1100 Lecture Version A Note for multiplechoice questions Choose the closest answer Geometric Average On Nov 1 2013 Slacky Green Slacks was worth 100 per share On Nov 1 2001 it was worth 50 per share What is the geometric average rate of return over this 12year period ID: 640273
Download Presentation The PPT/PDF document "Quiz 4 solution sketches" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Quiz 4 solution sketches
11:00 Lecture, Version A
Note for multiple-choice questions: Choose the closest answerSlide2
Geometric Average
On Nov. 1, 2013,
Slacky
Green Slacks was worth $100 per share. On Nov. 1, 2001, it was worth $50 per share. What is the geometric average rate of return over this 12-year period?
(100/50)
1/12
= (2)
1/12
= 1.05946
R
G
= 1.05946 – 1 = 5.946%Slide3
Loan Amortization
Gladman
Goldie will borrow $100,000 on Jan. 1, 2014. He will make 15 yearly payments, on Nov. 1 of years 2015-2029, to completely pay back the loan. How much will each payment be if the EAR is 12%?Slide4
Loan Amortization
If paid on Jan. 1, 2015-2029:
100,000 = C/.12 * [1 – 1/1.12
15
]
100,000 = 6.81086 * C
C
= $14,682
Add 10 months of interest to account for payments on Nov. 1:
14,682 * (1.12)
10/12
= $16,137Slide5
Future Value
Kokomo Jack invests $6,000 today, November 25, 2013. Find the future value on November 25, 2025 if the stated annual interest rate is 10%, compounded every 18 months.
Interest every 18 months = .1*18/12 = .15
Number of times compounded = 12/1.5 = 8
FV = 6000 * (1.15)
8
= $18,354Slide6
CAPM
The risk-free rate of return is 6%. For a stock, assume that beta is 1.5. The market return of a well-diversified portfolio is 19%. What is the expected return for this stock?
Exp. Ret. = Risk-free rate +
β
*risk premium
Exp. Ret. = 6% + 1.5 * (19% – 6%)
Exp. Ret. = 25.5%Slide7
Returns in States of the World
For the following three questions, assume that there are two known states of the world, each with 50% probability of occurring: Good and Bad. When times are good, Stock A has a rate of return of 7% and Stock B has a return of 15
%. When times are
bad
, Stock A has a rate of return of
9%
and Stock B has a return of
5
%. Slide8
Returns in States of the World
What is the standard deviation of Stock A’s return?
Avg
return = .5 * .07 + .5 * .09 = .08
Var
= 1/2 * [(.07-.08)
2
+ (.09-.08)
2
]
Var
= 1/2 * [.0001 + .0001] = .0001
Std. Dev. = (.0001)
1/2
= .01 = 1%Slide9
Returns in States of the World
What is the covariance of the two stocks’ returns?
A’s
avg
return = .5 * .07 + .5 * .09 = .08
B’s
avg
return = .5 *
.15
+ .5 * .
05
=
.10
Cov
= 1/2 * [(.
07-.08
)(.15-.1) +
(.
09-.
08)(.05-.1)]
Cov
= 1/2 * [-.0005 + (-.
0005)]
Cov
= -0.0005Slide10
Returns in States of the World
What is the correlation coefficient of the two stocks’ returns?
A’s
s.d.
= .01 (from question 5)
B’s variance = 1/2
*
[(.15-.1)
2
+
(.05-.1)
2
]
B’s variance
= 1/2 * [.
0025+.0025]
= .
0025
B’s
s.d.
=
(.
0025)
1/2
=
.05
ρ =
Cov
/[
s.d.
(A)*
s.d.
(B)]
ρ = -0.0005/(.01*.05) = -1Slide11
CAPM
Assume that the risk-free rate is 9%. A stock has an expected return of 15%, and the expected return on the market is 14%. What is the beta for this stock?
Exp. Ret. = Risk-free rate +
β
*risk premium
15% = 9% +
β
* (14% - 9%)
6% =
β
* 5%
β = 1.2Slide12
Cash Cow & Retained Earnings
Taco Bill Boots, Inc. is currently a cash cow. Without any re-investment of their earnings, they will earn $12 per share every year forever. The effective annual discount rate for owning this stock is 14%. Assume that the next dividend payment will be made later today. Slide13
Cash Cow & Retained Earnings
Suppose that Cow Bell Boots could retain all of its earnings
5
years from today, and earn 8
%
on these earnings over the following
year.
(a) What is the PV of this stock if it continues to act as a cash cow?
PV = 12 + 12/.14 = $97.71Slide14
Cash Cow & Retained Earnings
(b) Should Taco Bill Boots retain its earnings 5 years from today? Why/why not?
No, because:
NPV is negative for this option
Rate of return on retained earnings (8%) is less than the Discount rate (14%)
Note that correct answers must use one of the two justificationsSlide15
Cash Cow & Retained Earnings
(c) How much does the present value of Taco Bill Boots change if the company retains its earnings 5 years from today?
NPV of retaining earnings
= -12/1.14
5
+ 12(1.08)/1.14
6
= -$0.3280