **Incorrect:** One-half of one percent is 50 basis points.

**1. Concept:** A yield curve plots interest rates (yields) against the maturities of debt securities. Answer: C — Yield curve. A: **Incorrect:** GDP growth is a macro variable, not a plot of rates against maturity. B: **Incorrect:** 'Maturity chart' is not the standard term. C: **Correct:** The yield curve shows interest rates for different maturities. D: **Incorrect:** Inflationary expectations are not a graph of rates by maturity.

**1. Given:** Money triples in 15 years. **2. Formula:** \((1+r)^{15}=3\). **3. Solve:** \[1+r=3^{1/15}=e^{1.0986/15}\approx1.0760\Rightarrow r\approx7.60\%\] Answer: C — 7.60%. A: **Incorrect:** 5.42% gives about 2.2× in 15 years. B: **Incorrect:** 12.5% gives about 5.8× in 15 years. C: **Correct:** \(3^{1/15}-1\approx0.0760\). D: **Incorrect:** 20% gives about 15× in 15 years.

**1. Given:** 3,000 at year 3, 5,000 at year 5, 7,000 at year 7, \(r=10\%\). **2. Formula:** \(PV=\sum\dfrac{C_t}{1.1^t}\). **3. Substitute:** \[PV=\frac{3000}{1.331}+\frac{5000}{1.6105}+\frac{7000}{1.9487}=2253.94+3104.61+3592.11\] **4. Add:** \(PV\approx8{,}951\). Answer: D — Rs 8,951. A: **Incorrect:** 15,000 is the undiscounted total. B: **Incorrect:** 11,598 is not the sum of the correct discounted values. C: **Incorrect:** 10,000 is not the sum of the correct discounted values. D: **Correct:** The discounted values add to about 8,951.

**1. Given:** End-of-year deposits 35,000; 50,000; 72,500; 40,000 at 8%. Balance needed at the end of year 4. **2. Compound each deposit to year 4:** - Year 1: \(35000(1.08)^3=44{,}089.92\) - Year 2: \(50000(1.08)^2=58{,}320\) - Year 3: \(72500(1.08)=78{,}300\) - Year 4: \(40{,}000\) **3. Add:** \(44089.92+58320+78300+40000\approx220{,}710\). Answer: C — Rs 220,710. A: **Incorrect:** 162,209 is lower than the compounded total. B: **Incorrect:** 189,467 is lower than the compounded total. C: **Correct:** The compounded deposits add to about 220,710. D: **Incorrect:** 268,754 is higher than the compounded total.

**1. Concept:** A bubble is a price rise above fundamental value, driven by traders buying because prices are rising. **2. Check:** Momentum trading (buy what is rising) pushes prices up further and makes bubbles more likely. The other statements are wrong: a bubble is a price *above* the fundamental value (not a quick rise in the fundamental itself), and bubbles can occur even when trading is frequent. **Review note:** Option B could also be argued as true, because easy selling reduces bubble risk. The supplied key selects only C, and C is clearly true, so C is submitted. Answer: C — Momentum trading strategies make bubbles more likely to occur. A: **Incorrect:** A bubble is when the price rises above the fundamental value, not when the fundamental value rises quickly. B: **Incorrect:** The source key marks this as incorrect, although easy selling (short selling) is generally thought to reduce bubble risk. See the review note. C: **Correct:** Momentum trading amplifies price rises and makes bubbles more likely. D: **Incorrect:** Bubbles can occur even when trades are frequent.

**1. Given:** \(P=100\), \(r=8\%\) continuous, \(t=2\). **2. Formula:** \(A=Pe^{rt}\). **3. Substitute:** \[A=100e^{0.16}=100\times1.1735=117.35\] Answer: C — 117.35. A: **Incorrect:** 108.34 is not \(100e^{0.16}\). B: **Incorrect:** 116.64 is annual compounding (\(1.08^2\)), not continuous. C: **Correct:** \(100e^{0.16}=117.35\). D: **Incorrect:** 121.65 is too high for 8% over 2 years.

**1. Given:** \(C_1=3000\), \(g=3\%\), \(r=9\%\). **2. Formula:** \(PV=\dfrac{C_1}{r-g}\). **3. Substitute:** \[PV=\frac{3000}{0.09-0.03}=\frac{3000}{0.06}=50{,}000\] Answer: B — Rs 50,000. A: **Incorrect:** 100,000 would need \(r-g=3\%\). B: **Correct:** 3000/0.06 = 50,000. C: **Incorrect:** 33,333 is 3000/0.09, which ignores growth. D: **Incorrect:** 9,000 is not the result of the formula.

**1. Given:** Cost 400, value 80,000, \(n=30\) years. **2. Formula:** \((1+r)^{30}=\dfrac{80000}{400}=200\). **3. Solve:** \[1+r=200^{1/30}=e^{5.2983/30}\approx1.1932\Rightarrow r\approx19.32\%\] Answer: C — 19.32%. A: **Incorrect:** 6.67% would give only about 7× in 30 years. B: **Incorrect:** 11.67% would give about 28× in 30 years. C: **Correct:** \(200^{1/30}-1\approx0.1932\). D: **Incorrect:** 26.54% would give far more than 200× in 30 years.

**1. Given:** Deposit \(C=100\) at the end of each day, \(r=8\%\), daily rate \(i=0.08/365\approx0.000219178\), \(n=5\times365=1825\). **2. Formula (ordinary annuity):** \(FV=C\dfrac{(1+i)^n-1}{i}\). **3. Substitute:** \[(1+i)^{1825}\approx1.49175\] \[FV=100\times\frac{0.49175}{0.000219178}\approx224{,}365\] Answer: C — Rs 224,365. A: **Incorrect:** 182,500 is just the total deposits, without interest. B: **Incorrect:** 214,131 is lower than the annuity formula result. C: **Correct:** The annuity formula gives about 224,365. D: **Incorrect:** 254,689 is higher than the annuity formula result.

