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Corporate Finance
In the Hull-White model, a = 0.08 and σ = 0.01. Calculate the price of a one-year European call option on a zero-coupon bond that will mature in five years when the term structure is flat at 10%,
Suppose that a = 0.05 and σ = 0.015 in the Hull-White model with the initial term structure being flat at 6% with semiannual compounding. Calculate the price of a 2.1-year European call option on a
Suppose a = 0.05, σ = 0.015, and the term structure is flat at 10%. Construct a trinomial tree for the Hull-White model where there are two time steps, each one year in length.
Explain the difference between a Markov and a non-Markov model of the short rate.
"An option adjusted spread is analogous to the yield on a bond." Explain this statement.
Prove the formula for the variance, V(T), of the swap rate in equation (33.17).
Show that the result in (33.19) is correct..
In an annual-pay cap the Black volatilities for at-the-money caplets which start in one, two, three, and five years and end one year later are 18%, 20%, 22%, and 20%, respectively. Estimate the
(a) The holder can choose whether any caplet is exercised, but there is a limit of N on the total number of caplets that can be exercised.(b) Once the holder chooses to exercise a caplet all
Prove the relationship between the drift and volatility of the forward rate for the multifactor version of HJM in equation (33.6).
"When the forward rate volatility s(t, T) in HJM is constant, the Ho-Lee model results." Verify that this is true by showing that HJM gives a process for bond prices that is consistent with the
"When the forward rate volatility, s(t, T) in HJM is σe-a(T-t) the Hull-White model results." Verify that this is true by showing that HJM gives a process for bond prices that is consistent with the
What is the advantage of LMM over HJM?
Provide an intuitive explanation of why a ratchet cap increases in value as the number of factors increase.
Show that equation (33.10) reduces to (33.4) as the δi tend to zero.
Explain why a sticky cap is more expensive than a similar ratchet cap.
Explain why IOs and POs have opposite sensitivities to the rate of prepayments
Suppose that you are trading a LIBOR-in-arrears swap with an unsophisticated counterparty that does not make convexity adjustments. To take advantage of the situation, should you be paying fixed or
Suppose that all 12-month LIBOR forward rates are 5% with annual compounding. The OIS zero curve is flat at 4.8% with continuous compounding. In a five-year swap, company X pays a fixed rate of 6%
How would you calculate the initial value the equity swap in Business Snapshot 34.3 if OIS discounting were used?
Suppose that a swap specifies that a fixed rate is exchanged for twice the LIBOR rate. Can the swap be valued using the "assume forward rates are realized" rule?
What is the value of a two-year fixed-for-floating compounding swap where the principal is $100 million and payments are made semiannually? Fixed interest is received and floating is paid. The fixed
What is the value of a five-year swap where LIBOR is paid in the usual way and in return LIBOR compounded at LIBOR is received on the other side? The principal on both sides is $100 million. Payment
Calculate the total convexity/timing adjustment in Example 34.3 of Section 34.4 if all cap volatilities are 18% instead of 20% and volatilities for all options on five-year swaps are 13% instead of
Explain why a plain vanilla interest rate swap and the compounding swap in Section 34.2 can be valued using the "assume forward rates are realized" rule, but a LIBOR-in-arrears swap in Section 34.4
In the accrual swap discussed in the text, the fixed side accrues only when the floating reference rate lies below a certain level. Discuss how the analysis can be extended to cope with a situation
LIBOR zero rates are flat at 5% in the U.S and flat at 10% in Australia (both annually compounded). In a four-year diff swap Australian LIBOR is received and 9% is paid with both being applied to a
What is meant by HDD and CDD?
What are the characteristics of an energy source where the price has a very high volatility and a very high rate of mean reversion? Give an example of such an energy source.
How can an energy producer use derivative markets to hedge risks?
Explain how a 5 × 8 option contract for May 2017 on electricity with daily exercise works. Explain how a 5 × 8 option contract for May 2017 on electricity with monthly exercise works. Which is
Explain how CAT bonds work.
Consider a commodity with constant volatility σ and an expected growth rate that is a function solely of time. Show that, in the traditional risk-neutral world, where ST is the value of the
How is the tree in Figure 35.2 modified if the 1- and 2-year futures prices are $21 and $22 instead of $22 and $23, respectively. How does this affect the value of the American option in Example 35.3.
How is a typical natural gas forward contract structured?
Distinguish between the historical data and the risk-neutral approach to valuing a derivative. Under what circumstances do they give the same answer?
Suppose that each day during July the minimum temperature is 68° Fahrenheit and the maximum temperature is 82° Fahrenheit. What is the payoff from a call option on the cumulative CDD during July
Why is the price of electricity more volatile than that of other energy sources?
Why is the historical data approach appropriate for pricing a weather derivatives contract and a CAT bond?
Would you expect the volatility of the one-year forward price of oil to be greater than or less than the volatility of the spot price? Explain your answer.
