FINS3625 Applied Corporate Finance S2 2011
Solutions to Tutorial Problems - Week 5
11-8
Total corporate value = Value of operations + marketable securities
= $756 + $77 = $833 million.
Value of equity = Total corporate value – debt – Preferred stock
= $833 – ($151 + $ 190) - $76 = $416 million.
11-9
Total corporate value = Value of operations + marketable securities
= $651 + $47 = $698 million.
Value of equity = Total corporate value – debt – Preferred stock
= $698 – ($65 + $131) - $33 = $469 million.
Price per share = $469 / 10 = $46.90.
11-10 a. NOPAT2010 = $108.6(1-0.4) = $65.16
NOWC2010 = ($5.6 + $56.2 + $112.4) – ($11.2 + $28.1) = $134.9 million.
Capital2010 = $134.9 + $397.5 = $532.4 million.
FCF2010 = NOPAT – Investment in Capital = $65.16 – ($532.4 - $502.2)
= $65.16 - $30.2 = $34.96 million.
b. HV2010 = [$34.96(1.06)]/(0.11-0.06) = $741.152 million.
c. VOp at 12/31/2009 = [$34.96 + $741.152]/(1+0.11) = $699.20 million.
d. Total corporate value = $699.20 + $49.9 = $749.10 million.
e. Value of equity = $749.10 – ($69.9 + $140.8) - $35.0 = $503.4 million.
Price per share = $503.4 / 10 = $50.34.
14-1
a. Real options occur when managers can influence the size and risk of a project’s cash
flows by taking different actions during the project’s life. They are referred to as real
options because they deal with real as opposed to financial assets. They are also called
managerial options because they give opportunities to managers to respond to changing
market conditions. Sometimes they are called strategic options because they often deal
with strategic issues. Finally, they are also called embedded options because they are a
part of another project.
b. Investment timing options give companies the option to delay a project rather than
implement it immediately. This option to wait allows a company to reduce the
uncertainty of market conditions before it decides to implement the project. Capacity
options allow a company to change the capacity of their output in response to changing
market conditions. This includes the option to contract or expand production. Growth
options allow a company to expand if market demand is higher than expected. This
includes the opportunity to expand into different geographic markets and the
opportunity to introduce complementary or second-generation products. It also includes
the option to abandon a project if market conditions deteriorate too much.
c. Decision trees are a form of scenario analysis in which different actions are taken in
different scenarios.
14-3
a.
0
1
2
20
13%
|-────|─--─-|---───    ─------|
-300
40
40
40
NPV = -$19.0099 million. Don’t purchase.
b. Wait 1 year:
50% Prob.
0
1
r = 13%
|
|
0
-300
2
|
30
3
|
30
4
|
30
50% Prob.
|
0
|
50
|
50
|
50
|
-300


NPV @
Yr. 0
21
|
30
-$78.9889
|
50
45.3430
If the cash flows are only $30 million per year, the NPV of the project is negative.
However, we’ve not considered the fact that the company could then be sold for $280
million. The decision tree would then look like this:
50% Prob.
0 r = 13% 1
|
|
0
-300
2
|
30
3
|
30 + 280
4
|
0
50% Prob.
|
0
|
50
|
50
|
50
|
-300


NPV @
Yr. 0
21
|
0
-$27.1468
|
50
45.3430
The expected NPV of waiting 1 year is 0.5(-$27.1468) + 0.5($45.3430) = $9.0981 million.
Given the option to sell, it makes sense to wait 1 year before deciding whether to
make the acquisition.
14-4
a.
0
1
12%
|
| 
-6,200,000
600,000
14
15
600,000
600,000
Using a financial calculator, input the following data: CF0 = -6,200,000;
CF1-15 = 600,000; I = 12; and then solve for NPV = -$2,113,481.31.
b.
0
1
12%
|
| 
-6,200,000
1,200,000
14
15
1,200,000
1,200,000
Using a financial calculator, input the following data: CF0 = -6,200,000;
CF1-15 = 1,200,000; I = 12; and then solve for NPV = $1,973,037.39.
c. If they proceed with the project today, the project’s expected NPV = (0.5  -$2,113,481.31)
+ (0.5  $1,973,037.39) = -$70,221.96. So, Hart Enterprises would not do it.
d. Since the project’s NPV with the tax is negative, if the tax were imposed the firm would
abandon the project. Thus, the decision tree looks like this:
NPV @
0
1
2
15
Yr. 0
r= 12%
50% Prob.
|
|
|

|
Taxes
-6,200,000
6,000,000
0
0
-$ 842,857.14
No Taxes
50% Prob.
|
-6,200,000
|
1,200,000
|
1,200,000

|
1,200,000
1,973,037.39
Expected NPV $ 565,090.13
Yes, the existence of the abandonment option changes the expected NPV of the project
from negative to positive. Given this option the firm would take on the project because its
expected NPV is $565,090.13.
e.
50% Prob.
Taxes
0
1
r = 12%
|
|
NPV = ?
-1,500,000
+300,000 = NPV @ t = 1
No Taxes
50% Prob.
|
NPV = ?
|
-1,500,000
+4,000,000 = NPV @ t = 1
NPV @
Yr. 0
wouldn’t do
$
0.00
2,232,142.86
Expected NPV $1,116,071.43
If the firm pays $1,116,071.43 for the option to purchase the land, then the NPV of the
project is exactly equal to zero. So the firm would not pay any more than this for the
option.
14-5
a.
40% Prob.
Good
0
1
r = 10%
|
|
-20,000
25,000
2
|
25,000
NPV = 23,388
Bad
60% Prob.
|
-20,000
|
5,000
NPV = -11,322
|
5,000
ENPV = 23,388 (0.40) – 11,322 (0.60) = $2,562
b.
40% Prob.
Good
0 r = 10% 1
|
|
-20,000
25,000
Bad
60% Prob.
|
-20,000
|
5,000
2
3
|
|
25,000
25,000
-20,000 (r = 6%)
|
5,000
|
0
4
|
25,000
|
0
The PV of the 20,000 payment in year 2 at the risk free rate is 20,000/(1.06)2 = 17,800. The
PV of the 4 cash flows of 25,000 in years 1 through 4 at the cost of capital of 10% is 79,247.
The NPV of the top row is 79,247 – 20,000 – 17,800 = 41,447.
The NPV of the bottom row is still -11,332, as it was in part a.
The ENPV is 41,447 (0.40) -11,332 (0.60) = $9,786.
ENPV = 23,388 (0.40) – 11,322 (0.60) = $2,562. This is the ENPV of the project including
the growth option. The value of the growth option itself is the difference:
Value of growth option = 9,786 – 2,562 = 7,224.