**1. Given:** \(D_1=30\), \(g=4\%\), \(r=10\%\), price \(=400\). **2. Gordon growth model:** \(P_0=\dfrac{D_1}{r-g}=\dfrac{30}{0.06}=500\). **3. Compare:** Fair value \(500>400\), 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 500 is above the price 400, 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 5,000; payoffs 3,000 (year 1) and 4,000 (year 2). **2. IRR condition:** \(5000=\dfrac{3000}{1+r}+\dfrac{4000}{(1+r)^2}\). **3. Let \(x=1+r\):** \(5000x^2=3000x+4000\Rightarrow5x^2-3x-4=0\). \[x=\frac{3+\sqrt{9+80}}{10}=\frac{3+9.434}{10}=1.2434\] **4. Conclude:** \(r\approx24.34\%\). Answer: A — 24.34%. A: **Correct:** Solving \(5x^2-3x-4=0\) gives \(x=1.2434\), so \(r=24.34\%\). B: **Incorrect:** 40% is the total gain relative to cost; it ignores timing. C: **Incorrect:** 33.33% does not satisfy the IRR equation. D: **Incorrect:** 18.56% does not satisfy the IRR equation.

**1. Check each statement:** - IRR cannot always be computed (e.g. cash flows with no sign change). False. - IRR can be zero (when total inflows equal the cost). False. - Projects with several sign changes can have multiple IRRs. False. - IRR and NPV rules can disagree (e.g. when ranking mutually exclusive projects). True. **2. Conclude:** The last statement is correct. Answer: D — The IRR capital budgeting rule may give a different answer than the NPV rule. A: **Incorrect:** IRR may not exist for some cash flow patterns. B: **Incorrect:** IRR is zero when undiscounted inflows equal the cost. C: **Incorrect:** Some projects have multiple IRRs. D: **Correct:** IRR and NPV rankings can differ.

**1. Given:** Cost 500; payoffs 500 at years 5, 10, 15; \(r=10\%\). **2. PV of payoffs:** \[500\left(\frac1{1.1^5}+\frac1{1.1^{10}}+\frac1{1.1^{15}}\right)=500(0.6209+0.3855+0.2394)=622.9\] **3. Profitability index:** \(PI=\dfrac{622.9}{500}\approx1.25\). Answer: C — 1.25. A: **Incorrect:** 122.93 is not PV divided by cost; PV is 622.9. B: **Incorrect:** 3.56 is not PV divided by cost. C: **Correct:** \(622.9/500\approx1.25\). D: **Incorrect:** 0.80 would be below 1, but the PV exceeds the cost.

**1. Concept:** Payback period is the time to recover the initial cost of 1,000 from cash inflows. **2. Project 1:** After year 1: 500. During year 2, it gets 1,000 more, so payback is within 2 years (about 1.5 years). **3. Project 2:** 100 per year gives \(1000/100=10\) years. **4. Project 3:** Pays 4,000 only at year 5, so payback is 5 years. **5. Conclude:** Project 1 has the shortest payback. Answer: A — Project 1. A: **Correct:** Project 1 recovers the cost in about 1.5 years, the shortest. B: **Incorrect:** Project 2 needs 10 years. C: **Incorrect:** Project 3 needs 5 years. D: **Incorrect:** The payback periods are different.

**1. Given:** Total 2-year return \(50\%\), first year \(30\%\). **2. Formula:** \((1.30)(1+r_2)=1.50\). **3. Solve:** \[1+r_2=\frac{1.50}{1.30}=1.1538\Rightarrow r_2\approx15\%\] Answer: D — 15%. A: **Incorrect:** 30% in year two would give a total of 69%. B: **Incorrect:** 25% in year two would give a total of 62.5%. C: **Incorrect:** 20% in year two would give a total of 56%. D: **Correct:** 1.5/1.3 − 1 = 15.38%, which rounds to 15%.

**1. Given:** 100 grows to 200 in 10 years. **2. Formula:** \((1+r)^{10}=2\). **3. Solve:** \[1+r=2^{0.1}\approx1.0718\Rightarrow r\approx7.18\%\] Answer: B — 7.18%. A: **Incorrect:** 10% per year would give about 2.59× in 10 years. B: **Correct:** \(2^{0.1}-1\approx0.0718\). C: **Incorrect:** 5.97% would give only about 1.79× in 10 years. D: **Incorrect:** 3.76% would give only about 1.45× in 10 years.

**1. Given:** Deposit \(C=25{,}000\) each year (end of year), \(r=8\%\). Find the smallest \(n\) with \(FV\ge1{,}000{,}000\). **2. Formula:** \(FV=C\dfrac{(1.08)^n-1}{0.08}\). **3. Condition:** \((1.08)^n\ge1+\dfrac{1000000\times0.08}{25000}=4.2\Rightarrow n\ge\dfrac{\ln4.2}{\ln1.08}=18.65\). **4. Check:** \(n=18\): \(FV\approx936{,}256<10^6\). \(n=19\): \(FV\approx1{,}036{,}157\ge10^6\). **5. Conclude:** The earliest year is 19 (deposits at the end of each year). Answer: C — 19. A: **Incorrect:** 40 years is much later than needed. B: **Incorrect:** 25 years is later than needed. C: **Correct:** At the end of year 19 the balance is about 1.036 million, the first time above 1 million. D: **Incorrect:** At the end of year 15 the balance is only about 0.68 million.