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principles of finance

Questions and Answers of Principles Of Finance

b. Create a two- dimensional data table showing the sensitivity of NPV to the year 1 cash flow and to the discount rate. Use the same range for the cash flow as above and use discount rates from 8%
a. Create a one- dimensional data table showing the sensitivity of the NPV and IRR to the year 1 cash flow (currently $10,000). Use a range of $9,000 to $12,000 in increments of $500.
c. Use CountIf to determine the number of companies whose share price is greater or equal to $30.
b. Use Count to determine the number of share prices in the list in column B.
18. Using the list of DJ30 companies from the previous exercise:
e. Use Rank to determine the relative ranking of Microsoft’s stock price among the DJ30.
d. Use Large to determine the smallest of the stock prices. Do the same using Min.
c. Use Large to determine the largest of the stock prices. Do the same using Max.
b. What was the media price?
a. What was the average price of a DJ30 stock?
17. On the companion website for the book is a list of companies in the Dow Jones 30 Industrials (DJ30) and their share prices on 27 August 2004. Part of the list is given below.
14. The companion website for this book contains a spreadsheet with IBM stock prices and dividends from February 1990 through August 2004.Part of this spreadsheet is given below; note that column D
13. You’ve been offered a financial asset which costs $1,000 today and pays back$1,100 in 1 year.
b. What is your effective annual interest rate (EAIR) on the fund?(Although you don’t need it to answer this question, you may want to remind yourself what the EAIR is by reviewing Chapter 5.)
a. If you deposit $100,000 into the fund today and the 3% interest rate holds for the next 10 years, how much will you have in 10 years?
9. Your money market fund pays 3% interest annually, compounded continuously.
a. Use Rate to compute the monthly interest rate he’s offering. Confirm your answer by using IRR.
7. You’ve offered to finance Joe’s purchase of a $20,000 car. Joe offers to repay you $500 per month for the next 48 months.
b. Design a loan table showing that the payment you computed in the first part of this problem indeed pays off the mortgage.
a. Use PMT to compute the monthly payment.
5. You’ve taken a 30-year, $60,000 mortgage to finance the purchase of your new house. The mortgage has an interest rate of 10% annually and requires monthly flat payments of interest and principal
RATE is shorter; IRR requires you to specify all the cash flows.
Click on the graph title to mark it, and then go to the formula bar and insert an equal sign to indicate a formula. Then point at cell D20 with the formula and click [Enter]. In the picture below,
Create the title you want in a cell. In the example above, cell D20 contains the formula: = “Cash Flow Graph when Growth =” &TEXT(B2,“0.0%”).
Changing the axis parameters of a chart
Making a graph with non-contiguous data series
b. Calculate the value today of a 1- year European put option on the stock with an exercise price of $30.
a. What is the value today of a 1- year European call option on the stock with an exercise price of $30?
13. (Option pricing with sigma) A stock traded for $25 today. The annual standard deviation of the stock returns is 50%. If the interest rate is 3%,
b. Will you ever exercise the option early?
a. What is its value today?
9. (Two- period model, call with changing exercise price) A call option is written on a stock whose current price is $50. The option has maturity of 2 years, and during this time the annual stock
5. (Multi- period binomial model, American and European options) Consider the following two- period binomial model, in which the annual interest rate is 3% and in which the stock price goes up by 15%
b. How would your answer to part a be changed if the probabilities of these events are 0.5 and 0.5, respectively?
a. What is the value of a call option on ABC whose exercise price is$50 and which matures in 1 year?
3. (Pricing a call) All reliable analysts agree that a share of ABC Corporation, selling today for $50, will be priced 1 year from now at either $65 or $45.They further agree that the probabilities
c. Show that put– call parity holds: That is parts a andb, show the following:Call price Xr+ Stock price today Put price+= +1
b. Calculate the value today of a 1- year European put option on the stock with exercise price $30.
a. What is the value today of a 1- year European call option on the stock with exercise price $30?
1. (Pricing a call and put) A stock traded for $25 today will, in 1 year, be worth either $35 or $20. If the interest rate is 3%:
e. The sensitivity of the put price to changes in the exercise price X.
d. The sensitivity of the Black– Scholes call price to changes in the interest rate r.
c. The sensitivity of the Black– Scholes call price to changes in the time to maturity T.
b. The sensitivity of the Black– Scholes put price to changes in σ.
a. The sensitivity of the Black– Scholes call price to changes in the initial stock price S.
18. (Call and put price sensitivity) Consider a call option and a put option on a stock whose current price S is 50, both with exercise price X = $50, T = 0.5, r = 3%, and σ = 25%. Use Data Table to
. (Implied volatility) The table below gives June option prices for Pfizer (PFE)on 31 May 2015. On this date, Pfizer’s stock price was $34.75 and the interest rate was 0.10% annually. Compute the
12. (Black–Scholes and put– call parity) The price of a share of ABC Corporation stock is currently S = $55. Assume that the yearly interest 2% and that the stock’s annual volatility is 0.4.
b. Make a table showing the option’s price for maturities ranging from T = 0.2, 0.4, . . ., 2.0. (Excel hint: By far the easiest way to do this is to use Data Table, explained in Chapter 24.)
a. Find the put option price using the Black– Scholes model.
3. (Pricing a put) A put option with 0.5 year to maturity is written on a stock whose current price is $40. The option’s exercise price is $38, the interest rate is 4%, and the stock’s volatility
b. Make a table showing the option’s price for volatilities ranging from 10%, 20%, . . ., 60%. (Excel hint: By far the easiest way to do this is
a. Find the call option price using the Black– Scholes model.
