NICAR 2016 | Denver 1
TIME VALUE OF MONEY: AN INTRODUCTION TO PRESENT VALUECezary Podkul |
@Cezary
3/11/2016
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Link to Class Materials
• Everything you need is in Dropbox:
bit.ly/1XiGytY
3/11/2016 NICAR 2016 | Denver
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Roadmap• What we hope to cover today:
1. Sales Pitch: Why is it useful for you to know present value?
2. Example: We’ll model out a simple example together3. Application: We’ll apply what we
learned to a real-life example – CalSTRS
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Why Learn PV?Part 1
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Why Learn PV?• What is it?– A way to put a value today on a stream of
payments owed in the future, such as:• Pension payments• Lottery winnings• That Social Security check you’ll be getting in 40
years• Any flow of money
– All you need to know is the amounts, the time when they’ll be paid, and the interest rate
– Answers the question, “What is that flow of money worth to me today?”
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Why Learn PV?• Can lead to some great
reporting
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- The Washington Post, August 25, 2015
- The Wall Street Journal, October 19, 2012
- Bloomberg News, August 13, 2015
- ProPublica and The Washington Post, July 10, 2015
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Why Learn PV?• If you understand PV,
you can make sense of documents like this– Sample structured
settlement sale from Terry McCoy’s reporting
– Sells $1.6 million in nominal payments worth $844,00 for $40,000, or 5 cents on the present dollar
– Clearly a ripoff3/11/2016 NICAR 2016 | Denver
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Why Learn PV?• And documents like this
– Bond disclosure from NJ saying that their pension liability increased to $82.8 billion from $37.3 billion
– Fine print that made local and national headlines
– The culprit? Discount rate used in PV analysis: 4.29% vs. 7.9% makes a big impact; see our explainer here.
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Why Learn PV?• Better understand
headlines like these– Why is Michael Dell
willing to pay $67 billion for EMC?
– Depends on how much EMC’s business is worth to him today
– How do you find out? Present value of future earnings – plus takeover premium
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- Forbes, October 12, 2015
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Why Learn PV?• Plus, the math makes for great
visuals
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Why Learn PV?• And these concepts are coming to a
state legislature near you!– Anyone here from Alaska? This one’s yours:
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Why Learn PV?• So it’s worth knowing the
mechanics of these calculations
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Simple ExamplePart 2
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Simple Example• Formula for calculating present value
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Present ValueFuture Value
Discount Factor =
Where:Discount Factor = (1+ i )n
i = expected rate of returnn = number of time periods
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Simple Example
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Let’s test drive it!Open a blank Excel worksheet and
let’s pencil out an example together
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0 1 2 3 4 5 6 7 8 9 10 $-
$10
$20
$30
$40
$50
$60
$70
$80
$90
$100
Present value Cumulative annual payments
Simple Example• Mathematically, this is always true – why?
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Year
Amou
nt
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0 1 2 3 4 5 6 7 8 9 10 $-
$20
$40
$60
$80
$100
$120
Present value Cumulative annual payments Reinvested value
Simple Example• Mathematically, this is always true – why?
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Year
Amou
nt
Because of this
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Simple Example• A related formula that is worth knowing
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Net Present Value
Future ValueDiscount Factor
=
Where:
Discount Factor = (1+ i )n
i = expected rate of returnn = number of time periods
– C +
– C = Initial investment (negative because spending money)
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Application: CalSTRSPart 3
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Application: CalSTRS• Let’s apply what we just learned to a
public pension plan– CalSTRS: The 2nd largest U.S. public pension• Has $179.4bn in assets• Pays $1bn+ in monthly benefits• Covers 896,000 members and
beneficiaries–What’s the liability today? • Depends on future payments due to
retirees
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Application: CalSTRS• Projected cumulative pension payments of
$1.7 trillion due over the next 100 years
Present value of those payments = liability today3/11/2016 NICAR 2016 | Denver
20152019
20232027
20312035
20392043
20472051
20552059
20632067
20712075
20792083
20872091
20952099
21032107
2111$0
$200,000,000,000
$400,000,000,000
$600,000,000,000
$800,000,000,000
$1,000,000,000,000
$1,200,000,000,000
$1,400,000,000,000
$1,600,000,000,000
$1,800,000,000,000
Cumulative Benefits Due
$1.7 trillion of pension benefit
payments
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Application: CalSTRS• First a bit of pension accounting–The accrued liability (AAL) is the present
value of future payments to retirees–The pension asset value (AVA) is what’s
available today to pay future liabilities– If pension liabilities exceed assets, then
there is an unfunded liability (UAAL)–The size of the funding gap is measured
using the funded ratio (AVA/AAL) . . . More key terms available here
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Simple Example
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Goal: Calculate the AAL and use it to estimate the UAAL
Let’s walk through it together
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Application: CalSTRS• So how do we know if we’re right?
– Check the Comprehensive Annual Financial Report– ‘Schedule of Funding Progress’ is your best friend
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Application: CalSTRS
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- The Los Angeles Times, November 18, 2015
• The assumed rate of return matters – a lot!– CalPERS, the other big California pension,
shows why:
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Application: CalSTRS
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(See CalPERS’ response to Crane)
• Once you fall behind, catching up is hard– Taxpayers or markets have to pick up the tab– Even if markets do their part, it may not be
enough
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Application: CalSTRS• Homework: CalPERS
- CalPERS also provided us data for this exercise BUT:- Projections only for 30 years- ‘True-up’ based on partial data
. . . So take it with a grain of salt
- Benefit projections include future normal cost- Discount rate is same as CalSTRS, 7.5%
- PV the benefits and see how sensitive they are to the discount rate assumption
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