Raj Singh Colt Industries
RSP Holdings after the deal
Price of the Stub
Proposed Dividend 5 10 15 20 25
70 52.83% 37.39% 29.73% 25.15% 22.10%
75 54.43% 38.82% 30.94% 26.18% 23.00%
80 55.93% 40.19% 32.10% 27.18% 23.87%
85 57.33% 41.49% 33.23% 28.16% 24.73%
90 58.65% 42.74% 34.32% 29.11% 25.56%
Rough Interest Calculation (Assuming a fixed rate swap for all debt)
Interest on existing debt (estimated) 37.00
10.54% (LIBOR + 2.5%) on $700M senior 73.78
10.04% (LIBOR + 2%) on $200M revolver 20.08
12.5% on $525M 65.63
196.49
Rough Cash Flow Analysis
1985 1986 1987 1988 1989 1990 1991
EBIT 232.4 217.9 259.4 273.9 293.9 318.7 335.4
Interest (5.6) (98.0) (196.5) (191.2) (186.0) (180.7) (170.1)
EBT 226.8 119.9 62.9 82.7 108.0 138.0 165.3
Taxes @43% (97.5) (51.6) (27.1) (35.6) (46.4) (59.3) (71.1)
NI 129.3 68.3 35.9 47.1 61.5 78.7 94.2
Discont. Oper 8.7 - - - - - -
Add Depr 31.6 42.4 43.3 46.9 50.7 54.7 57.1
Subtract CapEx (41.3) (53.0) (62.0) (61.0) (59.5) (51.7) (51.9)
Subt. Chg in WC (136.7) (39.0) (22.1) (7.6) (10.2) (14.2) (5.5)
Principal payment (50.0) (50.0) (50.0) (100.0) (100.0)
Change in Cash (8.4) 18.7 (54.9) (24.6) (7.5) (32.5) (6.1)
Cumm Cash Impact 10.3 (44.6) (69.2) (76.7) (109.2) (115.3)
Assumptions:
1. All projections from exhibit 6
2. Interest from the actual deal.
3. 1986 interest is Half of 1987 interest.
Raj Singh Colt Industries
Fraction Held by RSP
Fraction of Debt Dividend Paid
that enhances Val 70 75 80 85 90
0.300 32.3% 40.2% 52.6% 75.0% 127.9%
0.325 30.2% 36.6% 46.2% 61.6% 91.2%
0.350 28.4% 33.8% 41.3% 52.6% 71.6%
0.375 26.9% 31.4% 37.5% 46.2% 59.4%
0.400 25.5% 29.4% 34.5% 41.3% 51.1%
0.425 24.4% 27.7% 32.0% 37.5% 45.0%
0.450 23.3% 26.3% 29.9% 34.5% 40.4%
0.475 22.4% 25.0% 28.2% 32.0% 36.8%
0.500 21.6% 23.9% 26.7% 29.9% 33.9%
0.525 20.9% 23.0% 25.4% 28.2% 31.5%
0.550 20.2% 22.1% 24.2% 26.7% 29.5%
0.575 19.6% 21.3% 23.2% 25.4% 27.8%
0.600 19.1% 20.6% 22.3% 24.2% 26.4%
0.615 18.7% 20.2% 21.8% 23.6% 25.6%
0.650 18.1% 19.4% 20.8% 22.3% 24.0%
0.675 17.7% 18.8% 20.1% 21.5% 23.0%
0.700 17.3% 18.4% 19.5% 20.8% 22.1%
Price of the Stub
Fraction of Debt Dividend Paid
that enhances Val 70 75 80 85 90
0.300 12.98 9.37 5.77 2.16 -1.44
0.325 14.60 11.12 7.63 4.14 0.65
0.350 16.23 12.86 9.49 6.12 2.75
0.375 17.86 14.61 11.35 8.10 4.84
0.400 19.49 16.35 13.21 10.07 6.93
0.425 21.12 18.10 15.07 12.05 9.03
0.450 22.75 19.84 16.93 14.03 11.12
0.475 24.37 21.58 18.79 16.00 13.21
0.500 26.00 23.33 20.66 17.98 15.31
0.525 27.63 25.07 22.52 19.96 17.40
0.550 29.26 26.82 24.38 21.94 19.50
0.575 30.89 28.56 26.24 23.91 21.59
0.600 32.52 30.31 28.10 25.89 23.68
0.615 33.49 31.36 29.22 27.08 24.94
0.650 35.77 33.80 31.82 29.85 27.87
0.675 37.40 35.54 33.68 31.82 29.96
0.700 39.03 37.29 35.54 33.80 32.06
Early Exercise of American Call? Multi period pricing (American Call)
0
Early exercise of an American call is never 169
p+
optimal on a non-dividend paying stock. 130
p 6
100 104
Let price of stock be St and compare strategies: p-
80
46
• A: Early exercise and obtain (St-X) 64
• B: Short the stock and obtain St.
