Questions and Answers of Theory Of Corporate Finance

If the annualized 5-year rate of return is 10%, and if the first year’s rate of return is 15%, and if the returns in all other years are equal, what are they?
If the annualized 5-year rate of return is 10%, what is the total 5-year holding rate of return?
The following were the daily values of an investment in January 2001:2-Jan 3-Jan 4-Jan$1,283.27 $1,347.56 $1,333.34 5-Jan 8-Jan 9-Jan$1,298.35 $1,295.86 $1,300.80 If returns had accumulated at the
Return to Question 5.3. What were the compounded and the annualized rates of return on the S&P 500 over the first 6 years (i.e., from 1991 to 1996 inclusive)?
Stock A alternates between +20% and −10%with equal probability. Stock B earns 4.5% per annum.(a) What is the average rate of return for stock A?(b) What is the average rate of return for stock
Compare two stocks. Both have earned on average 8% per year. However, stock A has oscillated between 6% and 10%. Stock B has oscillated between 3% and 13%. (For simplicity, say that they alternated.)
Are you better off if a project first returns−10% followed by +30%, or if it first returns +30% followed by −10%?
If inflation were to remain at 1.6% per year, the plain Treasury bond would offer a higher real rate of return because 1.056/1.016 − 1 ≈ 3.9% per year. But if inflation were to rise in the
(a) For the 1-year bond, the value of a $100 bond changes from $100/1.0800 ≈ $92.59259 to $100/1.0801 ≈$92.58402. This is about a –0.009% change.(b) For the 10-year bond, the value of a $100
r0, 5= 1.03355 − 1 ≈ 17.91%. Therefore, 1 + r3, 5= 1.03355/1.02853 − 1 ≈ 8.38%, which is√1.0838 −1 ≈ 4.10% in annualized terms.
Yes. The answers are right in the table. The 3-year rate of return is 1.02853 − 1 ≈ 8.80%. The forward rate is 1.088/1.0523 ≈ 3.39%.
Bills, notes, and bonds. T-bills have maturities of less than 1 year. T-notes have maturities from 1 to 10 years.T-bonds have maturities greater than 10 years.
The nominal interest rate is 1.03 . 1.08 − 1 = 11.24%. Therefore, the cash flow is worth about$500,000/1.1124 ≈ $449,479.
1.20/1.05 ≈ 1.1429. The real interest rate is 14.29%.
(1 + rnominal) = (1 + rreal) . (1 + π)
The CPI is the average price change to the consumer for a specific basket of goods. The PPI measures the price that producers are paying. Taxes, distribution costs, government subsidies, and basket
This project is worth−$200 + $100 1.03+ $300 1.042+ $500 1.0453≈ $612.60
The annualized 5-year rate of return is the same 10%.
r0, 5= 50% (1 + r5)5 = 1.50 ⇒ r5= 1.501/5 − 1 ≈ 8.45%.
r12= 12√1 + 167.1% − 1 ≈ 8.53%
The compounded rate of return is always higher than the sum, because you earn interest on interest. The annualized rate of return is lower than the average rate of return, again because you earn
The annualized rate of return is√1.4 − 1 ≈ 18.32%. It is therefore lower than the 20% average rate of return.
1.0512/4 ≈ 15.76%
The returns were (−33%, +50%, −67%, +100%), so the overall rate of return was −33.33%.
Compounding, the returns were (1.2631 − 1) = 26.31% for the first year, (1.2631 . 1.0446) − 1 ≈31.94% for the second year, and so on. The sequence compounds further into 41.26%, 39.08%, 86.52%,
Solve (1 + x) . (1 + 22%) = (1 − 50%), so the project had a rate of return of −59.00%.
r0, 2= (1 + r0, 1) . (1 + r1, 2) − 1 = 1.02 . 1.03 − 1 = 5.06%
A 10-year and a 1-year zero-bond both offer an interest rate of 8% per annum.(a) How does an increase of 1 basis point in the prevailing interest rate change the value of the 1-year bond? (Use 5
Repeat the calculation with the 5-year annualized rate of return of 3.35%. That is, what is the 5-year holding rate of return, and how can you compute the forward interest rate for a 2-year
Compute the 3-year holding rate of return on December 31, 2004. Then, using the 2-year holding rate of return on December 31, 2004, of 5.23%and your calculated 3-year holding rate of return, compute
What are the three types of Treasuries? How do they differ?
If the real interest is 3% per annum and the inflation rate is 8% per annum, then what is the present value of a $500,000 nominal payment next year?
The nominal interest rate is 20%. Inflation is 5%.What is the real interest rate?
From memory, write down the relationship between nominal rates of return (rnominal), real rates of return (rreal), and the inflation rate (π).
A project costs $200 and will provide cash flows of +$100, +$300, and+$500 in consecutive years. The annualized interest rate is 3% per annum over 1 year, 4%per annum over 2 years, and 4.5% per annum
If the per-year interest rate is 10% for each of the next 5 years, what is the annualized 5-year rate of return?
