# Chapter03_xlsSol by g6qAmXc4

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```									Problems

Problem 3-4
Problem 3-6
Problem 3-7
Problem 3-12
Problem 3-14
Problem 3-16
Problem 3-4

Suppose the risk-free interest rate is 4%.

a. Having \$200 today is equivalent to having what amount in one year?
Amount today          \$200.00
Interest rate           4.00%
Value in 1 year       \$208.00

b. Having \$200 in one year is equivalent to having what amount today?
Amount in 1 year      \$200.00
Interest rate           4.00%
Value today           \$192.31

c. Which would you prefer, \$200 today or \$200 in one year?
\$200 today
Does your answer depend on when you need the money? Why or why not?
The answer does not depend on when the money is needed.
at amount in one year?

ng what amount today?

in one year?

he money? Why or why not?
ey is needed.
Problem 3-6

You run a construction firm. You have just won a contract to build a government office
building. Building it will require an investment of \$10 million today and \$5 million in one
year. The government will pay you \$20 million in one year upon the building’s
completion. Suppose the cash flows and their times of payment are certain, and the risk-
free interest rate is 10%.

a. What is the NPV of this opportunity?
Interest rate                            10.00%
Year
0

Investment                      (\$10,000,000.00)
Government payment
Net cash flow                    (10,000,000.00)
Value today                      (10,000,000.00)
NPV                                3,636,363.64

b. How can your firm turn this NPV into cash today?
Borrow                          13,636,363.64
Use                            (10,000,000.00)
Pay back loan plus interest     15,000,000.00
a contract to build a government office
f \$10 million today and \$5 million in one
n one year upon the building’s
es of payment are certain, and the risk-

Year
1

(\$5,000,000.00)
\$20,000,000.00
15,000,000.00
13,636,363.64

ash today?
today
today for investment
with cash inflow in 1 year
Problem 3-7

Your firm has identified three potential investment projects. The projects
and their cash flows are shown here:

Cash Flow             Cash Flow
Project       Today (\$)          in One Year (\$)
A              -10                    20
B               5                     5
C              20                    -10
Suppose all cash flows are certain and the risk-free interest rate is 10%.

a. What is the NPV of each project?
Interest rate           10.00%

Year
0            1
Project A
Cash flows               (10.00)      20.00
Value today              (10.00)      18.18
NPV of A                   8.18

Project B
Cash flows                 5.00        5.00
Value today                5.00        4.55
NPV of B                   9.55

Project C
Cash flows                20.00      (10.00)
Value today               20.00       (9.09)
NPV of C                  10.91

Summary
Project                NPV
Project A                 8.18
Project B                 9.55
Project C                10.91

b. If the firm can choose only one of these projects, which should it
choose?
Project C

c. If the firm can choose any two of these projects, which should it
choose?
Projects B and C
Problem 3-12

The promised cash flows of three securities are listed here. If the cash flows are
risk-free, and the risk-free interest rate is 5%, determine the no-arbitrage price
of each security before the first cash flow is paid.

Cash Flow               Cash Flow
Security       Today (\$)            in One Year (\$)
A              500                     500
B               0                     1000
C             1000                      0

Interest rate            5.00%

Cash flow Cash flow in No-arbitrage
Security     today     one year       price
A        500.00      500.00        976.19
B         0.00    1000.00         952.38
C     1000.00          0.00     1,000.00
the cash flows are
o-arbitrage price
Problem 3-14

Consider two securities that pay risk-free cash flows over the next two years and
that have the current market prices shown here:
Cash Flow           Cash Flow
Security Price Today (\$)      in One Year (\$) in Two Years (\$)
B1            94                  100                  0
B2            85                   0                 100

Cash flow            Cash flow
Security      Price Today           in one year          in two years
B1              (94.00)                100.00                 0.00
B2              (85.00)                  0.00               100.00

a. What is the no-arbitrage price of a security that pays cash flows of \$100 in
one year and \$100 in two years?
179.00 since this is just like buying both B1 and B2

b. What is the no-arbitrage price of a security that pays cash flows of \$100 in
one year and \$500 in two years?
519.00 since this is just like buying 1 B1 and 5 B2s

c. Suppose a security with cash flows of \$50 in one year and \$100 in two
years is trading for a price of \$130. What arbitrage opportunity is
available?
130.00 is the price the security trades at.
132.00 is the correct price for the security.

You could do arbitrage by buying the security. You could then
either sell it after the price adjusts or just collect the cash flows at
their alotted times. Either way, you'll receive more than you
should.
two years and

flows of \$100 in

and B2

flows of \$100 in

5 B2s

d \$100 in two
unity is
Problem 3-16

Xia Corporation is a company whose sole assets are \$100,000 in cash and three projects th
undertake. The projects are risk-free and have the following cash flows:

Cash Flow                    Cash Flow
Project         Today (\$)                 in One Year (\$)
A              -20,000                      30,000
B              -10,000                      25,000
C              -60,000                      80,000

Xia plans to invest any unused cash today at the risk-free interest rate of 10%. In one year,
will be paid to investors and the company will be shut down.

Interest rate            10.00%

a. What is the NPV of each project? Which projects should Xia undertake and
much cash should it retain?

Cash flow    Cash flow in
Project       today        one year
A         (20000.00)    30000.00
B         (10000.00)    25000.00
C         (60000.00)    80000.00
Accept Projects           A                B

b. What is the total value of Xia’s assets (projects and cash) today?
Value of company is the sum of its projects' NPVs
Plus its cash
Total value of the company

c. What cash flows will the investors in Xia receive? Based on these cash flow
is the value of Xia today?
They will receive the sum of the cash flows above plus the proceeds
from the investment of \$10,000 extra cash. Its value is
They will receive the sum of the cash flows above plus the proceeds
from the investment of \$10,000 extra cash. Its value is

d. Suppose Xia pays any unused cash to investors today, rather than investing
are the cash flows to the investors in this case? What is the value of Xia no
Xia's shareholders will get the same amount, regardless. If the company p
excess cash now, shareholders will get \$10,000 plus the present value of th
flows Xia will get in one year.

e. Explain the relationship in your answers to parts (b), (c), and (d).
No matter how Xia's shareholders get their cash, they're entitled to the sam
amount becaause in every case the values are discounted.
0,000 in cash and three projects that it will
ing cash flows:

Cash Flow
in One Year (\$)
30,000
25,000
80,000

e interest rate of 10%. In one year, all cash
own.

projects should Xia undertake and how

NPV
7,272.73
12,727.27
12,727.27
and                 C

rojects and cash) today?
jects' NPVs                        32,727.27
100,000.00
132,727.27

a receive? Based on these cash flows, what

ws above plus the proceeds
h. Its value is
ws above plus the proceeds
h. Its value is                   132,727.27

vestors today, rather than investing it. What
case? What is the value of Xia now?
unt, regardless. If the company pays out
10,000 plus the present value of the cash

to parts (b), (c), and (d).
eir cash, they're entitled to the same
s are discounted.

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