You are operating a gas turbine power station (GTPS). The risk factor driving cash inflows (revenues) is the electricity price. The risk factor driving cash outflows (expenses) is the gas price. At current prices, the yearly gas bill is EUR 50m (assume payment upfront) for producing a volume of electric power that can be sold for EUR 55m on the market (assume payment upfront).The electricity and gas price follow a multiplicative binomial distribution with the parameters u=1.8 and d =0.6 (electricity) and u=1.5 and d=0.8 (gas). Also for simplicity, we assume perfect correlation. The objective probability q for an upward movement is 0.5. The risk-free rate is equal 8.00% per yearWhat is the value of the GTPS closest to, if it lives for two years and one binomial step is equal one year? Conduct the valuation on a risk-neutral basis.

Question

BlackTom AI · Accepted Answer

Question restatement: You operate a GTPS where the revenue-driving risk factor is electricity price and the expense-driving risk factor is gas price. At current prices, yearly gas bill = EUR 50m (paid upfront) for producing power that can be sold for EUR 55m on the market (paid upfront). Electricity price follows a multiplicative binomial with u = 1.8 and d = 0.6; gas price with u = 1.5 and d = 0.8. Prices move perfectly correlated. The objective probability of an upward move in a step is q = 0.5. The risk-free rate is 8% per year. The GTPS lives for two years with one binomial step per year. Evaluate on a risk-neutral basis. Options provided: A. 15.00 million EUR.

Now, let’s analyze the cash flows and the pricing framework step by step.

Step 1 – Determine year-by-year payoffs under each state
- If electricity goes up (multiplier uE = 1.8) and gas goes up (multiplier uG = 1.5) in a year, revenue = 55m × 1.8 = 99m and cost = 50m × 1.5 = 75m, so profit for that year = 99m − 75m = 24m.
- If electricity goes down (multiplier dE = 0.6) and gas goes down (multiplier dG = 0.8) in a year, revenue = 55m × 0.6 = 33m and cost = 50m × 0.8 = 40m, so profit for that year = 33m − 40m = −7m.
- Because prices move perfectly correlated, in any given year the state is either UP (both prices move up) or DOWN (both move down). There are two possible year-end payoffs per year: +24m in an UP year and −7m in a DOWN year.

Step 2 – Risk-neutral probability for an up move
- For the electricity asset: p* = (1 + r − d) / (u − d) = (1.08 − 0.6) / (1.8 − 0.6) = 0.48 / 1.2 = 0.4.
- For the gas asset (with the same structure under perfect correlation): p* = (1.08 − 0.8) / (1.5 − 0.8) = 0.28 / 0.7 = 0.4.
- Since moves are perfectly correlated, the risk-neutral probability of an UP move in each year is 0.4, and DOWN is 0.6. The real-world q = 0.5 is not used for pricing under risk neutrality; we use p* = 0.4 for each year.

Step 3 – Build the two-year binomial tree and terminal payoffs
- Year 1 UP (prob 0.4): profit = +24m; Year 1 DOWN (prob 0.6): profit = −7m.
- Year 2 experiences the same UP/DOWN mechanics conditioned on Year 1, so terminal paths are: UU (24m then 24m), UD (24m then −7m), DU (−7m then 24m), DD (−7m then −7m).
- Terminal payoffs across two years:
  • UU: 24m + 24m = 48m
  • UD: 24m − 7m = 17m
  • DU: −7m + 24m = 17m
  • DD: −7m − 7m = −14m

Step 4 – Compute the risk-neutral probabilities of terminal states
- Path probabilities under p* in a two-step binomial with equal step probabilities: UU = 0.4 × 0.4 = 0.16; UD = 0.4 × 0.6 = 0.24; DU = 0.6 × 0.4 = 0.24; DD = 0.6 × 0.6 = 0.36.

Step 5 – Value the two-year cash flows under risk-neutral pricing
- Expected terminal payoff under risk-neutral measure = 0.16×48 + 0.24×17 + 0.24×17 + 0.36×(−14)
  = 7.68 + 4.08 + 4.08 − 5.04
  = 10.80 (in million EUR).
- Present value with risk-free rate r = 8% over two years: discount factor = (1 + r)^2 = 1.08^2 = 1.1664.
- Net present value = 10.80 / 1.1664 ≈ 9.26 million EUR.

Step 6 – Compare with the given option
- The calculated risk-neutral value of the GTPS, based on the two-year binomial model with the stated parameters, is approximately 9.26 million EUR.
- The provided option 15.00 million EUR is higher than this calculated value. Given the structure and numbers, 9.26m is the result you would expect from standard risk-neutral valuation in this setup, not 15.00m.

Summary of key points to avoid common pitfalls:
- Do not mix real-world q with risk-neutral pricing; use p* derived from r, u, d for each asset, here both assets share p* = 0.4 due to identical structure and perfect correlation.
- Multiply payoffs year by year before aggregating, since profits depend on both revenue and cost multipliers in each year.
- Discount back two years using (1.+r)^2, not simply once per year at risk-free rate.

Result (for completeness of the calculation): the GTPS value under the given risk-neutral framework is about 9.26 million EUR, not 15.00 million EUR.

View Explanation

Log in for full answers

Similar Questions

For some value of p, the payoff associated with node F is 4045.16, and the payoff associated with G is -842.99. What is the payoff associated with node C?

A stock is selling for $53.20. Interest rates are 6.0% and the returns on the stock have a standard deviation of 24.0%. What is the forecasted up movement in the stock over 6 months, Suu, assuming two periods of 3 months each, h=3months?

In the binomial option pricing model, how is the asset price assumed to behave in each time period?

More Practical Tools for International Students

Exam Browser Assistant

Stylized Writing Assistant

Plagiarism Checker Assistant

Citation Assistant

In-Class Translation Assistant

Class Notes Assistant

Quiz Search Assistant

Past Exam Questions by School

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler