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theory of corporate finance

Questions and Answers of Theory Of Corporate Finance

A coupon bond costs $100, pays $10 interest each year, and in 10 years pays back $100 principal (ceasing to exist).What is the coupon bond’s plain duration?
At today’s prevailing 1-year and 2-year Treasury rates,(a) What is the 1-year forward interest rate on Treasuries?(b) How would you commit today to borrowing$100,000 next year at this forward rate?
The annualized interest rates are as follows:Year 1 2 3 4 5 6 Interest Rate 3% 4% 5% 6% 6% 6%Year 7 8 9 10 11 12 Interest Rate 7% 7% 7% 6% 5% 4%(a) Compute the full set of forward rates.(b) Plot the
Explain the difference between shorting in the real world, and shorting in a perfect world.
(a) To compute the YTM for the 12-month note:which solves to YTM ≈ 1.91%.(b) Do it.(c) The $150 coupon is worth $150/1.01910.5 ≈ $148.59. Therefore, the 1-year, zero note with one payment of
A 10% continuously compounded interest rate is a simple interest rate of r0, 1= e0.10 − 1 ≈ 10.52%, so you would have $110.52 after 1 year. A 20% cc interest rate is a simple interest rate of f1,
The simple interest rate is 50%. The continuously compounded interest rate is ln(1 + 50%) ≈ 40.55%.
For the bond with cash flows of $25,000, −$1,000, and −$26,000, the durations (all quoted in units of years, because we quote the multiplication factors “1” and “2” in years) are as
To commit to saving in year 3, you would need a cash outflow of $500,000 in year 3. To get this, you need a cash inflow of $500,000/1.02853 ≈ $459,575.76. Buy 4-year Treasuries for this amount
The 3-year rate is 2.85%. The 5-year rate is 3.35%. First, interpolate the 4-year interest rate: r4=(2.85% + 3.35%)/2 = 3.10%. Buy $1,000 of the 4-year, zero note and short $1,000 of the 3-year, zero
r0, 3 was computed in the text as 8.80%. The 4-year holding rate of return is r0, 4≈ 1.0314 ≈ 12.99%. Therefore, the 1-year forward rate from year 3 to year 4 is r3, 4= (1 + r0, 4)/(1 + r0, 3)
ADVANCED: Let me lead you along in working out how you can “STRIP”a Treasury coupon bond. Assume the 12-month Treasury note costs$10,065.22 and pays a coupon of $150 in 6 months, and interest
Confirm my claim that you can add continuously compounded interest rates. That is, a bond pays a continuously compounded interest rate of 10%. Upon maturity, the money can be reinvested at a
A bond pays $150 for every $100 invested. What is its continuously compounded interest rate?
A 2-year bond costs $25,000 today. It pays $1,000 interest at the end of the first year and $1,000 interest at the end of the second year. At the end of the second year, it also repays the principal
If you want to commit to saving $500,000 in 3 years (i.e., you will deposit$500,000) at an interest rate of f3, 4≈ 3.85% (i.e., you will receive about$519,250), given r3= 2.85% and r4= 3.10%, what
If you want to commit to saving at an interest rate of f3, 4 in December 2004, what would you have to do? (Assume any amount of investment you wish, and work from there.)
Continuing the yield curve example in the text, compute the 1-year forward interest rate r3, 4 from year 3 to year 4 if the 4-year annualized interest rate was 3.10%.
Does the evidence suggest that long-term bonds tend to earn higher average rates of return than short-term bonds? If yes, why is this the case? If no, why is this not possible?
The yield curve is usually upward sloping.What does this mean?(a) Investors earn a higher annualized rate of return from long-term T-bonds than short-term T-bills.(b) Long-term T-bonds are better
Look at this week’s interest rate on ordinary Tbonds and on TIPS. (You should be able to find this information, e.g., in theWall Street Journal or through a fund on the Vanguard website.)What is
A 5-year, zero-coupon bond offers an interest rate of 8% per annum.(a) How does a 1-basis-point increase in the prevailing interest rate change the value of this bond?(b) What is the ratio of the
Do long-termbonds paymore than short-term bonds because you only get money after a long time—money that you could need earlier?
The annualized interest rates are as follows:Year 1 2 3 4 5 6 Interest rate 3% 4% 5% 6% 6% 6%Year 7 8 9 10 11 12 Interest rate 7% 7% 7% 6% 5% 4%(a) Draw the yield curve.(b) Compute the 12 n-year
The 1-year forward interest rates are as follows:Year 1 2 3 4 5 6 Interest rate 3% 4% 5% 6% 6% 6%Year 7 8 9 10 11 12 Interest rate 7% 7% 7% 6% 5% 4%(a) Draw the yield curve.(b) Compute the 12 n-year
At today’s prevailing Treasury rates, how much money would you receive from an investment of $100 in 1 year, 10 years, and 30 years? What are their annualized rates of return? What are their total
Look up today’s yield curve on a financial website. What is the 1-year rate of return on a risk-free Treasury? What is the 10-year rate of return on a risk-free Treasury? What is the 30-year rate
At your own personal bank, what is the prevailing savings account interest rate?
If the real rate of return has been about 1%per month for long-term bonds, what would be the value of an investment that costs $100 today and returned $200 in 10 years?
You must value a perpetual lease. It will cost$100,000 each year in real terms—that is, its proceeds will not grow in real terms, but just contractually keep pace with inflation. The prevailing
Inflation is 2% per year; the interest rate is 8%per year. Your perpetuity project has cash flows that grow at 1% faster than inflation forever, starting with $20 next year.(a) What is the real
If the real interest rate is −1% per annum and the inflation rate is 3% per annum, then what is the present value of a $1,000,000 nominal payment next year?
If the annualized rate of return on insured tax-exempt municipal bonds will be 3% per annum and the inflation rate remains at 2%per annum, then what will be their real rate of return over 30 years?
The inflation rate is 1.5% per year. The real rate of return is 2.0% per year. A perpetuity project that paid $100 this year will provide income that grows by the inflation rate. Show what this
If the nominal interest rate is 7% per year and the inflation rate is 2% per year, what is the exact real rate of return?
Using the information from Questions 5.30 and 5.31, compute the annualized current real interest rate on 30-day Treasuries.
Using information from a current newspaper or a financial website, find the annualized current nominal interest rate on 30-day U.S.Treasury bills.
Using information from a current newspaper or a financial website, find out the current inflation rate.
A project has cash flows of +$100 (now at time 0), and −$100, +$100, and −$100 at the end of consecutive years. The interest rate is 6% per annum.(a) What is the project’s NPV?(b) How does the
The annual interest rate from year t to year t + 1 is rt , t+1= 5% + 0.3% . t (e.g., the rate of return fromyear 5 to year 6 is 5% + 0.3% .5 = 6.5%).(a) What is the holding rate of return of a
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?

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