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Questions and Answers of
Corporate Finance
Compute estimated profit in 1 year if Telco buys a call option with a strike of $0.95, $1.00, or $1.05. Draw a graph of profit in each case.€¢XYZ mines copper, with fixed costs of $0.50/lb and
Compute estimated profit in 1 year if Telco sells a put option with a strike of $0.95, $1.00, or $1.05. Draw a graph of profit in each case.€¢XYZ mines copper, with fixed costs of $0.50/lb and
Construct Table 5.1 from the perspective of a seller, providing a descriptive name for each of the transactions.
The S&R index spot price is 1100 and the continuously compounded risk-free rate is 5%. You observe a 9-month forward price of 1129.257.a. What dividend yield is implied by this forward price?b.
Suppose the S&P 500 index futures price is currently 1200. You wish to purchase four futures contracts on margin.a. What is the notional value of your position?b. Assuming a 10% initial margin,
Suppose the S&P 500 index is currently 950 and the initial margin is 10%. You wish to enter into 10 S&P 500 futures contracts.a. What is the notional value of your position? What is the
Verify that going long a forward contract and lending the present value of the forward price creates a payoff of one share of stock whena. The stock pays no dividends.b. The stock pays discrete
Verify that when there are transaction costs, the lower no-arbitrage bound is given by equation (5.12).
Suppose the S&R index is 800, and that the dividend yield is 0. You are an arbitrageur with a continuously compounded borrowing rate of 5.5% and a continuously compounded lending rate of 5%.
Suppose the S&P 500 currently has a level of 875. The continuously compounded return on a 1-year T-bill is 4.75%. You wish to hedge an $800,000 portfolio that has a beta of 1.1 and a correlation
Suppose you are selecting a futures contract with which to hedge a portfolio. You have a choice of six contracts, each of which has the same variability, but with correlations of −0.95, −0.75,
Suppose the current exchange rate between Germany and Japan is 0.02 =C/¥. The euro-denominated annual continuously compounded risk-free rate is 4% and the yen-denominated annual continuously
Suppose the spot $/¥ exchange rate is 0.008, the 1-year continuously compounded dollar-denominated rate is 5% and the 1-year continuously compounded yendenominated rate is 1%. Suppose the 1-year
A $50 stock pays a $1 dividend every 3 months, with the first dividend coming 3 months from today. The continuously compounded risk-free rate is 6%.a. What is the price of a prepaid forward
Suppose we wish to borrow $10 million for 91 days beginning next June, and that the quoted Eurodollar futures price is 93.23.a. What 3-month LIBOR rate is implied by this price?b. How much will
A $50 stock pays an 8% continuous dividend. The continuously compounded riskfree rate is 6%.a. What is the price of a prepaid forward contract that expires 1 year from today?b. What is the price
Suppose the stock price is $35 and the continuously compounded interest rate is 5%.a. What is the 6-month forward price, assuming dividends are zero?b. If the 6-month forward price is
Suppose you are a market-maker in S&R index forward contracts. The S&R index spot price is 1100, the risk-free rate is 5%, and the dividend yield on the index is 0.a. What is the no-arbitrage
Repeat the previous problem, assuming that the dividend yield is 1.5%.
The S&R index spot price is 1100, the risk-free rate is 5%, and the dividend yield on the index is 0.a. Suppose you observe a 6-month forward price of 1135. What arbitrage would you
The S&R index spot price is 1100, the risk-free rate is 5%, and the continuous dividend yield on the index is 2%.a. Suppose you observe a 6-month forward price of 1120. What arbitrage would you
Suppose that 10 years from now it becomes possible for money managers to engage in time travel. In particular, suppose that a money manager could travel to January 1981, when the 1-year Treasury bill
The spot price of a widget is $70.00 per unit. Forward prices for 3, 6, 9, and 12 months are $70.70, $71.41, $72.13, and $72.86. Assuming a 5% continuously compounded annual risk-free rate, what are
Using Table 6.6, what is your best guess about the current price of gold per ounce? Explain with detail.
