# Laura Martin: Real Options and the Cable Industry Harvard Case Solution & Analysis

Question 1
The valuation of the real option using the Black Scholes Binomial Option Pricing model is the same as computed in exhibit 10 by Martin. This is because we have used the same inputs for the five variables as shown in exhibit 10. The Black Scholes value of the real option which is primarily a call option is \$ 22.4533. The real option modelling has been performed in the excel spreadsheet and is also shown below:
BLACK SCHOLES REAL OPTION VALUATION
Input Data
PV of Potential Project/Home Passed (S) \$23.15
Investment Cost (X) \$1.22
Time to Maturity (T, years) 10.00
Risk Free Rate (rf)— 5%
Volatility (σ) 50%
Output Data
Present Value of Exercise Price (PV(EX)) 0.7217
s*t^.5 1.5811
d1 2.9840
d2 1.4029
Delta N(d1) Normal Cumulative Density Function 0.9986
Bank Loan N(d2)*PV(EX) 0.6637
Value of Call 22.4533
Times: Number of empty 6 MHz channels on the Stealth Tier 17
Asset Value of the Stealth Tier 381.71
Less: current investment/home passed 40
Value of the Stealth Tier/home passed 341.71
Current Market valuation/home passed 2500
Stealth Tier/current valuation 14%
Question 2
Part a).
Laura Martin Real Options and the Cable Industry Harvard Case Solution & Analysis
We have developed the 10 step binomial tree option pricing model in the excel spreadsheet and computed the value of the real call option. The inputs that we have used are summarized in the table below:
10 Step BINOMIAL OPTION PRICING MODEL

Inputs
Option Type: 1=Call, 0=Put 1
PV of Potential Project/Home Passed (S) \$23.15
Up Movement / Period 50.00%
Down Movement / Period 45.00%
Risk-free Rate / Period 5.25%
Investment Cost (X) \$1.22
Time To Maturity (Years) 10.00
Number of Periods 10
The real option value based on the 10 step binomial option pricing model is \$ 22.34 and it is slightly lower than the real option value that we computed in question 1. The 10 step binomial option tree model is shown below:
Now Maturity
Period 0 1 2 3 4 5 6 7 8 9 10
Time 0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000

Asset Tree \$23.15 \$34.73 \$52.09 \$78.13 \$117.20 \$175.80 \$263.69 \$395.54 \$593.31 \$889.96 \$1,334.95
\$33.57 \$50.35 \$75.53 \$113.29 \$169.94 \$254.90 \$382.35 \$573.53 \$860.30 \$1,290.45
\$48.67 \$73.01 \$109.51 \$164.27 \$246.41 \$369.61 \$554.41 \$831.62 \$1,247.43
\$70.58 \$105.86 \$158.80 \$238.19 \$357.29 \$535.93 \$803.90 \$1,205.85
\$102.33 \$153.50 \$230.25 \$345.38 \$518.07 \$777.10 \$1,165.66
\$148.39 \$222.58 \$333.87 \$500.80 \$751.20 \$1,126.80
\$215.16 \$322.74 \$484.11 \$726.16 \$1,089.24
\$311.98 \$467.97 \$701.96 \$1,052.93
\$452.37 \$678.56 \$1,017.84
\$655.94 \$983.91
\$951.11

Call Option Tree \$22.34 \$33.87 \$51.19 \$77.19 \$116.20 \$174.75 \$262.59 \$394.38 \$592.09 \$888.74 \$1,333.73
\$32.71 \$49.45 \$74.58 \$112.30 \$168.89 \$253.80 \$381.20 \$572.31 \$859.08 \$1,289.23
\$47.78 \$72.06 \$108.52 \$163.22 \$245.31 \$368.45 \$553.19 \$830.40 \$1,246.21
\$69.63 \$104.87 \$157.75 \$237.09 \$356.13 \$534.71 \$802.68 \$1,204.63
\$101.34 \$152.46 \$229.15 \$344.22 \$516.85 \$775.88 \$1,164.44
\$147.34 \$221.48 \$332.71 \$499.58 \$749.98 \$1,125.58
\$214.06 \$321.58 \$482.89 \$724.94 \$1,088.02
\$310.82 \$466.75 \$700.74 \$1,051.71
\$451.15 \$677.34 \$1,016.62
\$654.72 \$982.69
\$1,332.51
Part b).
i).
We have changed the volatility variable to account for the degrading of the cable equipment signal at the rate of 1.5% per period. We have incorporated this with a down movement of -48.50% based on the implied volatility of 50% as shown in exhibit 10. Since, the signals would degrade on a per year basis, therefore, this increases the volatility of the future returns of the stealth tier hence, we change this variable. The new value of the real option has slightly increased and it is around \$ 22.36..........................

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