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theory of corporate finance

Questions and Answers of Theory Of Corporate Finance

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
A project has cash flows of −$1,000, −$2,000, +$3,000, and +$4,000 in consecutive years. Your cost of capital is 30% per annum. Use the IRR rule to determine whether you should take this project.
For the following projects, plot the NPVs as a function of the prevailing interest rate and determine the appropriate IRRs.
Give an example of a project that has no IRR.
Give an example of a problem that has multiple IRR solutions.
Compute the yield-to-maturity of a two-year bond that costs $25,000 today and pays $1,000 at the end of each of the 2 years. At the end of the second year, it also repays $25,000.What is the bond’s
What is the YTM of a 5-year zero-bond that costs $1,000 today and promises to pay $1,611?
What is the YTM of an x% annual level-coupon bond whose price is equal to the principal paid at maturity? For example, take a 5-year bond that costs $1,000 today, pays 5% coupon ($50 per year) for 4
A project has cash flows of −$100, $55, and $70 in consecutive years.Use a spreadsheet to find the IRR.
What is the IRR of a project that costs $1,000 now and produces $900 next year and $900 the year after?
What is the IRR of a project that costs $1,000 now and produces $600 next year and $600 the year after?
What is the IRR of a project that costs $1,000 now and produces $500 next year and $500 the year after?
What is the IRR of a project that costs $1,000 now and produces $1,000 next year?
From memory, write down the equation that defines IRR.
You have $500 and really, really want to go to the Superbowl tonight(which will consume all your funds). You cannot wait until your project completes: The project costs $400 and offers a rate of
What is the main assumption that allows you to independently consider investment (project) choices without regard to when you need wealth(or how much money you currently have at hand)?
The discount rate is 12.68% per annum. Your competitor offers a 5-year airplane lease for an upfront cost of $30,000. The lessee will have to pay $3,000 per year in insurance (each year in advance)
You can sell your building for $200,000. Alternatively, you can lease out your building.The lessee will pay you $2,000 per month. You will have to budget $700 per month for upkeep, attention, and so
(a) Machine A is PV(Cost) = $10,000 + Annuity($1,000, 18 years, 12%)(b) The equivalent rental values are(c) The 18-year machine has the lower rental cost, so it is the better deal—of course, under
This contract costs $2,000 plus $450/0.005 . (1 − 1/1.00547) ≈ $18,807 for a total of $20,807. The EAC is therefore $488.65, payable at the end of every month. The difference is $532.93 −
ADVANCED: You are valuing a firmwith a “pro forma” (i.e., with your forward projection of what the cash flows will be). The firm had cash flows of $1,000,000 today, and is growing by a rate of
Structure a mortgage bond for $150,000 so that its monthly payments are $1,000. The prevailing interest rate is quoted at 6% (APR)per year.
If you have to pay off an effective 6.5% loan within the standard 30 years, then what are the per-month payments for the $1,000,000 mortgage? As in Question 3.26, consider both an effective 6.5%
What maximum price would you pay for a standard 8% level-coupon bond (with semiannual payments and a face value of $1,000) that has 10 years to maturity if the prevailing discount rate (your cost of
A tall Starbucks coffee costs $1.65 a day. If the bank’s quoted interest rate is 6% per annum, compounded daily, and if the Starbucks price never changed, what would a lifetime free subscription to
A stock pays an annual dividend of $2. The dividend is expected to increase by 2% per year(roughly the inflation rate) forever. The price of the stock is $40 per share. At what cost of capital is
Your firm just finished the year, in which it had cash earnings of $400 (thousand). You forecast your firm to have a quick growth phase from year 0 to year 5, in which it grows at a rate of 40% per
Economically, why does the growth rate of cash flows have to be less than the discount rate?
A tall Starbucks coffee costs $1.65 a day. If the bank’s quoted interest rate is 6% per annum and coffee prices increased at a 3% annual rate of inflation, what would an endless, inheritable free