Consider production ratios of 2:1:1, 3:2:1, and 5:3:2 for oil, gasoline, and heating oil. Assume that other costs are the same per gallon of processed oil.a. Which ratio maximizes the per-gallon
Suppose you know nothing about widgets. You are going to approach a widget merchant to borrow one in order to short-sell it. (That is, you will take physical possession of the widget, sell it, and
The current price of oil is $32.00 per barrel. Forward prices for 3, 6, 9, and 12 months are $31.37, $30.75, $30.14, and $29.54. Assuming a 2% continuously compounded annual risk-free rate, what is
Given a continuously compounded risk-free rate of 3% annually, at what lease rate will forward prices equal the current commodity price? (Recall the copper example in Section 6.3.) If the lease rate
Suppose that copper costs $3.00 today and the continuously compounded lease rate for copper is 5%. The continuously compounded interest rate is 10%. The copper price in 1 year is uncertain and copper
Suppose the gold spot price is $300/oz, the 1-year forward price is 310.686, and the continuously compounded risk-free rate is 5%.a. What is the lease rate?b. What is the return on a cash-and-carry
a. What are some possible explanations for the shape of this forward curve?b. What annualized rate of return do you earn on a cash-and-carry entered into in December of Year 0 and closed in March of
a. Suppose that you want to borrow a widget beginning in December of Year 0 and ending in March of Year 1. What payment will be required to make the transaction fair to both parties?b. Suppose that
a. Suppose the March Year 1 forward price were $3.10. Describe two different transactions you could use to undertake arbitrage.b. Suppose the September Year 1 forward price fell to $2.70 and
Consider Example 6.1. Suppose the February forward price had been $2.80. What would the arbitrage be? Suppose it had been $2.65. What would the arbitrage be? In each case, identify the transactions
Suppose you observe the following par coupon bond yields: 0.03000 (1-year), 0.03491 (2-year), 0.03974 (3-year), 0.04629 (4-year), 0.05174 (5-year). For each maturity year compute the zero-coupon bond
What is the rate on a synthetic FRA for a 90-day loan commencing on day 90? A 180-day loan commencing on day 90? A 270-day loan commencing on day 90?
What is the rate on a synthetic FRA for a 180-day loan commencing on day 180? Suppose you are the counterparty for a borrower who uses the FRA to hedge the interest rate on a $10m loan. What
Suppose you are the counterparty for a lender who enters into an FRA to hedge the lending rate on $10m for a 90-day loan commencing on day 270. What positions in zero-coupon bonds would you use to
Using the information in Table 7.1, suppose you buy a 3-year par coupon bond and hold it for 2 years, after which time you sell it. Assume that interest rates are certain not to change and that you
As in the previous problem, consider holding a 3-year bond for 2 years. Nowsuppose that interest rates can change, but that at time 0 the rates in Table 7.1 prevail. What transactions could you
Consider the implied forward rate between year 1 and year 2, based on Table 7.1.a. Suppose that r0(1, 2) = 6.8%. Showhowbuying the 2-year zero-coupon bond and borrowing at the 1-year rate and implied
Suppose the September Eurodollar futures contract has a price of 96.4. You plan to borrow $50m for 3 months in September at LIBOR, and you intend to use the Eurodollar contract to hedge your
A lender plans to invest $100m for 150 days, 60 days from today. (That is, if today is day 0, the loan will be initiated on day 60 and will mature on day 210.) The implied forward rate over 150 days,
Consider the same facts as the previous problem, only nowconsider hedging with the 3-month Eurodollar futures. Suppose the Eurodollar futures contract that matures 60 days from today has a price on
Consider the bonds in Example 7.8. What hedge ratio would have exactly hedged the portfolio if interest rates had decreased by 25 basis points? Increased by 25 basis points? Repeat assuming a
Using the information in the previous problem, find the price of a 5-year coupon bond that has a par payment of $1,000.00 and annual coupon payments of $60.00.
