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theory of corporate finance

Questions and Answers of Theory Of Corporate Finance

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?
The interest rate has just increased from 6% to 8%. How many basis points is this?
Your stock costs $100 today, pays $5 in dividends at the end of the period, and then sells for $98.What is your rate of return?
In the text, I assumed you received the dividend at the end of the period. In the real world, if you received the dividend at the beginning of the period instead of the end of the period, could this
What is the difference between a bond and a loan?
What is a perfect market? What were the assumptions made in this chapter that were not part of the perfect market scenario?
No! The market will already have adjusted the price.
Again, call 2000 your year 0. The firm’s present value in 2000 is based on dividends of $100, $150, and $250 in the next three years. The firm value in 2000 is the $402.70 from page 33. The firm
For easier naming, call 2000 your year 0. The firm’s present value in 2000 is $536/1.103 ≈ $402.70—but you already knew this. If you purchase this company, its value in 2001 depends on a cash
Lease A has an NPV of −$6,535. Lease B has an NPV of −$6,803. Therefore, lease A is cheaper.
For the 3-year building leases:(a) Your preference depends on the interest rate. If the interest rate is zero, then you would prefer the $2 million sum-total payment to the $2.1 million rent. If the
−$900 + $200/(1.08)1 + $200/(1.08)2 + $400/(1.08)3 + $400/(1.08)4 − $100/(1.08)5 ≈ $0.14. The NPV is positive. Therefore this is a worthwhile project that you should accept.
Accept if NPV is positive. Reject if NPV is negative.
If you cannot write down the NPV formula by heart, do not go on until you have it memorized.
The first tuition payment is worth $30,000/(1.06)1/2 ≈ $29,139. The second tuition payment is worth$30,000/(1.06)3/2 ≈ $27,489. Thus, the total present value is $56,628.
The original interest rate is $100/$95 − 1 ≈ 5.26%. Increasing the interest rate by 150 basis points is 6.76%.This means that the price should be $100/(1.0676) ≈ $93.67. A price change from $95
Good. Your future payments would be worth less in today’s money.
The rate of return and additional factors are unit-less. The latter two are in dollars (though the former is dollars in the future, while the latter is dollars today).
It is today’s value in dollars for 1 future dollar, that is, at a specific point in time in the future.
1/[(1.05) . (1.05)] ≈ 0.9070
$150/[1 + (5%/365)]365 ≈ $142.68
$150/(1.05) ≈ $142.86
r = 30% = ($250 − x)/x. Thus, x = $250/1.30 ≈ $192.31.
The bank quote of 8% means that you will have to pay an interest rate of 8%/12 ≈ 0.667% per month. This earns an actual interest rate of (1 + 0.667%)12 − 1 ≈ 8.30% per annum. You will have to
The bank quote of 6% means that it will pay an interest rate of 6%/365 ≈ 0.0164384% per day. This earns an actual interest rate of (1 + 0.0164384%)365 − 1 ≈ 6.18% per annum. Therefore, each
With 12% in nominal APR interest quoted, you earn 12%/365 ≈ 0.032877% per day. Therefore, the annual rate of return is (1 + 0.032877%)365 − 1 ≈ 12.747462%. Your $100,000 will grow into
With 12% in nominal APR interest quoted, you earn 12%/365 ≈ 0.032877% per day. Therefore, the weekly rate of return is (1 + 0.032877%)7 − 1 ≈ 0.23036%. Your $100,000 will grow into $100,230.36.
The true daily interest rate, assuming 365 days, is 1.121/365 − 1 ≈ 0.031054%. To compute your true rate of return, compound this over 7 days: (1 + 0.03105%)7 = 1.000310547 ≈ 1.0021758. (You
The bank means to collect 12%/365 ≈ 3.288 bp/day.
(1 + r)365 = 1.12. Therefore, 1.12(1/365) − 1 ≈ 0.00031054 = 0.031054% ≈ 3.1 bp/day.
Tripling is equivalent to earning a rate of return of 200%. Therefore, solve (1 + 6%)x = (1 + 200%), or x . log(1.06) = log(3.00) or x = log(3.00)/ log(1.06) ≈ 18.85 years.
r100= (1 + r1)100 − 1 = 1.05100 − 1 = 130.5 ≈ 13,050%. In words, this is about 130 times the initial investment, and substantially more than 500% (5 times the initial investment).
r10= (1 + r1)10 − 1 = 1.0510 − 1 ≈ 62.89%
r2= (1 + r0, 1) . (1 + r1, 2) − 1 = 1.05 . 1.05 − 1 = 10.25%
(1 + r0.25)4 = (1 + r1). Thus, r0.25= 4√1 + r1− 1 = 1.51/4 − 1 ≈ 10.67%.
(1 + 100%)1/5 − 1 ≈ 14.87%
Losing one-third is a rate of return of −33%. To find the holding rate of return, compute [1 + (−1/3)]5 − 1≈ −86.83%. About (1 − 86.83%) . $20,000 ≈ $2,633.74 remains.
The total holding rate of return is 1.0520 − 1 ≈ 165.33%, so you would end up with $200 .(1 + 165.33%) ≈ $530.66.
$2,000 . 1.2515 ≈ $56,843.42
1.205 − 1 ≈ 148.83%
r = 30% = (x − $250)/$250 ⇒ x = 1.3 . $250 = $325
20 basis points are 0.2%, so the interest rate declined from 10.0% to 9.8%.
1% = 100 basis points, so an increase of 3% is 300 basis points.
The dividend yield would be $1/$40 = 2.5%, the capital gain would be $45 − $40 = $5, so that its capital gain yield would be $5/$40 = 12.5%, and the total rate of return would be ($46 − $40)/$40
Yes, 10 = 1,000%.
r = $25$1, 000= 2.5%
r = ($1,050 − $1,000)/$1,000 = 5%
A savings deposit is an investment in a series of short-term bonds.
The four perfect market assumptions are no taxes, no transaction costs, no differences in opinions, and no large buyers or sellers.
One month ago, a firm suffered a large court award against it that will force it to pay compensatory damages of $100 million next January 1.Are shares in this firm a bad buy until January 2?
Assume that company G pays out the full cash flows (refer to the text example) in earnings each period.What is G’s market value at time 1, 2, and 3?What is your rate of return in each year?
Assume that company G pays no interim dividends, so you receive $536 at the end of the project. What is G’s market value at time 1, 2, and 3?What is your rate of return in each year? Assume that
Use a spreadsheet to answer the following question: Car dealer A offers a car for $2,200 up front (first payment), followed by $200 lease payments over the next 23 months. Car dealer B offers the
You are considering a 3-year lease for a building, where you have to make one payment now, one in a year, and a final one in 2 years.(a) Would you rather pay $1,000,000 up front, then $500,000 each
Determine the NPV of the project in Table 2.1, if the per-period interest rate were 8% per year, not 5%. Should you take this project?
What is the NPV capital budgeting rule?
Write down the NPV formula from memory.
Work out the present value of your tuition payments for the next 2 years.Assume that the tuition is $30,000 per year, payable at the start of the year. Your first tuition payment will occur in
The price of a bond that offers a safe promise of $100 in 1 year is $95.What is the implied interest rate? If the bond’s interest rate suddenly jumped up by 150 basis points, what would the bond
Would it be good or bad for you, in terms of the present value of your liabilities, if your opportunity cost of capital increased?
What are the units on rates of return, discount factors, future values, and present values?

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