UGBA 103
Midterm Solutions
20091016
Multiple choice questions:
1. E
2. E
3. A
4. D
5. C
6. E
7. B
8. D
Long questions:
1. We are given that
IRR
A
= 12
.
61% and
NPV
A
=
Yen
12
,
030, and need to say
something (if we can) about
NPV
B
and
IRR
B
. Let
C
1
,...,C
T
be bank A’s cash
flows. Then bank B’s cash flows are

C
1
,...,

C
T
, and it must be the case that
IRR
B
=
IRR
A
:
0 =
T
summationdisplay
t
=1
C
t
(1 +
IRR
A
)
t
0 =
T
summationdisplay
t
=1

C
t
(1 +
IRR
A
)
t
=
⇒
IRR
A
=
IRR
B
i.e. it must be the case that the IRR for firm
B
is the same:
IRR
B
=
IRR
A
=
12
.
61%.
Regarding NPV, whatever the cash flows exchanged by the banks are, they have
the same risk, so they should have the same discount rate in calculating both
NPV
A
and
NPV
B
. So the only difference in NPV is the sign of the cash flows,
and this means that
NPV
B
=

NPV
A
=

Yen
12
,
030.
2. We want to find the rate
r
∗
such that the present value of future subscription
payments (10 for 480 months) is 500:
500 =
10
r
bracketleftbigg
1

1
(1 +
r
∗
)
480
bracketrightbigg
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so you could just solve that directly on a graphing calculator. But we can also
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 Fall '09
 ODEAN
 Net Present Value, 177.77M 1.1 1.12 1.13 1.14 1.15 1.1 Page 3

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