Quiz 3 solution sketches
11:00 Lecture, Version A
Note for multiple-choice questions:
Choose the closest answer
Stock Returns

A stock can be purchased today for
$100. The next dividend of $4 will be
paid one year from today. The value of
the stock one year from today will be
$98. What is the total dollar return over
the next year for owning 10 shares of
this stock?
Stock Returns


Total dollar return per share
= 4 + (98-100) = $2
Total dollar return for 10 shares = $20
Average Rates of Return

Use the following information for the
next two questions: On Oct. 31, 2013,
the Dow Jones was at 15,545.75. On
Oct. 31, 2003, the Dow Jones was at
9,801.12. (Please note that this may or
may not be enough information to
answer each question.)
Average Rates of Return

What is the geometric average rate of
return over this 10-year period?


Geom. avg =(1+holding period return)1/n –1
= (15,545.75/9,801.12)1/10 – 1
= (1.58612)1/10 – 1
= 1.0472096 – 1
Geom. avg = 4.72096%
Average Rates of Return

We need individual year returns to be
able to calculate the arithmetic mean,
so there is not enough information to
answer this question.
Loan Amortization

Goliath Gladwell will borrow $60,000 on
Jan. 1, 2014. He will make 12 equal
yearly payments, on Oct. 1 of years
2015-2026, to completely pay back the
loan. How much will each payment be if
the EAR is 10%?
Loan Amortization


If paid on Jan. 1, 2015-2026:
60,000 = C/.1 * [1 – 1/1.112]
60,000 = 6.8137 * C
C = 8,805.80
Add 9 months of interest to account for
payments on Oct. 1:
8,805.80 * (1.1)3/4 = $9,458.30
Growing Perpetuity

Mortimer will receive $1,000 today. He
will receive 8% more each subsequent
year. If his effective annual discount
rate is 20%, what is the PV of this
stream of payments?



PV = 1,000 + (1,000 * 1.08)/(.2 - .08)
PV = 1,000 + 1,080/.12
PV = $10,000
Expected NPV

Sallie is trying to invent a new type of tent.
The invention costs $1 million to develop,
which must be paid whether or not it is
successful. If the invention is successful, she
will sell $20 million in tents (in PV), and the
cost to produce the tents is $8 million (in PV).
If the invention does not succeed, the
respective PVs for tent sales are $3 million
and $2.8 million.
Expected NPV

If the invention is successful with 10%
probability, what is the expected NPV of
Sallie’s tent business?




(in $Millions)
NPV = -1 + .1 * (20 – 8) + .9 * (3 – 2.8)
NPV = -1 + 1.2 + 1.8
NPV = 0.38, so NPV is $380,000
Bond Yields

Bruce is quoted a price for a bond of
$1,000. This bond has a face value of
$900 and pays a 12% coupon once per
year. Two coupons will be paid. One
coupon will be later today and the other
will be paid one year from today. If the
bond matures in one year, what is the
yield of this bond (expressed as an
effective annual interest rate)?
Bond Yields




1,000 = 900(.12) + 900(1.12)/(1+r)
892 = 1008/(1+r)
1+r = 1008/892 = 1.13004
r = 13.004%
Real Rate of Return

In 1981, large-company stocks had an
effective annual return of -4.92%. The
Consumer Price Index, which is used as
a measure of inflation, was 8.92%.
What is the real effective annual return
of large-company stocks in 1981?



(1+real)*(1+inflation) = (1+nominal)
(1+real)*(1.0892) = 0.9508
Real = 0.9508/1.0892 – 1 = -12.707%
Cash Cow & Retained Earnings

Cow Bell Boots, Inc. is currently a cash
cow. Without any re-investment of their
earnings, they will earn $8 per share
every year forever. The effective annual
discount rate for owning this stock is
10%. Assume that the next dividend
payment will be made in 1 year.
Cash Cow & Retained Earnings


Suppose that Cow Bell Boots could
retain all of its earnings 4 years from
today, and earn 20% 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 = 8/.1 = $80
Cash Cow & Retained Earnings

(b) Should Cow Bell Boots retain its
earnings 4 years from today? Why/why
not?

Yes, because either:


NPV is positive
Rate of return (20%) > Discount rate (10%)
Cash Cow & Retained Earnings

(c) How much does the present value of
Cow Bell Boots change if the company
retains its earnings 4 years from today?

NPV of retaining earnings
= -8/1.14 + 8(1.2)/1.15
= 0.4967