Questions and Answers of Theory Of Corporate Finance

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
You already learned that the value of one fixed future payment and the interest rate move in opposite directions (page 28). What happens to the bond price of $91,501.42 in the level-coupon bond
What is the monthly payment on a 15-year mortgage for every $1,000 of mortgage at an effective interest rate of 6.168% per year (here, 0.5%per month)?
Rental agreements are notmuch different frommortgages. For example, what would your rate of return be if you rented your $500,000 warehouse for 10 years at amonthly lease payment of $5,000? If you
In L’Arithmetique, written in 1558, Jean Trenchant posed the following question: “In the year 1555, King Henry, to conduct the war, took money from bankers at the rate of 4% per fair [quarter].
Solve Fibonacci’s annuity problem given in the Anecdote: Compare the PV of a stream of quarterly cash flows of 75 bezants versus the PV of a stream of annual cash flows of 300 bezants. Payments are
What is the PV of a 360-month annuity paying $5 permonth, beginning at $5 next month (time 1), if the monthly interest rate is a constant 0.5%/month (6.2%/year)?
Recall from memory the annuity formula.
How many years does it take for an annuity to reach three-quarters the value of a perpetuity if the interest rate is 5%? If the interest rate is r? To reach fraction f of the value?
How would the patent contract value change if the first payment did not occur next year, but tonight?
An eternal patent contract states that the patentee will pay the patentor a fee of $1.5 million next year. The contract terms state a fee growth with the inflation rate, which runs at 2% per annum.
Here is an example of the most common use of the growing perpetuity model (called a pro forma). Your firm just finished the year, in which it had cash earnings of $100 million. You forecast your firm
What is the PV of a perpetuity paying $8 each month, beginning this month (in 1 second), if the monthly interest rate is a constant 0.5%/month (6.2%/year) and the cash flows will grow at a rate of
What is the PV of a perpetuity paying $5 each month, beginning this month (in 1 second), if the monthly interest rate is a constant 0.5%/month (6.2%/year) and the cash flows will grow at a rate of
From memory, write down the growing perpetuity formula.
In Britain, there are Consol bonds that are perpetuity bonds. (In the United States, the IRS does not allow companies to deduct the interest payments on perpetual bonds, so U.S. corporations do not
Under what interest rates would you prefer a perpetuity that pays $2 million per year beginning next year to a one-time payment of $40 million?
What is the PV of a perpetuity paying $15 each month, beginning next month, if the effective annual interest rate is a constant 12.68% per year?
What is the PV of a perpetuity paying $5 each month, beginning next month, if the monthly interest rate is a constant 0.5%/month?
From memory, write down the perpetuity formula. Be explicit on when the first cash flow occurs.
The prevailing discount rate is 15% per annum.Firm F’s cash flows start with $500 in year 1 and grow at 20% per annum for 3 years.Firm S’s cash flows also start with $500 in year 1 but shrink at
If the interest rate is 5% per annum, what would be the equivalent annual cost (see Question 2.39) of a $2,000 lease payment up front, followed by $800 for three more years?
Assume you are a real estate broker with an exclusive contract—the condo association rules state that everyone selling their condominiums must go through you or a broker designated by you. A
A project has the following cash flows in periods 1 through 4: −$200, +$200, −$200,+$200. If the prevailing interest rate is 3%, would you accept this project if you were offered an upfront
Assume you are 25 years old. The IAW insurance company is offering you the following retirement contract (called an annuity): Contribute$2,000 per year for the next 40 years.When you reach 65 years
On April 12, 2006, Microsoft stock traded for$27.11 and claimed to pay an annual dividend of $0.36. Assume that the first dividend will be paid in 1 year, and that it then grows by 5%each year for
Consider the same project that costs $25,000 with cash flows of $15,000, $10,000, and$5,000. At what prevailing interest rate would this project be profitable? Try different interest rates, and plot
A project has cash flows of $15,000, $10,000, and $5,000 in 1, 2, and 3 years, respectively. If the prevailing interest rate is 15%, would you buy the project if it costs $25,000?
You can choose between the following rent payments:(a) A lump sum cash payment of $100,000;(b) 10 annual payments of $12,000 each, the first occurring immediately;(c) 120 monthly payments of $1,200
What is the 1-year discount factor if the interest rate is 33.33%?
Go to the website of a bank of your choice.What kind of quote does your bank post for a CD, and what kind of quote does your bank post for a mortgage?Why?
A bank quotes you a loan interest rate of 14%on your credit card. If you charge $15,000 at the beginning of the year, how much will you have to repay at the end of the year?
From Fibonacci’s Liber Abaci, written in the year 1202: “A certain man gave 1 denaro at interest so that in 5 years he must receive double the denari, and in another 5, he must have double 2 of
If the interest rate is 8% per annum, how long will it take to double your money?
If the interest rate is 5% per annum, how long will it take to double your money? How long will it take to triple it?
There is always disagreement about what stocks are good purchases. The typical degree of disagreement is whether a particular stock is likely to offer, say, a 10% (pessimistic) or a 20% (optimistic)
An investment for $50,000 earns a rate of return of 1% in each month of a full year. How much money will you have at year’s end?
A project returned +50%, then −40%. Thus, its arithmetic average rate of return was +5%.Is your rate of return positive or negative?
A project returned +30%, then −30%. Thus, its arithmetic average rate of return was 0%.If you invested $25,000, how much did you end up with? Is your rate of return positive or negative? How would
Over 20 years, would you prefer 10% per annum, with interest compounding, or 15%per annum but without interest compounding?(That is, you receive the interest, but it is put into an account that earns
Assume an interest rate of 10% per year. How much would you lose over 5 years if you had to give up interest on the interest—that is, if you received 50% instead of compounded interest?

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