What is the prevailing interest rate if a perpetual bond were to pay $100,000 per year beginning next year (time 1) and payments grow with the inflation rate at about 2% per year, assuming the bond
What is the prevailing interest rate if a perpetual bond were to pay $100,000 per year beginning next year and costs $1,000,000 today?
What is the PV of a perpetuity paying $30 each month, beginning next month, if the annual interest rate is a constant effective 12.68% per year?
If you could pay for your mortgage forever, how much would you have to pay per month for a $1,000,000 mortgage, at a 6.5% annual interest rate? Work out the answer (a) if the 6.5% is a bank APR quote
A tall Starbucks coffee costs $1.65 a day. If the bank’s quoted interest rate is 6% per annum, compounded daily, and if the Starbucks price never changed, what would an endless, inheritable free
The solution is $4,000/(0.08 − 0.02) .1 − 1.0235 1.0835≈ $57,649.23.
For 6 months, (1 + 2.47%)2 − 1 ≈ 5%. Now, define 6 months to be 1 period. Then, for t 6-month periods, you can simply compute an interest rate of (1 + 2.47%)t − 1. For example, the 30 months
The interest rate is 5% per half-year. Be my guest if you want to add 40 terms. I prefer the annuity method.The coupons are worthThe final payment is worth PV(Principal Repayment) = $100, 000
The semiannual interest rate would now increase from 2.47% to r = 2 √1 + 6% − 1 = √1.06 − 1 ≈ 2.9563%To get the bond’s new present value, reuse the annuity formulaThis bond would have
For $1,000 of mortgage, solve for C1 inIn other words, for every $1,000 of loan, you have to pay $8.44 per month. For other loan amounts, just rescale the amounts. PV = C $1,000 = - [1/(1+r)] |
To find the implicit cost of capital of the lease, you need to solveThe solution is r ≈ 0.31142% per month, or 3.8% per annum. This is the implied rate of return if you purchase the warehouse and
For each ecu (e), the perpetuity is worth 1e/0.04 = 25e. The annuity is worth 1e/0.05 . (1 − 1/1.0541) ≈17.29e. Therefore, the perpetuity is better.
For 1 year, the 300 bezants paid once at year-end are worth 300b/1.0212 ≈ 236.55 bezants today. Now for the quarterly payment schedule: The quarterly interest rate is 1.023 − 1 ≈ 6.12%.
Your 360-month annuity is worth G . {1 } - [1/(1+r)] 5 = $5- $5 - [1/(1+0.005)1360 0.005 0.166 0.005 $833.96
The annuity formula is C1 .{1 − [1/(1 + r)]T}/r.
Compare the annuity and perpetuity formulas. The difference between them is the 1 − 1/(1 + r)t term.To be three-quarters of the value, this term has to be 3/4. So you must solve 1 − 1/(1 + r)t =
g = r − E/P = 12% − $5/$100 = 7% per annum
First work out what the value would be if you stood at 1 month. The interest rate is (1 + 9%)1/12 − 1 ≈0.7207% per month, and 1.0072073 − 1 ≈ 2.1778% per quarter. Thus, in 1 month, you will
The immediate dividend would be worth $1.5 million. In addition, you now have a growing perpetuity that starts with a payment of $1.530 million. Therefore, the PV would be $1.500 + $1.530/12% =
$1.5 million/(14% − 2%) = $12.5 million.
Your earnings will be as follows:Therefore, the PV is $884 million fromcash flows that you computed explicitly, plus $4,540 million fromthe cash flows that is the terminal value stand-in for all cash
This is a nonsensical question, because the value would be infinite if g ≥ r.
You get C0= $5 today, and next month you will receive a payment of C1= (1 + g) . C0= 1.001 . $5 =$5.005. The growing perpetuity is worth PV = C1/(r − g) = $5.005/(0.5% − 0.1%) = $1,251.25. The
C1/(r − g).
PV = $2,000/4% = $50,000
Rearrange P = C1/r into r = C1/P = $2/$40 = 5%. At a 5%interest rate you are indifferent. If the interest rate is above 5%, the immediate one-time payment is better, because future cash flows are
The interest rate is 1.1268(1/12) − 1 ≈ 1% per month. Thus, PV = C1/r ≈ $15/0.01 ≈ $1,500.
PV = C1/r = $5/0.005 = $1,000
C1/r. The first cash flow occurs next period, not this period.
In many defined-contribution pension plans, the employer provides a fixed-percentage contribution to the employee’s retirement. Assume that you must contribute $4,000 per annum beginning next
Check that the rates of return in the coupon bond valuation example on page 52 are correct.
Assume that the 3% level-coupon bond discussed in this chapter has not just 5 years with 10 payments, but 20 years with 40 payments. Also, assume that the interest rate is not 5% per annum, but

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