If the total holding interest rate is 50% for a 5-year investment, what is the annualized rate of return?
Return to Question 5.3. What was the annualized rate of return on the S&P 500 over these 12 years?
Is the compounded rate of return higher or lower than the sum of the individual rates of return? Is the annualized rate of return higher or lower than the average of the individual rates of
Assume that the 2-year holding rate of return is 40%. The average(arithmetic) rate of return is therefore 20% per year. What is the annualized(geometric) rate of return? Is the annualized rate the
If you earn a rate of return of 5% over 4 months, what is the annualized rate of return?
A project lost one-third of its value the first year, then gained fifty percent of its value, then lost two-thirds of its value, and finally doubled in value.What was the overall rate of return?
From 1991 to 2002, the stock market (specifically, the S&P 500) had the following annual rates of return:Year ˜rS&P 500 Year ˜rS&P 500 Year ˜rS&P 500 1991 +0.2631 1995 +0.3411 1999 +0.1953 1992
Although a 2-year project had returned 22% in its first year, overall it lost half of its value. What was the project’s rate of return after the first year?
If the first-year interest rate is 2% and the second year interest is 3%, what is the 2-year total interest rate?
What are the most prominent methods for capital budgeting in the real world? Which make sense?
The prevailing cost of capital is 9% per annum.What would various capital budgeting rules recommend for the following projects?Cash Flow in Year Project 0 1 2 3 4 A –$1,000 $300 $400 $500 $600 B
Consider the following project:Year 0 1 2 3 4 5 6 7 Cash $0 −$100 $50 $80 $30 $30 $30 −$60 Flow(a) What is the IRR?(b) What is the payback time?(c) What is the profitability index?
Consider the following project:Year 0 1 2 3 4 5 6 Cash Flow −$10 $5 $8 $3 $3 $3 −$6(a) What is the IRR?(b) What is the payback time?(c) What is the profitability index?
What are the profitability indexes and the NPVs of the following two projects: project A that requires an investment of $5 and gives$20 per year for 3 years, and project B that requires an investment
The prevailing interest rate is 10%. If the following three projects are mutually exclusive, which should you take?What does the NPV rule recommend? What does the IRR rule recommend? Cash Flow in
You can invest in a project with returns that depend on the amount of your investment.Specifically, the formula relating next year’s payoff (cash flow) to your investment today is C1=−C0−
If a project has a cash inflow of $1,000 followed by cash outflows of $600 in two consecutive years, then under what discount rate scenario should you accept this project?
A project has cash flows of −$100, +$55, and+$60.50 in consecutive years. If the hurdle rate is 10%, should you accept the project?
A project has cash flows of +$400, −$300, and−$300 in consecutive years. The prevailing interest rate is 5%. Should you take this project?
Your project has cash flows of −$1,000 in year 0, +$3,550 in year 1, −$4,185 in year 2, and −$1,638 in year 3.What is its IRR?
Your project has cash flows of −$1,000 in year 0, +$3,550 in year 1, −$4,185 in year 2, and +$1,638 in year 3.What is its IRR?
Give an example of a problem that hasmultiple IRR solutions.
Under what circumstances is an IRR a rate of return? Under what circumstances is a rate of return an IRR?
A project has cash flows −$100, +$55, and+$60.50 in consecutive years. How can you characterize the “rate of return” (loosely speaking)embedded in its cash flows?
A coupon bond costs $100, then pays $10 interest each year for 10 years, and pays back its$100 principal in 10 years. What is the bond’s YTM?
What is the YTM of a standard 6% level semiannual 10-year coupon bond that sells for its principal amount today (i.e., at par =$100)?
A project has cash flows of −$1,000, +$600, and +$300 in consecutive years. What is the IRR?
What is the difference between YTM and IRR?
How bad a mistake is it to misestimate the cost of capital in a long-term project? Please illustrate.
How bad a mistake is it to misestimate the cost of capital in a short-term project? Please illustrate.
Given the same NPV, would you be willing to pay extra for a project that bears fruit during your lifetime rather than after you are gone?
The first project has present values of future cash flows of $520.66; the second of $52.07; the third of$60.74. The profitability indexes are $520.66/$500 ≈ 1.04, $52.07/$50 ≈ 1.04, and
The IRR is 6.81%. This is between the 1-year 5% and the 2-year 10% interest rates. Therefore, the IRR capital budgeting rule cannot be applied. The NPV rule gives you −$1,000 + $600/1.05 +
The first project has an NPV of $20.66 and an IRR of 13.07%. The second project has an NPV of $2.07 and the same IRR of 13.07%. The third project has an NPV of $10.74 and an IRR of 25.69%. Still, you
Project A has an NPV of+$500,000 +−$200,000 1.25+−$200,000(1.25)2+−$200,000(1.25)3= $109,600 It has an IRR of 9.70%. Project B has an NPV of $70,000, and no IRR (it is always positive).