Compute Macaulay and modified durations for the following bonds:a. A 5-year bond paying annual coupons of 4.432% and selling at par.b. An 8-year bond paying semiannual coupons with a coupon
Consider the following two bonds which make semiannual coupon payments: a 20 year bond with a 6% coupon and 20% yield, and a 30-year bond with a 6% coupon and a 20% yield.a. For each bond, compute
An 8-year bond with 6% annual coupons and a 5.004% yield sells for $106.44 with a Macaulay duration of 6.631864. A 9-year bond has 7% annual coupons with a 5.252% yield and sells for $112.29 with a
A 6-year bond with a 4% coupon sells for $102.46 with a 3.5384% yield. The conversion factor for the bond is 0.90046. An 8-year bond with 5.5% coupons sells for $113.564 with a conversion factor of
a. Compute the convexity of a 3-year bond paying annual coupons of 4.5% and selling at par.b. Compute the convexity of a 3-year 4.5% coupon bond that makes semiannual coupon payments and that
Suppose a 10-year zero-coupon bond with a face value of $100 trades at $69.20205.a. What is the yield to maturity and modified duration of the zero-coupon bond?b. Calculate the approximate
Suppose you observe the following effective annual zero-coupon bond yields: 0.030 (1-year), 0.035 (2-year), 0.040 (3-year), 0.045 (4-year), 0.050 (5-year). For each maturity year compute the
Suppose you observe the following 1-year implied forward rates: 0.050000 (1 year), 0.034061 (2-year), 0.036012 (3-year), 0.024092 (4-year), 0.001470 (5-year). For each maturity year compute the
Suppose you observe the following continuously compounded zero-coupon bond yields: 0.06766 (1-year), 0.05827 (2-year), 0.04879 (3-year), 0.04402 (4-year), 0.03922 (5-year). For each maturity year
Suppose you observe the following par coupon bond yields: 0.03000 (1-year), 0.03491 (2-year), 0.03974 (3-year), 0.04629 (4-year), 0.05174 (5-year). For each maturity year compute the zero-coupon bond
Using the information in Table 7.1,a. Compute the implied forward rate from time 1 to time 3.b. Compute the implied forward price of a par 2-year coupon bond that will be issued at time 1.
Suppose that in order to hedge interest rate risk on your borrowing, you enter into an FRAthat will guarantee a 6%effective annual interest rate for 1 year on $500,000.00.On the date you borrow the
Using the same information as the previous problem, suppose the interest rate on the borrowing date is 7.5%. Determine the dollar settlement of the FRA assuminga. Settlement occurs on the date the
Suppose that 1- and 2-year oil forward prices are $22/barrel and $23/barrel. The 1 and 2-year interest rates are 6% and 6.5%. Show that the new 2-year swap price is $22.483.
Using the zero-coupon bond prices and oil forward prices in Table 8.9, what is the price of an 8-period swap for which two barrels of oil are delivered in even-numbered quarters and one barrel of oil
Using the zero-coupon bond prices and natural gas swap prices in Table 8.9, what are gas forward prices for each of the 8 quarters?
Using the zero-coupon bond prices and natural gas swap prices in Table 8.9, what is the implicit loan amount in each quarter in an 8-quarter natural gas swap?
What is the fixed rate in a 5-quarter interest rate swap with the first settlement in quarter 2?
Using the zero-coupon bond yields in Table 8.9, what is the fixed rate in a 4-quarter interest rate swap? What is the fixed rate in an 8-quarter interest rate swap?
What 8-quarter dollar annuity is equivalent to an 8-quarter annuity of =C1?
Using the assumptions in Tables 8.5 and 8.6, verify that equation (8.13) equals 6%.Table 8.5
Using the assumptions in Tables 8.5 and 8.6, verify that equation (8.13) equals 6%.
Using the information in Table 8.9, verify that it is possible to derive the 8-quarter dollar interest swap rate from the 8-quarter euro interest swap rate by using equation (8.13).
Suppose that oil forward prices for 1 year, 2 years, and 3 years are $20, $21, and $22.The 1-year effective annual interest rate is 6.0%, the 2-year interest rate is 6.5%, and the 3-year interest
Consider the same 3-year oil swap. Suppose a dealer is paying the fixed price and receiving floating. What position in oil forward contracts will hedge oil price risk in this position? Verify that
Consider the 3-year swap in the previous example. Suppose you are the fixed-rate payer in the swap. How much have you overpaid relative to the forward price after the first swap settlement? What is
Consider the same 3-year swap. Suppose you are a dealer who is paying the fixed oil price and receiving the floating price. Suppose that you enter into the swap and immediately thereafter all
Supposing the effective quarterly interest rate is 1.5%, what are the per-barrel swap prices for 4-quarter and 8-quarter oil swaps? (Use oil forward prices in Table 8.9.) What is the total cost of
Using the information in Table 8.9, what are the euro-denominated fixed rates for 4- and 8-quarter swaps?