Explain the difference between the net present value approach and the risk-neutral valuation approach for valuing a new capital investment opportunity. What are the advantages of the risk-neutral
The market price of risk for copper is 0.5, the volatility of copper prices is 20% per annum, the spot price is 80 cents per pound, and the six-month futures price is 75 cents per pound. What is the
Show that, if y is a commodity's convenience yield and u is its storage cost, the commodity's growth rate in a risk-neutral world is r − y + u, where r is the risk-free rate. Deduce the
The correlation between a company's gross revenue and the market index is 0.2. The excess return of the market over the risk-free rate is 6% and the volatility of the market index is 18%. What is the
A company can buy an option for the delivery of one million units of a commodity in three years at $25 per unit. The three year futures price is $24. The risk-free interest rate is 5% per annum with
A driver entering into a car lease agreement can obtain the right to buy the car in four years for $10,000. The current value of the car is $30,000. The value of the car, S, is expected to follow the
Suppose that the spot price, 6-month futures price, and 12-month futures price for wheat are 250, 260, and 270 cents per bushel, respectively. Suppose that the price of wheat follows the process in
In the example considered in Section 36.5(a) What is the value of the abandonment option if it costs $3 million rather than zero?(b) What is the value of the expansion option if it costs $5 million
A company just paid a dividend of $1.30 per share. The consensus forecast of financial analysts is a dividend of $1.80 per share next year and $2.20 per share two years from now. Thereafter, you
Suppose you plan to retire at age 70, and you want to be able to withdraw an amount of $62,000 per year on each birthday from age 70 to age 100 (a total of 31 withdrawals). If the account which
A company is considering a 5-year project to open a new product line. A new machine with an installed cost of $110,000 would be required to manufacture their new product, which is estimated to
A company has a proposed 2-year project with the cash flows shown below and would like to calculate the NPV of this project so that they can decide whether to pursue the project or not. The company
On January 1, 2009, your brother's business obtained a 30-year amortized mortgage loan for $250,000 at a nominal annual rate of 7.0%, with 360 end-of-month payments. The firm can deduct the interest
Write a memo to Mr. Hillbrandt and comment on the three questions below. Limit the memo to four or five paragraphs since CEOs want an initial succinct explanation to accompany the financial
You are CEO of Acme, Inc. located in the United States. You use the discounted payback period method and accept all projects that payback in three years. You are considering a project that will cost
Project A has cash flows of -$50,000, $29,400, $27,200, and $24,500 for years 0 to 3, respectively. Project B has an initial cost of $50,000 and an annual cash inflow of $26,500 for three years.
Your employer has agreed to place year-end deposits of $2,000, $3,000 and $4,000 into your retirement account. The $2,000 deposit will be one year from today, the $3,000 deposit two years from today,
Koy Corporation's 5-year bonds yield 7.00%, and 5-year T-bonds yield 5.15%. The real risk-free rate is r * = 3.0%, the inflation premium for 5-year bonds is IP = 1.75%, the liquidity premium for
Roadside Markets has a 6.75 percent coupon bond outstanding that matures in 10.5 years. The bond pays interest semiannually. What is the market price per bond if the face value is $1,000 and the
1. You have the following capital budgeting timeline:0 = ($21,000),1 = $6109,2 = $7276,3 = ?,4 = $4902,5 = $4195,6 = $6986.The discounted payback for the timeline is 4.626. k = 9.85%. What is the
The risk-free rate, KRF, is 6 percent and the market risk premium, (KM - KRF), is 5 percent. Assume that required returns are based on the CAPM. Your $1 million portfolio consists of $700,000
Suppose that market demand for answering machines is given by the expression QD = 1,000 - 150P + 25I. Assume that per capita disposable income I = $200 and the price of answering machines is P =
$1,000 is expected to be received 10 years from now. The present value of this $1,000 future cash flow is: 1: Always greater than $1,000. 2: Greater if the interest rate goes up. 3: Less than $1,000
A company has the opportunity to do any, none, or all of the projects for which the net cash flows per year are shown below. The company has a cost of capital of 12%. Which should the company do
Kenney Corporation reported the following income statement for the most recent year (numbers are in millions of dollars):Sales $7,000Total operating costs 3,000EBIT $4,000Interest 200Earnings before
An adjustable rate mortgage with a teaser start rate of 1.5%, an index of six month LIBOR, a margin of 2.0%, and periodic and lifetime caps of 2/6 with semi-annual adjustments, would have a maximum
You have just taken out a 10-year, $12,075 loan to purchase a new car. This loan is to be repaid in 120 equal end-of-month installments. If each of the monthly installments is $150, what is the
Your uncle has $1,025,000 and wants to retire. He expects to live for another 25 years, and he also expects to earn 7.5% on his invested funds. How much could he withdraw at the beginning of each of
Sam was injured in an accident, and the insurance company has offered him the choice of $49,000 per year for 15 years, with the first payment being today, or a lump sum. If a fair return is 7.5%, how
Last year Blease Inc had a total assets turnover of 1.33 and an equity multiplier of 1.75. Its sales were $295,000 and its net income was $10,600. The CFO believes that the company could have
One year ago, you purchased a 5-year, $1,000 face value, 6 percent coupon bond for $1,012. Interest is paid semi-annually. Today, you sold the bond at a market rate of return of 6.27 percent. What is
If a firms debt-to-equity ratio is 2.6, what is its total debt to total asset ratio?