2. (Pricing a call) A call option with 6 months to maturity is written on a stock whose current price is $40. The option’s exercise price is $38, the interest rate is 4%, and the stock’s
A risky stock may have a σ of as much as 80% or 100%.
An “average” U.S. stock has σ of between 30% and 50%.
If the stock is riskless, then σ = 0%. A stock is riskless if its future price is completely predictable.
5. σ (“sigma”) is a measure of the riskiness of the stock or underlying asset.Sigma is an important variable in determining the option price, and it is not a simple concept to explain. We
4. r, the risk- free interest rate. This is also given in annual terms. Meaning: If the interest rate is 6% per year and if an option has T = 0.25, then we write r = 6% in the Black– Scholes
3. T, the time to the option’s expiration (sometimes called the option maturity).In the Black– Scholes formula, T is always given in annual terms.Meaning: An option with 3 months to expiration
2. X, the exercise price of the option (this is also called the strike price).
. S0, the current price of the stock. By this we always mean the stock price on the date we’re calculating the option price.
b. Assume that the X = $60 put price is $8. Graph the profit pattern at maturity for the butterfly using Excel (let the stock prices at maturity range between $40 and $90). Does the graph indicate an
a. Use convexity to determine the upper bound for the X = $60 put price.
16. (Convexity property of put option prices) A butterfly spread is created using the following put options: The investor buys a put option with a strike price of $55 and pays $10, buys a put with a
In which case you are sure better off exercising the option?a. S = $20b. S = $3
. (Early exercising American put) You are trying to decide whether to early exercise a put option you hold that expires in 6 months. The put’s exercise price is X = $50 and the interest rate is r =
ii. You hold the option until its expiration date.
i. You exercise the put option today (assume that you invest your proceeds in bonds with an interest rate of 3%).
b. What is your net payoff if:
a. Consider a situation where the American put option is traded at $21.Show how you can gain from arbitrage.
13. (Lower bound and early exercising American put) Suppose that you are currently holding an American put option on National Australia Bank that has an exercise price of $45. The option expires in 6
. Consider a situation where the European put option is traded at $2.4.Show how you can gain from arbitrage.
a. Can a European put option that expires in 6- month trade at $2.50?Note that a European put option may sometimes be worth less than
12. (Lower bound of European put) ABC is a non- dividend paying stock.Suppose that S = $17, X = $20, r = 5% per annum.
b. If you can buy the above put for $5, how can you exploit the prices to make a riskless gain?
a. What is the minimum price the put will sell for?
11. (Lower bound of American put) You consider buying an American put option on Dell Computer Corporation, expiring in 6 months, with a strike price of$25. The current stock price is at $18.
9. (PCP) At the expiration date the put–call parity Put0 (X) = Call0 (X) + PV(X)S0 has the following form: Put X Call X X S T T T ( ) = ( ) + − or ST = CallT (X) –PutT (X) + X. Verify this
b. In general: If a European put and a call have the same price and expire at the same time, what can you say about the relationships between the stock price and the exercise price. S > X? S < X? S =
a. What is the current stock price?
8. (PCP finding S0) A European put and a call option both expire in a year and have the same exercise price of $20. The options are currently traded at the same market price of $3. Assume that the
Butterfly composed of puts: Buy one ABC June $180 put, sell two ABC June $200 puts, and buy one ABC June $220 put.Use put– call parity to show that the cost of a butterfly spread created from the
Butterfly composed of calls: Buy one ABC June $180 call for $20, sell two ABC June $200 calls each at $10, and buy one ABC June $220 call for $5.
6. (PCP and butterfly spread) Recall from Chapter 17 that a butterfly is an options strategy built on four trades at one expiration date and three different strike prices. For call options, one
b. Would the above market prices still provide an arbitrage opportunity if the option has a 1-month maturity and the stock price is $46.877?
a. If a 2- month call option with the same strike price is currently selling for $1, what opportunities are there for an arbitrageur? How can you exploit arbitrage?
5. (PCP) The current market price of a 2- month European put option on a nondividend-paying stock with strike price of $50 is $4. The stock price is $47 and the risk- free interest rate is 3%.
b. Assume that you can buy the call for $0.30 (which is less than the theoretical minimum). How can you exploit the mispricing to make a riskless gain?
a. Can the option price be lower than $0.30? Assume that the interest rate is 5%.
1. (Lower bound of call) You want to buy one American call option contract on ABC Computer, expiring in 6 months, with a strike price of $23. The current stock price is at $24.80.
b. Look at the following table. Is there an option which is clearly mispriced?
a. Should a put with an exercise price of $100 expiring on the 20 January 2017 sell for more than $0.6? Explain.
13. (The effect of exercise price on put option value) On May 2015 the stock price of Toyota Motor Corporation (symbol: TM) was $138. Put options on TM expiring on 15 January 2015 with an exercise
b. Look at the following table. Are there options that are clearly mispriced?
a. Should a call with an exercise price of $180.00 expiring on 15 January 2016 sell for more than $4.15? Explain.
12. (The effect of exercise price on call option value) On 11 May 2015 IBM’s stock price was $171 per share. Call options on IBM expiring on 16 October 2015 with an exercise price of $180.00 sold
a. You think that shares of MCD will fall in price in the immediate future, and you want to speculate on the stock. Compare (graphically)the following two alternatives: purchasing 1,000 MCD options
11. (Profit margin from two put options) On 16 May 2015 McDonald’s (MCD)stock is trading at $98 per share. The price of a put option on MCD expiring 18 September 2015 is $1.80 for options with X =
b. Compare the two strategies. Which is preferable?

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