Using the information in Table 8.9, what is the swap price of a 4-quarter oil swap with the first settlement occurring in the third quarter?
Given an 8-quarter oil swap price of $20.43, construct the implicit loan balance for each quarter over the life of the swap.
A stock currently sells for $32.00. A 6-month call option with a strike of $35.00 has a premium of $2.27. Assuming a 4% continuously compounded risk-free rate and a 6% continuous dividend yield, what
Suppose call and put prices are given byFind the convexity violations. What spread would you use to effect arbitrage? Demonstrate that the spread position is an arbitrage.
Suppose call and put prices are given byFind the convexity violations. What spread would you use to effect arbitrage?Demonstrate that the spread position is an arbitrage.
In each case identify the arbitrage and demonstrate how you would make money by creating a table showing your payoff.a. Consider two European options on the same stock with the same time to
Suppose the interest rate is 0% and the stock of XYZ has a positive dividend yield. Is there any circumstance in which you would early-exercise an American XYZ call? Is there any circumstance in
In the following, suppose that neither stock pays a dividend.a. Suppose you have a call option that permits you to receive one share of Apple by giving up one share of AOL. In what circumstance might
The price of a non-dividend-paying stock is $100 and the continuously compounded risk-free rate is 5%. A 1-year European call option with a strike price of $100 × e0.05×1= $105.127 has a premium
Suppose that to buy either a call or a put option you pay the quoted ask price, denoted Ca(K, T ) and Pa(K, T ), and to sell an option you receive the bid, Cb(K, T ) and Pb(K, T ). Similarly, the ask
In this problem we consider whether parity is violated by any of the option prices in Table 9.1. Suppose that you buy at the ask and sell at the bid, and that your continuously compounded lending
Consider the June 165, 170, and 175 call option prices in Table 9.1.a. Does convexity hold if you buy a butterfly spread, buying at the ask price and selling at the bid?b. Does convexity hold if you
A stock currently sells for $32.00. A 6-month call option with a strike of $30.00 has a premium of $4.29, and a 6-month put with the same strike has a premium of $2.64.Assume a 4% continuously
Suppose the S&R index is 800, the continuously compounded risk-free rate is 5%, and the dividend yield is 0%. A 1-year 815-strike European call costs $75 and a 1 year 815-strike European put
Suppose the exchange rate is 0.95 $/=C, the euro-denominated continuously compounded interest rate is 4%, the dollar-denominated continuously compounded interest rate is 6%, and the price of a
The premium of a 100-strike yen-denominated put on the euro is ¥8.763. The current exchange rate is 95 ¥/=C. What is the strike of the corresponding euro-denominated yen call, and what is its
The price of a 6-month dollar-denominated call option on the euro with a $0.90 strike is $0.0404. The price of an otherwise equivalent put option is $0.0141. The annual continuously compounded dollar
Suppose the dollar-denominated interest rate is 5%, the yen-denominated interest rate is 1% (both rates are continuously compounded), the spot exchange rate is 0.009$/¥, and the price of a
Suppose call and put prices are given byWhat no-arbitrage property is violated? What spread positionwould you use to effect arbitrage? Demonstrate that the spread position is an arbitrage.
Suppose call and put prices are given byWhat no-arbitrage property is violated? What spread positionwould you use to effect arbitrage? Demonstrate that the spread position is an arbitrage.
Let S = $100, K = $105, r = 8%, T = 0.5, and δ = 0. Let u = 1.3, d = 0.8, and n =a. What are the premium, ∆ and B for a European call?b. What are the premium, ∆ and B for a European put?
Let S = $100, K = $95, σ = 30%, r = 8%, T = 1, and δ = 0. Let u = 1.3, d = 0.8, and n = 2. Construct the binomial tree for an American put option. At each node provide the premium, ∆ and B.
Suppose S0 = $100, K = $50, r = 7.696% (continuously compounded), δ = 0, and T = 1.a. Suppose that for h = 1, we have u = 1.2 and d = 1.05. What is the binomial option price for a call option that
Let S = $100, K = $95, r = 8% (continuously compounded), σ = 30%, δ = 0, T = 1 year, and n = 3.a. Verify that the binomial option price for an American call option is $18.283.Verify that there is
Repeat the previous problem assuming that the stock pays a continuous dividend of 8% per year (continuously compounded). Calculate the prices of the American and European puts and calls. Which
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