Contents Introduction Definition and characteristics of unlisted infrastructure debt Valuation Framework Implementation
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1 DSCR t
2 DSCR t DSCR t
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8 25% 20% 15% 10% 5% dealflow share bond issuance /dealflow 0% North America Western Europe Latin America Australasia Middle East & N.Africa Asia Eastern Europe Sub-Saharan Africa Indian Sub-continent Caribbean
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10 t
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12 t DSCR t = t t t t t t < t DSCR t DSCR t t t < 1
13 t DSCR t = 1.x x 0 t p t = (DSCR t < 1.x min j<t DSCR j 1.x) DSCR
14 DD T T EDF T EDF T DD T
15 t
16 V t
17 B T t S t B t V t = B t + S t 0 < t < T V T < B B T = V T B V T B T V T V T
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19 CF ADS t
20 DSCR t
21 DSCR t = t t t DSCR t t DSCR t DSCR t DSCR t DSCR t t + 1 t t + 1 t DSCR t
22 µ σ V t = 1 V 0 [ = Φ ( V 0 ) + (µ 1σ ] B 2 V ) σ V = Φ [ DD] B DD := (V 0) ( B) σ V DD V 0 B σ V V 0
23 = [ ] [ ] [ ].[ ] t DD t = t t σ t t DSCR t DD t = 1 1 (1 ) σ t DSCR t DSCR t CF ADS t DSCR t CF ADS t = DSCR t t σ t t σ t = σ DSCRt t 1 B
24 DD t = 1 t 1 1 (1 ) σ DSCRt t DSCR t σ DSCRt DSCR DSCR t DD t ( q(t, T ) = N N 1 [p(t, T )] + µ r ) T t σ ( = N T + µ r ) T t σ µ r T σ T t N 1 [p(t, T )] ( F ( T t ) = N N 1 [F ( T t )] + µ r ) T t σ F ( T t ) T t
25 Z = N 1 [F ( )] ( q(t, T ) = N DD T + β ) m(µ m r) T t ( = N σ DD T + ρ (µ m r) σ m ) T t µ m β m = ρ σ σ m ρ σ m q(t, T ) = N ( DD T + ρ 1 p 1 (t, T ) + ρ 2 p 2 (t, T ) +...) F (.) p 1 (t, T ) p 2 (t, T ) ρ 1 ρ 2
26 DD t DSCR t λ = E[x+ ] E[x ] x + x λ = ϕ(s) + SΦ(S) ϕ( S) SΦ( S) ϕ(.) Φ(.) S
27 λ λ = E[x+ ] E[x ] = E[x+ ] T + E[x + ] N E[x ] = λt E[x ] T E[x ] + λn E[x ] N E[x ] = E[x ] T E[x ] λt + E[x ] N E[x ] λn
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29 (.) (.) i=4 V S (V t, t) = h i (V t, t) i=1 h i (V t, t) t i V S (V t, t) t V t t t (t) (t) i=t V t = E [ ] e ri,t(i t) i i=t T r i,t i t F (.)
