3D Green Finance City: Energy Transition, Green Bond, Carbon Price, Retrofit NPV and Abatement Cost Curve

Building the district...

Presets

Live readouts

Graphs

Carbon price paths, $/t (thick green: your scenario)

Cumulative cash flow of the funded programme, $M (blue nominal, orange discounted)

NPV against discount rate, $M (the IRR is where it crosses zero)

Green bond price against yield (dashed: duration + convexity estimate)

District emissions, kt CO2 per year (grey: no programme)

What is happening now

Press Play.

Marginal abatement cost curve ($/t against kt/yr): green funded, amber over budget, slate too expensive

Sensitivity (tornado): change of NPV when each input moves by -20 % / +20 %

Green bond service (teal) against operating cash of the programme (green), $M per year

Numerical checks

running...

How to use

Pick a preset or move the sliders. The six tiles show NPV, IRR, abatement, average cost, green bond price and coupon cover. In the marginal abatement cost curve each bar is a measure: its width is the tonnes it removes per year and its height the cost per tonne. Green bars are funded, amber ones are cheap enough but the bond budget ran out, slate ones cost more than the carbon price. Use the Year slider (or press Play) to watch measures come online year by year; dashed lines are the levelised carbon price (teal) and today's price (purple). Drag to orbit, wheel to zoom, click any object to see its measure. Space pauses, R restarts.

Things to try: (1) choose Policy stalls and see that only the measures that pay for themselves survive; (2) choose Budget-limited and see amber bars: the price is high but the bond is too small, so raise the face value; (3) set the discount rate to 12 % and watch the long-lived insulation and district heating drop out first; (4) raise the greenium to 30 bp and read its value in $M; (5) in the tornado chart find which single input moves the NPV most; (6) set a late policy shock and see the cash flow jump after the shock year.

The district, its buildings, street lamps, heat-pump units, solar arrays, turbines, hydrogen tanks, direct-air-capture fans, depot, buses and the bond tower with its turning coin were modelled in Blender 5.2 with baked PBR textures (window facade, stone, brushed steel and aluminium) and exported as one Draco GLB. Three.js r160 shows each measure when the finance model says it is online, turns the street lamps from orange to white, tints insulated houses, lets the turbines spin with the wind slider, and makes the chimney smoke and the haze follow the emissions curve.

The science

A city district emits 1,000 kt CO₂ per year (synthetic baseline). Ten decarbonisation measures could cut it. Which ones should a green bond pay for, and does the programme earn its cost of capital? The page answers with five standard tools of climate finance, all computed live from the sliders. All data are synthetic and rounded for teaching; this is not investment advice and not a model of any real city, bond or company.

1. Carbon price scenario. A real-terms price path with optional policy shock (a jump of size J at year t_s). The four presets mimic the shapes of the usual scenario families (stalled policy, orderly transition, late disorderly jump, high ambition); the numbers are not taken from any scenario set.

p(t) = p₀ (1 + g)^t · (1 + J · 1[t ≥ t_s])

2. Marginal abatement cost curve (MACC). Each measure i has capex K_i, yearly energy saving S_i (growing at the energy price rate g_e), opex O_i, abatement a_i (kt/yr) and life n_i. Its levelised cost of abatement in $/t is the annualised net cost per tonne:

c_i = [ K_i · CRF(r, n_i) + O_i − S_i · A_g/A₀ ] / a_i · 1000, CRF = r / (1 − (1+r)⁻ⁿ) A₀ = Σ_t=1..n (1+r)^−t, A_g = Σ_t=1..n ((1+g_e)/(1+r))^t

A negative c_i means the measure pays for itself through energy savings alone (LED lighting, building controls). Sorting by c_i and plotting bar width = a_i gives the MACC; the area above the zero line is the total cost of the programme per year.

3. Funding rule. A measure is worth doing when its cost per tonne is below the levelised carbon price the programme can earn, and it fits in the budget the green bond raises (cheapest first):

p̄ = Σ p(t)(1+r)^−t / Σ (1+r)^−t, fund i if c_i ≤ p̄ and Σ K ≤ F · P/100 · (1 − fee)

Funded measures are built in cost order over the roll-out period R; capex is paid the year before a measure goes online.

4. Cash flows, NPV, IRR, payback. In every year the programme has capex, energy savings, opex and the carbon value of the tonnes avoided (kt × $/t / 1000 = $M):

CF_t = −K_t + S_t − O_t + p(t) · A_t/1000, NPV = Σ_t=0..N CF_t (1+r)^−t, NPV(IRR) = 0

The IRR is found by bisection. Payback is the first year the cumulative cash flow turns positive (linear interpolation); the discounted payback uses discounted flows. The tornado chart re-runs the whole model with each input ±20 % to show what the answer is most sensitive to.

5. Green bond. A bullet bond of face F, coupon c and tenor T priced at the green yield y = y_m − greenium (the small yield discount green labels sometimes earn):

P = Σ_t=1..T 100c/(1+y)^t + 100/(1+y)^T, D_mod = (1/P) Σ t CF_t/(1+y)^t+1, C = (1/P) Σ t(t+1) CF_t/(1+y)^t+2 ΔP/P ≈ −D_mod Δy + ½ C (Δy)², coupon cover_t = (S_t − O_t + p(t) A_t/1000) / (F c)

The greenium value is the extra price paid for the green label, F(P_green − P_conventional)/100. Net proceeds after a 1 % issue fee are the budget of the programme. The price-yield graph shows the curvature that the duration + convexity estimate captures.

Numerical checks run in the page (11). (1) a par bond (coupon = yield) prices at 100; (2) modified duration against a central finite difference of the price; (3) convexity against a second difference; (4) annuity closed form against an explicit sum; (5) a flat carbon price equal to a measure's c_i gives NPV = 0 when re-summed independently; (6) NPV at the computed IRR is zero; (7) programme NPV equals the present values of its four cash-flow streams; (8) the MACC is sorted; (9) total abatement equals the sum of the measures; (10) p₀(1+g)¹⁰ against iterated compounding; (11) CRF × annuity factor = 1; funded capex never exceeds bond proceeds.

Simplifications. Real terms, no inflation, tax, subsidies or carbon-market frictions. Abatement of measures is simply additive (in reality heat pumps and insulation overlap, and a cleaner grid shrinks the benefit of solar PV and electrification). The carbon price is treated as a cash benefit (an avoided allowance cost or a shadow price) known in advance with perfect foresight. Measures stop at the end of their life with no replacement or residual value. Energy savings do not depend on the wind slider (wind speed only spins the turbines). The bond is a bullet with no default risk; DSCR-style cover compares operating cash with coupons only. Greenium is a user input, not a forecast: observed premiums are small and uncertain.