Quiz 4 solution sketches
11:00 Lecture, Version A
Note for multiple-choice 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 12-year period?


(100/50)1/12 = (2)1/12 = 1.05946
RG = 1.05946 – 1 = 5.946%
Loan Amortization

Gladman Goldie will borrow $100,000
on Jan. 1, 2014. He will make 15 yearly
payments, on Nov. 1 of years 20152029, to completely pay back the loan.
How much will each payment be if the
EAR is 12%?
Loan Amortization


If paid on Jan. 1, 2015-2029:
100,000 = C/.12 * [1 – 1/1.1215]
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 = $16,137
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 = $18,354
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%
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%.
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%
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 = -0.0005
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) = -1
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 = 1.2
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.
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 = $97.71
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 justifications
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
= -12/1.145 + 12(1.08)/1.146
= -$0.3280