Suppose that a firm is facing an upward-sloping yield curve and needs to borrow money to invest in production. Does this mean that the firm should consider borrowing only at short-term rates? A. Yes,
Moon software Inc. is planning to issue two types of 25-year. Non-callable bonds to raise a total of $6 million, $3 million from each type of bond. First, 3,000 bonds with a 10% semiannual coupon
Ritz Company sells fine collectible statues and has implemented activity-based costing. Costs in the shipping department have been divided into three cost pools. The first cost pool contains costs
You begin with 16 quarters, 4 years and then your job is up for review. You begin with rates at 4.5, inflation at 2.14% and unemployment at 4.75%. Make decisions on interest rates for the 16
The Rug Barn has paid annual dividends of $1.30, $1.36, $1.40, $1.42, and $1.45 over the last 5 years, respectively. What is the geometric average dividend growth rate?A). 2.77%B). 2.55%C). 2.11%D).
A new inventory management system for ABC Company could be developed at a cost of$260,000.The estimated net operating costs and estimated net benefits over six years of operationwould be:a. What
You have developed the following data on three stocks: Stock A has a standard deviation of .15 and a Beta of .79. Stock B has a standard deviation of .25 and a Beta of .61. Stock C has a standard
A retirement plan guarantees to pay to you or your estate a fixed amount for 20 years. At the time of retirement you will have $73,425 to your credit in the plan. the plan anticipates earning 9%
Jorge Cabrera paid $980 for a 15-year bond 10 years ago. The bond pays a coupon of 10 percent semiannually. Today, the bond is priced at $1,054.36. If he sold the bond today, what would be his
DYI Construction Co. is considering a new inventory system that will cost $750,000. The system is expected to generate positive cash flows over the next four years in the amounts of $350,000 in year
At shaw's Market, apples cost $10 per case and bananas cost $6 per case, if an order comes in for a total of 300 cases for $2,000, what was the specific number of cases of apples? A. 5 B. 15 C. 50 D.
High Tech Wireless just published its 2014 income statement, which shows net income equal to $240,000. The statement also shows that operating expenses were $500,000 before including depreciation,
One year ago, the Chinese e-commerce company Alibaba Group floated its shares in the biggest Initial Public Offering in US history. Alibaba Group priced its shares at $68 raising $21.8 bn and valuing
Amy is 12 years old now and will attend college at age 18. Her parents plan to fund her college for four years. College costs $20,000 per year as of the time when Amy turns to age 18. If her parents
Two stocks are available. The corresponding expected rates are r1 and r2; the corresponding variances and covariance’s are σ12, σ22, and σ12. What percentages of total investment should be
Last year Harrington Inc. had sales of $325,000 and a net income of $19,000, and its year-end assets were $250,000. The firm's total-debt-to-total-assets ratio was 67.5%. Based on the DuPont
DEFINE the term financial intermediary. What role to financial intermediaries play in U.S. corporate finance? How does this compare to the role of non-U.S. financial intermediaries?
Sally Mander is planning on retiring in 30 years and she believes that she will live for 25 years after she retires. To play it safe, Sally would like to set up a retirement plan that will pay
Lory Company has a total debt to total assets ratio of 45% and a current ratio of 4.1. The firm's stock sells for $ 71.0 per share. The total market value of the equity is $ 43.6 million. The
Discuss the various issues that must be considered in selecting an investment banker for an IPO. Which type of placement is usually preferred by the issuing firm? Why?
The Distribution Point plans to save $2,000 a month for the next 3 years for future emergencies. The interest rate is 4.5 percent compounded monthly. The first monthly deposit will be made today.
Johnson Entertainment Systems is setting up to manufacture a new line of video game consoles. The cost of the manufacturing equipment is $1,750,000. Expected cash flows over the next four years are
Assume that the corporate tax rate is 34% and the personal tax rate is 35%. The founders of a newly formed business are debating between setting-up the firm as a partnership versus a corporation. The
You have contracted to buy a house for $250,000, paying $30,000 down and taking out fully amortizing loan for the balance, at a 5.7% annual rate for 30 years. What will your monthly payment be
Suppose you were selling your home. A buyer has offered to pay you $115,000 now and another $85,000 in 2 years. What is the value today of the payment received in 2 years, given your required rate of
Tom's Hardware has inventory of $318,000, equity of $421,800, total assets of $647,700, and sales of $687,400. What is the common-size percentage for the inventory account?
1. Vernon is a cash basis taxpayer with a calendar tax year. On October 1, 2014 he entered into a lease to rent a building for use in his business at $3,000 a month. On that day Vernon paid 18 months
Domremy Drywall Inc. needs to purchase new equipment to better service its client accounts. The cost of the equipment is $175,000. It is estimated that the firm will save $35,000 annually (after tax)
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