30 P (T D, TD ) T D T P (τ, τ ) τ P (τ, τ ) τ p (t, t ) P (τ, τ ) t p (t, t ) P (T D, TD ) P (τ, τ ) T D p (t, t ), P (T, T ), P (τ, τ ), P (τ, τ ) κ(.) ( (.), (.) ) h 1 (V t, t)
31 h 1 (V t, t) = E [ e r T D,t(T D t) P (T D, TD ) ] = e r T D,t P (T D, TD )df ( T, T F t ) κ(t ) t T D TD [ ] h 4 (V t, t) = e r s,t(s t) p ( s, s)df ( s, s F t ) ds t κ(s) T T F T (T F t ) T F T (T F t ) T h 2 (V t, t) = h 3 (V t, t) = T t T t e r T,t(T t) P (T )df T (T F t ) e r T,t(T t) P (T )df T (T F t ) F T (T F t ) F T (T F t ) P (T ) P (T )
32 T V τ (τ, T ) = τ + E [ ] e r i,τ (i τ) i i=τ+1 τ τ τ τ V τ (τ, T ) τ T ( ) = ˆVτ (τ, T ) L τ, τ V D τ V E τ = 0 Vτ D τ Vτ E τ ˆV τ L τ τ
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34 ( Vτ D (τ, T ) = ˆV τ (τ, T ) L τ, 12 ) (V τ(τ, T ) R T ), τ Vτ E (τ, T ) = [ ] V τ (τ, T ) Vτ D + R τ V τ τ R τ ( ˆV τ (τ, T ) L τ, 1 2 (V τ(τ, T ) R T ), τ ) ( = τ + ˆV τ (τ, T ) τ L τ, 1 ) 2 (V τ(τ, T ) R T ) τ, 0 ( = τ + ˆV τ (τ + 1, T ) L τ, 1 ) 2 (V τ(τ + 1, T ) R T ), 0 ( = τ + τ (τ + 1, T ), 1 ) 2 τ(τ + 1, T ), 0 V D τ ( ˆV τ (τ + 1, T ) L τ, 1 2 (V τ(τ + 1, T ) R T ), 0 (τ, T ) = τ + ( = τ + τ (τ + 1, T ), 1 ) 2 τ(τ + 1, T ), 0 ) Vτ E (τ, T ) = [ V τ (τ + 1, T ) R τ Vτ D (τ, T ), 0 ] [ ( = τ (τ + 1, T ) τ (τ + 1, T ), τ(τ + 1, T ), 0)] τ (τ + 1, T ) τ (τ + 1, T )
35 V t ˆV t (t, T ) V t (t, T ) τ (τ, T ) L R τ τ (τ, T ) t
36 V τ (τ, T ) τ (τ, T ) V τ (τ, T ) V D τ (τ, T ) 1 2 τ(τ, T ) V E τ (τ, T ) τ (τ, T ) 1 2 τ(τ, T ) τ (τ, T ) V D τ (τ, T ) τ = + + T i=τ+1 T i=τ+1 e r i,τ (i τ) T i=τ+1 [ i e r i,τ (i τ) ( i )df ( i ) κ i Vi D (i, T ) df ( i ) F ( i ) ] i dft i 1 [ e r i,τ (i τ) Vi D (i, T ) df ] ( i ) i df i F T ( i ) i 1 df Vi D (i, T ) i i i
37 i Vi D (i, T ) ( Vi D (i, T ) = i + i (i + 1, T ), 1 ) 2 i(i + 1, T ), 0 Vi D (i, T ) i i i = τ + 1 T E[L D τ ] = V τ D (τ, T D ) Vτ D (τ, T ) = V τ D (τ, T D ) τ + ( τ (τ + 1, T ), 1 ) 2 τ(τ + 1, T ), 0 = lτ D ( τ τ ) [ ( + V τ D (τ + 1, T D ) τ (τ + 1, T ), 1 )] 2 τ(τ + 1, T ), 0 E[L D τ ] V τ D lτ D
38 E[L D τ ] = lτ D ( τ τ ) [ ( + V D τ (τ + 1, T D ) NP V τ (τ + 1, T D ) + ˆV )] τ (T D + 1, T ), 0 = lτ D ( τ τ ) + ( [ V D τ (τ + 1, T D ) NP V τ (τ + 1, T D ) + τ, NP V τ(τ + 1, T D ) + τ, 0 2 )] τ NP V τ (τ + 1, T D ) + τ > 1NP V 2 τ(τ + 1, T D ) + τ > 0 [ E[L D τ ] = lτ D ( τ τ ) + V D τ (τ + 1, T D ) NP ] V τ (τ + 1, T D ) τ [ TD ] P (τ) = (1 + c) e rate(i τ) i, i=τ c rate i i
39 h 1 (t, V t ) + h 4 (t, V t ) = T D i=t e r i,t(i t) i κ i d F ( i ) h 2 (t, V t ) = T D τ=t e r τ,t(τ t) [ τ P (τ, τ ) df ] ( τ ) τ df F T ( τ ) τ 1 h 3 (t, V t ) = T D τ=t τ e rτ,t(τ t) P (τ) dft τ 1 V D t (t, T D ) = h 1 (t, V t ) + h 2 (t, V t ) + h 3 (t, V t ) + h 4 (t, V t )
