BA 103 S
UMMER
2007
F
INAL
E
XAMINATION
J
UNE
29, 2007
1.
Amazing Technologies Corporation (ATC) just paid an annual dividend of $1.80. The
dividends are expected to grow at the rate of 16% per year for the next 4 years. From
t
=4
onwards, the dividends are expected to grow at 4.5% in perpetuity. The market
capitalization rate for the stock is 16%. Work out the current price of the stock.
[8 points]
The Dividend at t=1 is $1.8*1.16, and its present value is $1.8. Therefore the present
value of the first four dividends is $1.80*4 = $7.20. D5 = $1.80*1.16
4
*1.045 = $3.41.
Therefore P4 = D5/(r-gL) = $3.41/(.16 – 0.045) = 29.62. PV(P4) = $16.36. P0 = 16.36 +
7.20 = $23.56
2.
Ms. Heike Alvarez owns and manages an all-equity firm. The firm is currently valued at $1.5 million.
However, an additional investment of $6 million is needed for expansion, which can be raised either as debt
at 13.5%, or as equity. The annual cash flows that the expanded firm will generate depend, among other
things, on how hard Ms. Heike Alvarez works. If she works an average of 6 hours a day, the annual cash
flows that the firm generates are expected to be $900,000. On the other hand, if she works 10.5 hours a day,
the annual cash flows are expected to be higher by a factor of 1.35. Assuming that there are 250 working
days in a year, work out the Ms. Heike Alvarez’s average hourly compensation in all four cases:
(a) expansion is financed by debt and Ms. Heike Alvarez works 6 hours a day,
(b) expansion is financed by debt and Ms. Heike Alvarez works 10.5 hours a day,
(c) expansion is financed by equity and Ms. Heike Alvarez works 6 hours a day, and
(d) expansion is financed by equity and Ms. Heike Alvarez works 10.5 hours a day.
Also work out the hourly compensation that Ms. Heike Alvarez receives on the additional 1125 hours a
year (if she works 10.5 hours a day, she puts in an additional 4.5 hours a day for 250 days) (i) if the
expansion is financed by equity and (ii) if the expansion is financed by debt. Briefly comment on the
incentives that Ms. Heike Alvarez will have to work longer hours in the two cases.
[8 points]
The Annual cash flow with 10.5 hr days is $1.35*$900,000 = $1,215,000. If $6millon is
raised as debt, the interest on it is $6m*.135 = $810,000. With debt financing the hourly
compensation is as follows:
6-H
OUR
D
AYS
10.5-H
OUR
D
AYS
A
NNUAL
C
ASH
F
LOW
$900,000
$1,215,000
I
NTEREST
$810,000
$810,000
C
ASH
F
LOW
TO
O
WNER
-M
ANAGER
$90,000
$405,000
#(H
OURS
)/
YEAR
1500
2625
H
OURLY
C
OMPENSATION
$60
$154.29
With equity financing, other owners own $6m of the expanded $7.5m firm. Thus others’
stake is 80%
6-H
OUR
D
AYS
10.5-H
OUR
D
AYS
A
NNUAL
C
ASH
F
LOW
$900,000
$1,215,000
P
AYMENT
TO
O
THERS
(80%
OF
CF)
$720,000
$972,000
C
ASH
F
LOW
TO
O
WNER
-M
ANAGER
$80,000
$243,000