Valuation of the Student Loans Scheme By Ian Collins and Robbie Batley PwC 1
Agenda 1. The valuation 2. Projecting repayments 3. Student loan model 4. Modelling techniques 5. Challenges 6. Results 7. Cohort analyses 8. Impact of GFC on students PwC 2
The valuation • The Crown lends money to students • Inland Revenue (IR) collects the repayments • The loans are assets in the Crown’s accounts • The Crown must report the value of these loans when preparing its financial statements • Hence, a valuation of these loans is needed • Future repayments are projected and discounted to determine their value PwC 3
Projecting repayments • Annual repayment obligations: – If living in New Zealand: Obligation = 12% × max(0, Income - $19,084) – If living overseas: Outstanding balance Repayment obligation < $1,000 Outstanding balance $1,000 - $15,000 $1,000 $15,000 - $30,000 $2,000 $30,000 - $45,000 $3,000 $45,000 - $60,000 $4,000 $60,000+ $5,000 PwC 4
Projecting repayments • Consider a typical student: – John Smith starts uni aged 18 – Works part-time while studying – Completes his degree in 3 years – Goes overseas for 1 year (OE) – Comes back home – Gets a job – Eventually pays off his loan PwC 5
Projecting repayments • What will John’s repayments look like? Little to no repayments (not earning much) Studying Depends largely on John’s attitude towards Overseas repaying his loan Back in NZ Probably no repayments until he gets a job but not working yet Working in 12% of his income that is above $19,084 NZ PwC 6
Student loan model Payment models Interest Write offs (if overseas) Obligation Payments State NPV of cash flows = Balance before Opening Closing transition value of student loan interest and balance balance model debt w/o’s If NZ state… Key Income Obligation Payments Balances Calculations Sub-models Income Payment models models PwC 7
Modelling techniques - CART Key Example: Probability of making a voluntary repayment Rule node N0: 78% Yes: 22% Rule 1: Income < Output $25,000 node N0: 88% N0: 67% Yes: 12% Yes: 33% Rule 2: Total paid last Rule 3: Income < year < $1 $50,000 N0: 65% N0: 62% N0: 92% N0: 76% Yes: 35% Yes: 38% Yes: 8% Yes: 24% Rule 5: Income < Rule 6: Years since Rule 4: State last year Rule 7: Tax type = IR3 $5,000 last employed < 0.5 = study or overseas (self employed) Terminal Terminal Terminal Terminal node node 1: node 2: node 99: 100: N0: 90% N0: 82% N0: 67% N0: 85% Yes: 10% Yes: 18% Yes: 33% Yes: 15% PwC 8
Modelling techniques - GLM • Example: Probably of making a payment when overseas 𝑞 ln 1 − 𝑞 = 𝛾 0 + 𝛾 1 𝑌 1 + 𝛾 2 𝑌 2 + … Qualification type Repayment history 50% 100% Probability of making a repayment next year 45% 90% Probability of making a repayment 40% 35% 80% 30% 25% 70% 20% 60% 15% 10% 50% 5% 0% 40% 1 - 3 certificates 4 certificates 5 - 7 certificates Bachelors Postgraduate 0 1 2 3 4 5 6 7 8 9 10 11 Qualification (QACC code) Number of consecutive repayments Actual Data GLM Projections Actual Data GLM Projections PwC 9
Challenges • Dealing with scheme rule/policy changes • Environmental impacts on students, such as the Global Financial Crisis • Missing data • Data lags – income data incomplete in the latest year • Natural censoring (we only consider those with loans) • Wage inflation for student loan borrowers • Death and bankruptcy rates • Modelling techniques (eg CART, GLM, empirical distribution) • Interactions between sub-models PwC 10
Results Projected repayments: $1,400m $1,200m $1,000m $800m $600m $400m $200m $0m 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 Year ending 30 June Actual 30 June 2015 Total debt (30 June 2015) Value of debt = $14.8 billion = $8.9 billion PwC 11
Cohort analyses Qualification type • Bachelors and $8b 100% $7b post-graduates 80% $6b have better $5b 60% $4b repayment 40% $3b prospects $2b 20% $1b $0 0% Level 1-3 certs Level 4 certs Level 5-7 certs Bachelors Post-graduate Value of debt Total debt Ratio (value/total) Years earning below $20k (NZ borrowers not studying) • The longer a $3.5b 100% borrower spends $3.0b 80% $2.5b earning below 60% $2.0b $20k, the worse $1.5b 40% their repayment $1.0b 20% $0.5b prospects become $0 0% None 1 year 2 years 3 years 4 years 5+ years Value of debt Total debt Ratio (value/total) PwC 12
Impact of GFC on students Pre-GFC GFC Post-GFC GFC ? • The GFC significantly hurt young people • A few found jobs and came through it OK • Others were not so lucky PwC 13
Impact of GFC on students • The probability of earning more than $20k the year after study dropped • The impact was less severe G on those studying towards a F C Bachelors or higher • The GFC has made it G F C harder to break out of a low income (below $20k) and earn a higher income • Students are getting stuck on low incomes PwC 14
Any questions? PwC 15
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