April 9, 2014 Abt Associates | Relationship of Annualized Costs Across Options with Different Discount Rates | pg 1

Date April 9, 2014

To The Final Section 316(b) Existing Facilities Rule Record

From Abt Associates

Subject Changes in the Relationship Between Discounted and Annualized Social Costs Across 

Options with Different Discount Rates

This memorandum discusses the relationship between social costs discounted and annualized using two 

different discount rates – 3 percent and 7 percent – across regulatory options analyzed for existing units in 

support of the Final Section 316(b) Existing Facilities Rule. 

As shown in Table 1, at the 3-percent discount rate, EPA calculated annualized social costs for existing 

units of $272 million under the final rule, $252 million under Proposal Option 4, and $3,643 million 

under Proposal Option 2. At the 7-percent discount rate, these costs are $295 million under the final rule, 

$272 million under Proposal Option 4, and $3,583 million under Proposal Option 2 (for details on 

development of social costs, see Chapter 7: Total Social Costs of the Economic Analysis for the Final 

Section 316(b) Existing Facilities Rule (EA)). Accordingly, the social costs discounted and annualized at 

the 3-percent discount rate are lower than those annualized at the 7-percent discount rate for the final rule 

and Proposal Option 4, while the inverse is the case for Proposal Option 2: annualized costs at the 3-

percent discount rate are higher than at the 7-percent discount rate. Upon first examination, these results 

may appear counterintuitive; however, the differences in this relationship across options reflect 

differences in the time profile of costs across the options. In particular, when costs are relatively ‘frontloaded’, as they are for the final rule and Proposal Option 4 relative to Proposal Option 2, total costs 

annualized at the 3-percent discount rate are less than those annualized at the 7-percent discount rate. 

However, as the cost profile shifts to later years, as it does under Proposal Option 2, the relationship 

eventually switches, with total costs annualized at the 3-percent discount rate being greater than those

annualized at the 7-percent discount rate (see Table 1).

An example presented in Table 2 demonstrates this concept more precisely. In this example, the switch in 

the relationship of total costs annualized at the 3- and 7-percent discount rates as the time profile of costs 

changes occurs when the “lumpy” $1 million outlay goes from year eight to year nine. Table 2 illustrates 

the conflicting effects between present-value discounting and annualization. A lower discount rate for a 

given cost stream increases the present value of the cost stream. At the same time, for a given present 

value of costs, a lower discount rate decreases the annualized cost. Which of these competing effects wins 

when looking at a given cost profile depends on the distribution of costs over time as follows:

 When costs are relatively front-loaded, the effect of a higher discount rate in lowering present 

value is less important (because the mass of the distribution is closer to the present, and thus, is

discounted less) than the effect of the higher discount rate in increasing annualized cost: the cost 

annualized at the higher discount rate will tend to be higher than the cost annualized at the lower 

discount rate. 

 Looking in the other direction, when costs are relatively back-loaded, the effect of a higher 

discount rate in lowering present value is more important (because the mass of the distribution is 

more in the future, and thus, is subject to greater discounting) than the effect of the higher 

discount rate in increasing annualized cost: the cost annualized at the higher discount rate will 

tend to be less than that annualized at the lower discount rate.

Memorandum

Environment and Resources
April 9, 2014 Abt Associates | Relationship of Annualized Costs Across Options with Different Discount Rates | pg 2

Table 1: Time Profile of Total Social Costs for Existing Units, Including Compliance 

Costs for Facilities and Administrative Costs to States and Federal Government 

(Millions; $2011)