The first project has a positive NPV of NPV = $50,000 +−$250,000 1.25+ $467,500 1.252+−$387,500 1.253+ $120,120 1.254≈ $1.15 The second project has an NPV of −$1.15. You should take project
The problems are (a) you need to get the sign right to determine whether you should accept the project above or below its hurdle rate; (b) you need to make sure you have only one unique IRR (or work
(a) The IRR-maximizing investment choice of C0 is an epsilon. The IRR is then close to infinity. The NPV is 0. (b) The NPV-maximizing (and best) choice is an investment of $226,757. This also happens
The IRR is 8.44%. This is above the prevailing interest rate. However, the cash flows are like that of a financing project. This means that it is a negative NPV project of −$7.71. You should not
The IRR is 19.73%. This is lower than your 20% cost of capital, so you should not take this project. The NPV is −$23.92. IRR and NPV agree on the reject recommendation.
The (unique) IRR is 56.16%. This is higher than your 30% cost of capital, so you should take this project.The NPV is +$1,057.35. Because this is positive, it gives the same recommendation—accept.
For projects (A) and (B), the valid IRRs are 10%, 20%, 30%, and 40%. The plot for (A) follows. The figure for (B) has a y-scale that is 50 times larger. For project (C), there is no IRR, also shown
For example, C0= −$100, C1= −$200, C2= −$50. No interest rate can make their present value equal to zero, because all cash flows are negative. This project should never be taken, regardless of
For example, C0= −$100, C1= +$120, C2= −$140, C3= +$160, C4= −$20. (The solutions are IRR ≈ −85.96% and IRR ≈ +$9.96%. The important aspect is that your example has multiple inflows and
You are seeking the solution to −$25,000 + $1, 000(1+YTM)1+ $1, 000(1+YTM)2+ $25, 000(1+YTM)2= 0. It is YTM = 4%.
The YTM is 10%, because $1,000 + $1,611/1.105 ≈ 0.
The coupon bond’s YTM is 5%, because −$1,000 + $50 1.05+ $50 1.052+ $50 1.053+ $50 1.054+ $1, 050 1.055= 0. The YTM of such a bond (annual coupons) is equal to the coupon rate when a bond is
The spreadsheet function is called IRR(). The answer pops out as 15.5696%. Check: −$100 + $55/1.16 +$70/1.162 ≈ 0.
−$1,000 + $900/(1 + IRR) + $900/(1 + IRR)2 = 0 ⇒ IRR = 50%
−$1,000 + $600/(1 + IRR) + $600/(1 + IRR)2 = 0 ⇒ IRR ≈ 13.07%
−$1,000 + $500/(1 + IRR) + $500/(1 + IRR)2 = 0 ⇒ IRR = 0%
−$1,000 + $1,000/(1 + IRR) = 0 ⇒ IRR = 0%
The equation that defines IRR is Formula 4.1 on page 72.
If you invest $400, the project will give $400 . 1.15 = $460 next period. The capital markets will value the project at $460/1.10 ≈ $418.18. You should take the project and immediately sell it for
The fact that you can use capital markets to shift money back and forth without costs allows you to consider investment and consumption choices independently.
The prevailing interest rate is 10%. If the following three projects are mutually exclusive, which should you take?Year Project 0 1 2 1 −$500 +$300 +$300 2 −$50 +$30 +$30 3 −$50 +$35 +$35 You
The prevailing interest rate is 5% over the first year and 10% over the second year. That is, over 2 years, your interest rate is (1 + 5%) . (1 +10%) − 1 = 15.5%. Your project costs $1,000 and will
The prevailing interest rate is 10%. If the following three projects are mutually exclusive, which should you take?Year Project 0 1 2 1 −$500 +$300 +$300 2 −$50 +$30 +$30 3 −$50 +$35 +$35 What
The prevailing interest rate is 25%. If the following two projects are mutually exclusive, which should you take?Year Project 0 1 2 3 A +$500,000 −$200,000 −$200,000 −$200,000 B +$50,000
The prevailing interest rate is 25%. If the following two projects are mutually exclusive, which should you take?Year Project 0 1 2 3 4 A +$50,000 −$250,000 +$467,500 −$387,500 +$120,120 B
What are the problems with the IRR computation and criterion?
You can invest in a project with diminishing returns. Specifically, the formula relating next year’s payoff to your investment today is C1=√−C0, where C0 and C1 are measured in million dollars.
A project has cash flows of +$200, −$180, −$40 in consecutive years.The prevailing interest rate is 5%. Should you take this project?
A project has cash flows of −$1,000, −$2,000, −$3,000, +$4,000, and+$5,000 in consecutive years. Your cost of capital is 20% per annum.Use the IRR rule to determine whether you should take this

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