Homework 3
Cost–Benefit Analysis of Investment in CCUS
Homework Instructions
No Generative AI: You are not allowed to use generative AI tools for Homework Assignment 3.
Allowed Tools: You must use a calculator or computational tool such as R, Python, or Excel to perform the required cost–benefit and \(\text{PV}_{NB}\) calculations.
- Show your intermediate steps with formula and final numeric results clearly.
Deadline: Wednesday, November 12, 2025, at 10:30 A.M.
A mid-sized energy company is considering investing in Carbon Capture, Utilization, and Storage (CCUS) at one of its gas-fired power plants.
The project would allow the company to capture carbon dioxide (CO₂) before it reaches the atmosphere, then transport and store it underground or sell it to industrial users for other applications.
The total investment cost is $500 million, paid at the start of the project (Year 0).
Once operational, the system can capture 1 million metric tons of CO₂ per year.
The company’s cost of capital (discount rate) is 4%, and the Social Cost of Carbon (SCC) is $190 per metric ton of CO₂.
🌍 What Is CCUS?
Carbon Capture, Utilization, and Storage (CCUS) is a technology designed to reduce greenhouse gas emissions from power plants and industrial facilities. It involves three main stages:
- Capture – separating CO₂ from other gases in emissions.
- Utilization – reusing CO₂ to make products such as building materials or fuels.
- Storage – injecting CO₂ deep underground to store it permanently.
CCUS is a transitional technology, helping decarbonize existing fossil-fuel infrastructure while renewable energy capacity continues to expand.
- Industrial Decarbonization: Captures emissions from cement, steel, and fertilizer production—industries difficult to electrify.
- Carbon Recycling: Converts CO₂ into synthetic fuels or chemicals.
- Direct Air Capture (DAC): Removes CO₂ directly from the air for storage or reuse.
- Regional Storage Hubs: Shared “CO₂ pipeline and storage” networks now serve multiple emitters.
- Enhanced Oil Recovery (EOR) is one of the main utilization pathways in CCUS. Captured CO₂ is injected into depleted oil reservoirs to push out additional crude oil that would otherwise be unrecoverable.
- EOR creates a private revenue opportunity for CCUS operators by selling captured CO₂ to oil producers.
- However, its climate benefit depends on whether the injected CO₂ remains permanently stored underground and how much additional fossil fuel extraction it leads to overall.
- In practice, EOR can serve as a transitional market for CO₂ utilization while broader storage and industrial uses expand.
💵 Where Do the Costs and Benefits Come From?
| Type | Example Sources | Explanation |
|---|---|---|
| Private Costs | Building, operating, and maintaining capture units, pipelines, compression, monitoring | Upfront and ongoing expenses the company must pay. |
| Private Benefits | 1) 45Q tax credits per ton captured/stored; 2) CO₂ sales (e.g., to industry/EOR); 3) Avoided future carbon fees | Cash inflows that improve the firm’s bottom line. |
| Social Benefits | 1) Avoided climate damages (SCC = $190/tCO₂); 2) Local air-quality improvements | External benefits not reflected in market prices. |
| Social Costs | Construction disturbance, extra energy use (energy penalty), long-term monitoring | Typically smaller than the avoided climate damages. |
🏛️ Section 45Q Tax Credit
The Section 45Q tax credit was first created under the Energy Improvement and Extension Act of 2008 (Division B of the Emergency Economic Stabilization Act of 2008, Public Law 110–343) and later expanded under the Inflation Reduction Act of 2022.
In this homework, we refer to the updated policy framework as the One Big Beautiful Bill Act, which broadened support for both utilization and storage under Section 45Q by equalizing credit values across different CO₂ end uses and expanding eligibility for utilization projects.
