FAQ 906: PPA/ARP Shortfall Payment Calculation using Yield Curve Rates

Problem: How do you calculate the outstanding balance for the prior year shortfall amortization installments and the shortfall amortization installment for the current year when using a yield curve?

Solution: If your results use the 15-Year ARP21 shortfall amortization method, review the ARP21 Example. All PPA valuations beginning in 2022 are required to use 15-year amortizations. If your results use the 7-year PPA shortfall amortization method, review the PPA Example. The PPA Example reflects calculations for a 2021 valuation. ================================== ARP21 15-YEAR AMORTIZATION EXAMPLE ================================== The 15-year amortization method is required for PPA valuations starting in 2022. Amortization Period: 15 years Assumptions: 1/1/2026 valuation Yield curve: 202512 (spot rates as of 12/2025) Spot rates: Year 1.0: 3.89% Year 2.0: 3.95% Year 3.0: 4.03% Year 4.0: 4.14% Year 5.0: 4.27% Year 6.0: 4.41% Year 7.0: 4.55% Year 8.0: 4.69% Year 9.0: 4.83% Year 10.0: 4.95% Year 11.0: 5.07% Year 12.0: 5.18% Year 13.0: 5.28% Year 14.0: 5.37% 2024 shortfall amortization installment (determined using 15-year amortization period) = 50,000 2025 funding shortfall = 400,000 15-year installment factor calculation reflecting payments on 1/1 using the yield curve: Installment 1 = 1.000000 Installment 2 = (1/1.0389)^1 = 0.962557 Installment 3 = (1/1.0395)^2 = 0.925446 Installment 4 = (1/1.0403)^3 = 0.888227 Installment 5 = (1/1.0414)^4 = 0.850217 Installment 6 = (1/1.0427)^5 = 0.811340 Installment 7 = (1/1.0441)^6 = 0.771876 Installment 8 = (1/1.0455)^7 = 0.732372 Installment 9 = (1/1.0469)^8 = 0.693040 Installment 10 = (1/1.0483)^9 = 0.654078 Installment 11 = (1/1.0495)^10 = 0.616844 Installment 12 = (1/1.0507)^11 = 0.580409 Installment 13 = (1/1.0518)^12 = 0.545509 Installment 14 = (1/1.0528)^13 = 0.512276 Installment 15 = (1/1.0537)^14 = 0.480798 Sum of Installments 1 through 15 = 11.024989 Sum of Installments 1 through 14 = 11.024989 - 0.480798 = 10.544191 Present value of the 14 remaining 2024 shortfall payments: 50,000 x 10.544191 = 527,210 2025 shortfall balance = 400,000 - 527,710 = -127,210 2025 shortfall payment = -127,210 / 11.024989 = -11,538 ================================== PPA 7-YEAR AMORTIZATION METHOD ================================== Since the 7-year amortization method was replaced with the 15-year amortization method starting in 2022, this example uses a 2021 valuation date. Amortization Period: 7 years Assumptions: 1/1/2021 valuation Yield curve: 202012 (spot rates as of 12/2020) Spot rates: Year 1.0: 0.26% Year 2.0: 0.42% Year 3.0: 0.53% Year 4.0: 0.66% Year 5.0: 0.85% Year 6.0: 1.08% 2020 shortfall amortization installment = 50,000 2021 funding shortfall = 400,000 7-year installment factor calculation reflecting payments on 1/1 using the yield curve: Installment 1 = 1.00000 Installment 2 = (1/1.0026)^1 = 0.997407 Installment 3 = (1/1.0042)^2 = 0.991653 Installment 4 = (1/1.0053)^3 = 0.984267 Installment 5 = (1/1.0066)^4 = 0.974030 Installment 6 = (1/1.0085)^5 = 0.958563 Installment 7 = (1/1.0108)^6 = 0.937581 Sum of Installments 1 through 7 = 6.843500 Sum of Installments 1 through 6 = 6.843500 - 0.937581 = 5.905919 Present value of the 6 remaining 2020 shortfall payments: 50,000 x 5.905919 = 295,296 2021 shortfall balance = 400,000 - 295,296 = 104,704 2021 shortfall payment = 104,704 / 6.843500 = 15,300