Invest the proceeds in the Riskfree asset. • Suppose the probability of going up is 2/3
in the above tree.Price an American cal
Payoff on maturity at time T from strategy B: with X=120 and the riskfree rate is 10%.
ST >=X ST
Short pos. St(1+rf)-ST St(1+rf)- ST
Call ST-X 0 .
Total St(1+rf)-X St(1+rf)- ST
In both cases the payoff is greater than the
payoff from early exercise: (St-X)(1+rf)
Raj Singh Real Options 8 Raj Singh Real Options 9
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What are Real Options? Option to delay
• Lets start with an example: • Now suppose that
– The lease on my gold mine expires tomorrow. – Now suppose I can extend my lease for a year.
– I can extract all the gold(3000 ounces) instantly. – Everyone agrees P will either go up to 500 with
– Needs $1.25M today to make it operational. 80% probability of go down to 300 with 20%
– Price of gold (P) is $400 today. probability.
• Should I mine today? • What is the maximum I’d be willing to pay
to extend my lease by one year?
(a) 3000 ounces case
• Suppose there were 4000 ounces of gold
instead. (b) 4000 ounces case
Option equivalence?
Raj Singh Real Options 10 Raj Singh Real Options 11
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Decision tree analysis Option to Expand
• Expected value in 1 year (3000 ounces)? • Your school is considering investing in Happy-Berries
(HBS) by setting up a plant costing 100M. The cash flow
from this investment will arrive in 1 year. The expected
value of cashflows at the end of one year is 105M. After
studying the market response the dean at the end of one
year might decide to increase the scale of the plant by
three times. In that case the expected cashflows obtained
• Appropriate discount rate? in year two will be three times the realized cashflow in
year 1. The appropriate risk adjusted discount rate for this
project is 20% and riskfree rate is 10%. There will be no
market after year 2.
• Traditional analysis (Assuming commitment to invest)
E(CF): t=0 t=1 t=2
-100 -300
+105 +315
NPV = -100 - 300/1.1 + 105/1.2 + 315/(1.2)2 = -66.48
Homework:
– What if the investment required will go up by • Traditional analysis (expansion has same risk as CFs)
25% in one year?
NPV of expansion project at t=1 : -300 + 315/1.2 = -37.5
– What if 20% of the gold will get stolen in one NPV of initial project at t=0: -100 +(105-37.5)/1.2 = -43.75
year?
Raj Singh Real Options 12 Raj Singh Real Options 13
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Real Option analysis Other real options in investments
The first thing we will need to do option analysis is the • Option to defer
volatility (standard deviation of first year returns):
Suppose we know it is 30%. – Real estate development.
Value of the expansion option: – Natural resources.
The stock price analogue will be the PV of future CFs. • Growth Options
S = 315/(1.2)2 = 218.75 – Volatile demand products.
The exercise price will be the PV of committing to invest – Multiple products (Derivative products).
now:
X = 300/1.1 = 272.73 • Option to Abandon.
t = 1, rf = 0.1, σ = 0.3 – Airlines choice of service areas or airport gates.
– Acquiring stock for a takeoever.
Value of the call option from B&S: 15.97 • Flexibility options
– Flexible manufacturing systems.
Total Value of project is: -100+105/1.2+15.97 = 3.47
– Switching components.
– Switching products.
– Switching use for infrastructure.
• Option to Focus
– R&D projects.
– Combination of abandonment and growth
option.
Raj Singh Real Options 14 Raj Singh Real Options 15
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