Test 3

Spring 2014, 9 am Class

Multiple Choice #1

The current value of Souzark stock is $100 per share. The value of the stock one year from now will come from a uniform distribution, with lower bound $98 and upper bound $108. (There is an equal probability the stock’s value could be any amount between $98 and $108, and these probabilities add up to 100%. You can either assume a continuous distribution or a discrete distribution with one-cent increments.) What is the present value of a European call option with exercise price $105 and expiration one year from today? The effective annual interest rate is 10%.

Expected value of call option: Probability of option being exercised:

Multiple Choice #2

Gladiator Matchbiller, Inc., pays yearly dividends beginning with a $5 dividend one year from today. Each dividend is never higher than the dividend paid the previous year. What is the present value of the stock if the effective annual discount rate is 15%?

Upper bound on stock price:

Multiple Choice #3

Toad the Dry Mushroom is a band offering fans an investment opportunity. Fans can invest $100 today and receive $500 six years from now if the band is successful, but nothing otherwise. The band is successful with 50% probability. What must the discount rate be for fans to invest?

Multiple Choice #4

Walk Tall Shoes stock was valued at $80 four years ago. The stock has had a geometric average rate of return of 7% over the last four years. Mel bought an American call option with an exercise price of $90 a few weeks ago. The option expires today. What is the present value of the option if Mel’s effective annual discount rate is 14%?

Current stock price:

Multiple Choice #5

Which of the following does NOT occur if the efficient market hypothesis is true?

Delayed responseThe efficient market hypothesis implies an instant response to new information.

Multiple Choice #6

A stock will pay a $9 dividend every 6 months, starting 6 months from today. Assuming these dividends are paid forever, and the effective annual interest rate is 18%, what is the present value of this stock?

6-month effective rate:

Multiple Choice #7

A bond has a face value of $1000 and will pay out a 10% coupon six months and 18 months from today. The bond will also mature 18 months from today. If the effective annual interest rate is 14%, what is the present value of this bond?

Multiple Choice #8

Suppose you want an annual pass to Disneyland for the rest of your life. The current price for a annual pass is $699, but it increases 8% each year. If you buy a pass today and renew it yearly for the rest of your life, what is the present value of this cost? Assume the effective annual interest rate is 15% and that you will live for 60 more years.

Multiple Choice #9

The annual rate of return of stocks X and Y are uncorrelated. The standard deviations of the annual rates of return are 5% and 10%, respectively. A portfolio with half of the money in each stock will have a standard deviation of _____.

Multiple Choice #10

Which of the following products was analyzed in class early in the quarter?

The Perfect Bacon Bowl

Free Response #11

Zandra receives a $350,000 loan today. She will make equal payments every two years to pay back the loan, starting one year from today. If the effective annual interest rate is 20%, how much will each payment be? Assume the last payment will be made 31 years from today.

Two-year rate:

Free Response #12

Assume that Wolf will receive a $800 payment 6 years from today.

a) If the stated annual interest rate is 8% and compounding occurs continuously, what is the present value of the payment?

Six-year effective annual rate:

Free Response #12

Assume that Wolf will receive a $800 payment 6 years from today.

b) If the effective annual interest rate is 8% and compounding occurs continuously, what is the present value of the payment?

Free Response #13

There are 3 states of the world, each with 1/3 probability of occurring: Ascer, Balluth, and Crinkul. In Ascer, Stock X has a rate of return of 45%, and Stock Y has a rate of return of 10%. In Balluth, Stock X has a rate of return of 1% and Stock Y has a rate of return of 14%. In Crinkul, Stock X has a rate of return of 17%, and Stock Y has a rate of return of 12%.

a) What is the expected return for each stock?

Free Response #13

There are 3 states of the world, each with 1/3 probability of occurring: Ascer, Balluth, and Crinkul. In Ascer, Stock X has a rate of return of 45%, and Stock Y has a rate of return of 10%. In Balluth, Stock X has a rate of return of 1% and Stock Y has a rate of return of 14%. In Crinkul, Stock X has a rate of return of 17%, and Stock Y has a rate of return of 12%.

b) What is the covariance of the two stocks?

Free Response #14

The Ross-Westerfield Bathing Suit Company has a beta of 0.6 and an expected return of 11%. A risk-free asset has a rate of return of 5%.

a) What is the expected rate of return of an asset with a beta value of 1?

Free Response #14

The Ross-Westerfield Bathing Suit Company has a beta of 0.6 and an expected return of 11%. A risk-free asset has a rate of return of 5%.

b) What is the expected rate of return of an asset with a beta value of 2.5?

Free Response #14

The Ross-Westerfield Bathing Suit Company has a beta of 0.6 and an expected return of 11%. A risk-free asset has a rate of return of 5%.

c) Draw a graph showing the security market line. Label the risk-free rate, the expected return of the market, and the expected return of Ross-Westerfield.

Free Response #14

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Security Market Line

BETA

Retu

rn

Free Response #15

Alison Station Kraut Dogs, Inc. stock currently sells for $50 per share. The value of the stock will go up or down by $5, each with a 50% probability. Ron buys a European call option with expiration date 4 years from today for $60. If the effective annual interest rate is 15%, what is the present value of this option?

Option is only exercised if stock increases each year.

Free Response #16

The Laser Showinator 5000 can be purchased today for $5,000, and a maintenance cost of $2,000 must be paid 8 years from today. The machine lasts for 12 years. Assume that the effective annual discount rate is 10%.

a) What is the equivalent annual cost of the machine?

Free Response #16

The Laser Showinator 5000 can be purchased today for $5,000, and a maintenance cost of $2,000 must be paid 8 years from today. The machine lasts for 12 years. Assume that the effective annual discount rate is 10%.

b) You borrow all of the money needed to pay the present value of all costs of the machine today. You make nine annual payments to pay back the loan, starting one year from today. If each payment reduces the principal of the loan by the same amount, how much will the payment two years from today be?

Principal reduction each year:

Free Response #17Today Vanessa buys one share of stock for $100, one European call option with an exercise price of $80, and one European put option with an exercise price of $90. The options expire twelve months from today. Vanessa assumes that the effective annual discount rate is 8%.

Draw a well-labeled graph that shows the present value of the combination of the three assets as a function of the value of a single share of stock at the options’ expiration date. The vertical intercept should have the value of the combination of the three assets. The horizontal axis should have the value of a single share of stock at the options’ expiration date. Make sure to label your intercepts and other relevant numbers on each axis, where relevant. (Hint: You may want to look at the front page of the test to see a well-labeled graph.)

Please note that you need to justify the labels for the graph you provide. Please provide an explanation or math wherever necessary.

Free Response #17

Free Response #17

-10 10 30 50 70 90 110 130 1500

50

100

150

200

83.33 83.3392.59

166.67

PV of Assets