⚙️ Project Details
Construction and Operation Timeline
- Investment (Capital Outlay): Year 0
- Operation: 5 years (Years 1–5) for this exercise
- Project Lifetime: 20+ years (only the first 5 years are analyzed)
🏗️ Investment Cost
| Year | Investment Outlay (Million $) |
|---|---|
| 0 | 500 |
| Total | 500 |
💰 Expected Annual Net Benefits (Private, before discounting and without 45Q tax credits)
The company estimates the following annual net benefits (in millions of dollars), after paying all operating costs but before discounting.
| Year of Operation | Net Benefit (Million $) | Main Sources of Benefit |
|---|---|---|
| 1 | -15 | Ramp-up phase, limited CO₂ sales, no full-scale operation |
| 2 | 10 | Full CO₂ capture, CO₂ sales |
| 3 | 10 | Continued steady operation |
| 4 | 10 | Same as above |
| 5 | 5 | Slight drop due to maintenance and reduced output |
🏦 The Cost of Capital
- The cost of capital (4%) is the company’s required rate of return — what investors expect to earn.
- It also serves as the discount rate that a company uses to determine the present value of its future benefits and costs.
- This rate reflects the opportunity cost of money — the return they could earn from alternative investments.
- A project must earn at least this rate to be financially worthwhile.
✏️ Homework Tasks
Question 1. Private Present Value OF Net Benefit (\(\text{PV}_{NB}\))
- Use the annual benefits table to calculate the Present Value (PV) of benefits at 4%.
- Subtract the $500 million investment to find the Private \(\text{PV}_{NB}\).
- Interpret whether the project is financially attractive for the company.
| PV of Total Benefits (Million $) | PV of Costs (Million $) | Private \(\text{PV}_{NB}\) (Million $) |
|---|---|---|
| 500 |
From the table, the private net benefits (excluding 45Q and SCC) in millions of dollars are:
\((-15,\; 10,\; 10,\; 10,\; 5)\) for Years 1–5.
Compute the PV of benefits at 4%:
\[ \text{PV}_B(4\%) = \frac{-15}{1.04} + \frac{10}{1.04^2} + \frac{10}{1.04^3} + \frac{10}{1.04^4} + \frac{5}{1.04^5}. \]
Numerically (in millions):
- Year 1: \(-15/1.04 \approx -14.42\)
- Year 2: \(10/1.04^2 \approx 9.25\)
- Year 3: \(10/1.04^3 \approx 8.89\)
- Year 4: \(10/1.04^4 \approx 8.55\)
- Year 5: \(5/1.04^5 \approx 4.11\)
So
\[ \text{PV}_B(4\%) \approx -14.42 + 9.25 + 8.89 + 8.55 + 4.11 \approx 16.37\ \text{million}. \]
Now subtract the Year-0 investment of $500 million:
\[ \text{Private PV}_{NB}(4\%) = -500 + 16.37 \approx -483.63\ \text{million}. \]
| PV of Total Benefits (Million $) | PV of Costs (Million $) | Private \(\text{PV}_{NB}\) (Million $) |
|---|---|---|
| 16.37 | 500 | -483.63 |
Interpretation:
At a 4% discount rate, the private \(\text{PV}_{NB}\) is strongly negative (about -$484 million), so the project is not financially attractive for the company based only on private costs and benefits (ignoring SCC and 45Q).
Question 3. How Large Should the 45Q Credit Be? (Realism Check)
Part A
Using your \(\text{PV}_{NB}\) setup from Question 1 (at 4%), show that the project’s Private \(\text{PV}_{NB}\) with the current $85/t credit is negative.
Using the benefit stream that excludes 45Q from Q1, \((-15,\,10,\,10,\,10,\,5)\) (in millions), adding the existing 45Q credit contributes $85 million per year (since capture is 1 Mt/yr). The NPV at \(r=4\%\) is:
\[ \text{Private PV}_{NB}(4\%) \;=\; -500 + \left(\frac{-15}{1.04} + \frac{10}{1.04^2} + \frac{10}{1.04^3} + \frac{10}{1.04^4} + \frac{5}{1.04^5}\right) + \left(\frac{85}{1.04} + \frac{85}{1.04^2} + \frac{85}{1.04^3} + \frac{85}{1.04^4} + \frac{85}{1.04^5}\right). \]
Numerically (millions):
- Baseline PV (excl. 45Q): \(\approx 16.37\)
- PV of $85/t credit: \(85 \times \left(\frac{1}{1.04} + \cdots + \frac{1}{1.04^5}\right) \approx 85 \times 4.4518 \approx 378.41\)
So \[ \text{Private PV}_{NB}(4\%) \approx -500 + 16.37 + 378.41 \;=\; \mathbf{-105.23} \;<\; 0. \]
Conclusion: With the current $85/t credit, the private NPV is negative at 4%.