Year Proposal Option 4 Final Rule Proposal Option 2

2013 $0.0 $0.0 $0.0 

2014 $48.1 $48.1 $24.8 

2015 $90.2 $90.2 $36.5 

2016 $98.0 $98.0 $35.7 

2017 $90.5 $90.5 $36.0 

2018 $593.7 $657.8 $3,197.3 

2019 $876.7 $929.3 $4,825.2 

2020 $872.7 $1,089.0 $7,432.1 

2021 $611.6 $626.8 $9,839.8 

2022 $1,145.0 $1,230.4 $8,926.4 

2023 $118.8 $124.3 $9,014.3 

2024 $126.4 $131.9 $7,339.1 

2025 $128.2 $133.7 $6,517.0 

2026 $128.9 $134.4 $5,083.6 

2027 $128.1 $133.6 $4,854.8 

2028 $129.6 $135.1 $4,509.6 

2029 $133.4 $138.9 $4,259.4 

2030 $130.5 $136.0 $4,158.9 

2031 $129.1 $134.6 $3,244.7 

2032 $128.1 $133.6 $3,250.2 

2033 $129.6 $135.1 $3,252.9 

2034 $133.4 $138.9 $3,279.6 

2035 $130.5 $136.0 $3,301.6 

2036 $129.1 $134.6 $3,301.5 

2037 $128.1 $133.6 $3,301.2 

2038 $390.1 $412.8 $3,330.6 

2039 $409.9 $424.8 $3,323.6 

2040 $309.8 $324.6 $3,321.5 

2041 $351.5 $364.3 $3,365.1 

2042 $555.2 $572.3 $3,341.6 

2043 $163.0 $195.0 $3,356.9 

2044 $342.2 $367.6 $3,365.1 

2045 $393.2 $517.7 $3,465.3 

2046 $196.8 $202.3 $3,389.2 

2047 $322.4 $360.7 $3,365.4 

2048 $130.1 $138.0 $3,312.8 

2049 $133.4 $141.5 $3,336.2 

2050 $131.3 $138.0 $3,305.8 

2051 $131.2 $137.3 $3,302.4 

2052 $128.5 $134.8 $3,302.0 

2053 $129.6 $135.1 $3,301.1 

2054 $133.4 $138.9 $3,304.8 

2055 $130.5 $136.0 $3,301.6 

2056 $127.1 $132.6 $3,300.7 

2057 $124.4 $129.9 $3,299.8 

2058 $149.2 $156.4 $3,302.0 

2059 $137.9 $143.9 $3,302.3 

2060 $0.0 $0.0 $0.0 

2061 $0.0 $0.0 $0.0 

2062 $0.0 $0.0 $0.0 

2063 $0.0 $0.0 $0.0 

2064 $0.0 $0.0 $0.0 

Present Value, 3% $6,729.3 $7,280.7 $97,382.4 

Annualized, 3% $251.8 $272.4 $3,643.2 

Present Value, 7% $4,027.8 $4,370.5 $53,031.4 

Annualized, 7% $272.1 $295.3 $3,583.0 

Source: U.S. EPA Analysis for this memorandum
April 9, 2014 Abt Associates | Relationship of Annualized Costs Across Options with Different Discount Rates | pg 3

Table 2: Examples of Time Profiles of Costs and Their Impact on the Relationship of Costs 

Annualized at the 3- and 7-Percent Discount Rates

Time Profile of Costs

Year 1 2 3 4 5 6 7

1 $1,000,000 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000

2 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000

3 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000

4 $25,000 $1,000,000 $25,000 $25,000 $25,000 $25,000 $25,000

5 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000

6 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000

7 $25,000 $25,000 $1,000,000 $25,000 $25,000 $25,000 $25,000

8 $25,000 $25,000 $25,000 $1,000,000 $25,000 $25,000 $25,000

9 $25,000 $25,000 $25,000 $25,000 $1,000,000 $25,000 $25,000

10 $25,000 $25,000 $25,000 $25,000 $25,000 $1,000,000 $25,000

11 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000

12 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000

13 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000 $1,000,000

14 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000

15 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000

16 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000

17 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000

18 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000

19 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000

20 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000

21 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000

22 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000

23 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000

24 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000

At 3 Percent

Present 

Value

$1,369,990 $1,289,663 $1,216,153 $1,193,063 $1,170,645 $1,148,880 $1,087,316

Annualized $78,538 $73,933 $69,719 $68,395 $67,110 $65,863 $62,333

At 7 Percent

Present

Value

$1,197,948 $1,030,556 $893,914 $854,192 $817,069 $782,374 $691,324

Annualized $97,615 $83,975 $72,841 $69,604 $66,579 $63,752 $56,333

Annualized Costs: 3 Percent vs. 7 percent 

less less less less greater greater greater

Source: U.S. EPA Analysis for this memorandum