40 t Vt D V t T V t = E [ ] e ri,t(i t) i i=t i i = t e (µ λσ 1 2 σ2 )(i t)+σ i tz σ z i E [ i ] = t e (µ λσ)(i t) [ i=t T V t = e r(i t) E [ i ] = t i=t i=t e (µ λσ r)(i t) ] ( ) τ ( dft = N t ) (µ λσ 1 2 σ2 )τ) t σ τ ( ) + e 2/σ2 (µ λσ 1 2 σ2 ) ( ( ) t N t ) + (µ λσ 1 2 σ2 )τ) σ τ ( ) τ ( dft = N t ) + (µ λσ 1 2 σ2 )τ) t σ τ ( ) + e 2/σ2 (µ λσ 1 2 σ2 ) ( ( ) t N t ) (µ λσ 1 2 σ2 )τ) σ τ
41 τ τ τ df ( τ ) = 1 dft dft κ τ τ 1 τ 1 [ T P (τ) = τ + max τ e (µ λσ r)(i τ) L, 1 2 τ i=τ+1 T i=τ+1 e (µ λσ r)(i τ) R, 0 [ ( 1 e rate(t D )] τ) P (τ) = (1 + c) 1 + e rate 1 h 1 (t, V t ) + h 4 (t, V t ) = T D i=t e r i,t(i t) df ( i ) κ i ] h 2 (t, V t ) = T D τ=t [ τ e r τ,t(τ t) P (τ) df ] ( τ ) τ df F T ( τ ) τ 1 h 3 (t, V t ) = T D τ=t τ e rτ,t(τ t) P (τ) dft τ 1
42 P (τ) τ = [ T max τ e (µ λσ r)(i τ) L, 1 2 τ = + + T i=τ+1 T i=τ+1 T i=τ+1 i=τ+1 e r i,τ (i τ) df ( i ) κ i e r i,τ (i τ) [ i [ e r i,τ (i τ) P (i) df ( i ) i F ( i ) T i=τ+1 e (µ λσ r)(i τ) R, 0 P (i, i ) df ] ( i ) τ df F T ( i ) τ 1 ] τ dft τ 1 [ [ T ] [ T ] ] max τ e (µ λσ r)(i τ) L, 1 2 τ e (µ λσ r)(i τ) R, 0 = T i=τ+1 [ e r i,τ (i τ) i=τ+1 df ( i ) + 0 i=τ+1 ] ( i )df ( i ) ]
43 T D ) E t [Loss] = e r(i t) i (1 d F (CF ADS i ) h 2 (t, V t ) h 3 (t, V t ) i=t κ(i) h 2 (t, V t ) h 3 (t, V t ) E t [l] = E t [Loss] TD i=t e r(i t) i RR t = 1 E t [l] D t = 1 V D (t) V D (t) y = V D + (t) V D (t) 2 δy V D (t) V D + (t) t y δy V D (t) t y + δy V D (t) t y C t = 1 2 V D (t) V D (t) 2 y = V + D (t) + V D (t) 2V D (t) (2 δy) 2 V D (t)
44 t V D t = T D i=t e y t(i t)) i y t t t V D t = T D i=t e (r t,i+s t)(i t)) i s t t V D t E[ t ] = e r t V D t+1 r t t t + 1 E[ t ] t
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49 i th i th = 1.05
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57 CFADS Equity Payments DSCR=1.09) Equity Payments DSCR=1.12)
58 CFADS Base Case Debt Schedule Debt Payments (Liq Costs=5) Debt Payments (Liq Costs = 45) Debt Payments (Liq Costs=75) CFADS Base Case Equity Payments Equity Payments (Liq Costs=5) Equity Payments (Liq Costs=45) Equity Payments (Liq Costs = 75)
59 DSCR (Liq Costs = 10) DSCR (Liq Costs = 45) DSCR (Liq Costs = 75) DSCR (no reneg) Debt Payments (Liq Costs = 10) Debt Payments (Liq Costs = 45) Debt Payments (Liq Costs = 75) Debt Payments (no reneg)
60 PD (Liq Costs = 10) PD (Liq Costs = 45) PD (Liq Costs = 75) PD (no reneg) Loss (Liq Costs = 10) Loss (Liq Costs = 45) Loss (Liq Costs = 75) Loss (no reneg)
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