Part B
Calculate the minimum 45Q credit per ton needed to make the Private \(\text{PV}_{NB}\) ≈ 0 (breakeven).
| Scenario | Credit per ton ($) | Private \(\text{PV}_{NB}\) @ 4% (Million $) | Investment Decision |
|---|---|---|---|
| Current policy | 85 | Negative | Not attractive |
| Breakeven (your estimate) | ≈ 0 | Borderline | |
| Above breakeven | Positive | Attractive |
Let \(p_{\text{total}}\) be the total credit per ton (in $). Since 1 Mt is captured each year, this adds \(p_{\text{total}}\) million per year. Set NPV to zero:
\[ 0 \;=\; -500 + \underbrace{\left(\frac{-15}{1.04} + \frac{10}{1.04^2} + \frac{10}{1.04^3} + \frac{10}{1.04^4} + \frac{5}{1.04^5}\right)}_{\approx\,16.37} + \; p_{\text{total}} \!\!\left(\frac{1}{1.04} + \frac{1}{1.04^2} + \frac{1}{1.04^3} + \frac{1}{1.04^4} + \frac{1}{1.04^5}\right). \]
The sum of discount factors is \[ \frac{1}{1.04} + \frac{1}{1.04^2} + \frac{1}{1.04^3} + \frac{1}{1.04^4} + \frac{1}{1.04^5} \;\approx\; 4.4518. \]
Solve for \(p_{\text{total}}\): \[ p_{\text{total}} \;=\; \frac{500 - 16.37}{4.4518} \;\approx\; \mathbf{108.64\ \text{dollars per ton}}. \]
So a total credit of about $109/t is needed for breakeven at 4% (which implies an incremental \(\Delta p \approx \$24/t\) above today’s $85/t).
Decision Table (at 4%)
| Scenario | Credit per ton ($) | Private NPV @ 4% (Million $) | Investment Decision |
|---|---|---|---|
| Current policy | 85 | -105.23 | Not attractive |
| Breakeven (rounded) | 109 | ≈ 0.00 | Borderline |
| Above breakeven (ex.) | 120 | +50.59 | Attractive |
Question 4. Short Answer
Part A
Explain how per-ton tax credits (like 45Q) help align private and social goals. Why might higher per-ton credits be economically justified beyond simply achieving a positive social \(\text{PV}_{NB}\)? In your answer, discuss the underlying economic mechanisms and sources of market failure.
Per-ton tax credits (like 45Q) internalize the positive externality of carbon removal/storage by paying firms for the social benefit their actions create but cannot monetize privately. By raising the private return, the credit aligns private incentives with socially efficient levels of abatement or carbon storage.
Higher per-ton credits can be justified when there are additional market failures beyond the carbon externality itself. These include:
- Learning-by-doing and technology spillovers: Early CCUS deployment lowers future costs, but firms cannot capture these spillover benefits.
- Capital market failures and risk premiums: Long-lived, uncertain CCUS projects face financing frictions that suppress investment below the social optimum.
- Coordination failures (e.g., shared transport/storage infrastructure): Private actors underinvest when projects depend on complementary assets.
- Policy uncertainty: Expectations of future political reversal reduce investment; higher credits can counter this risk discount.
Thus, credits may need to exceed the “Pigouvian” level implied by social \(\text{PV}_{NB}\) to overcome compounded market failures and unlock socially optimal deployment.
Part B
Why might private investors hesitate to build CCUS projects without government incentives?
Private investors hesitate because CCUS projects involve high upfront capital costs, long payback periods, and uncertain revenue streams—especially when the market does not pay for avoided emissions. Carbon storage provides public benefits but generates little to no private cash flow.
Additional barriers include:
- Policy and regulatory uncertainty about future carbon credit rules or liability for stored CO₂.
- Technological and operational risks, which raise the required rate of return.
- Lack of pipeline and storage infrastructure, making early projects risky and expensive.
- No natural market demand for CO₂ storage, so without incentives there is no revenue model.
Because private returns are far below social returns, investors rationally underinvest absent government support.