The capitalisation profile for the residual interest is not straight line, but instead is subject to a constant uplift. This uplift ensures that the underlying charge to the OCS for services and capital charges remains constant, once inflation is excluded. This is reasonable given that the Body is basically receiving the same level of service throughout the concession. This method of write down for residual interest amplifies current guidance set out in Technical Note 1 - How to account for PPP Transactions and is based in part on advice from HM Treasury.
The uplift is related to the prevailing cost of capital rate. The formula for its derivation (set out below) is designed to compensate for the rate of increase of cost of capital as follows:
Rate of uplift: [2+ (cost of capital/100)]/[2- (cost of capital/100)] = 2.035/1.965
The full derivation of the residual value is set out below, excluding the effects of inflation and indexation.
Fig 3 - Derivation of the annual capitalization
|
|
| Discounted |
| PFI | Capital | Net | Capital |
| Cost of | |
| Period |
| Residual |
| Creditor | Element | Residual | Element |
| Capital | |
|
|
| £000 |
| £000 | £000 | £000 | £000 |
| £000 | |
| 1 | Commence PFI | 10,688.35 |
| 10,688.35 |
| - |
|
|
| |
|
| Unwind discount / Interest | 374.09 |
| 374.09 |
| 0.00 |
|
|
| |
|
| Repayment |
|
| -£581.14 | - | 207.05 | 581.14 | 581.14 |
| 10.17 |
| 2 | balance carried forward | 11,062.44 |
| 10,481.30 |
|
| 581.14 |
|
|
|
|
| Unwind discount / Interest | 387.19 |
| 366.85 |
|
| 20.34 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 214.29 | 581.14 | 601.48 |
| 30.87 |
| 3 | balance carried forward | 11,449.63 |
| 10,267.01 |
|
| 1,182.62 |
|
|
|
|
| Unwind discount / Interest | 400.74 |
| 359.35 |
|
| 41.39 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 221.79 | 581.14 | 622.53 |
| 52.29 |
| 4 | balance carried forward | 11,850.37 |
| 10,045.22 |
|
| 1,805.15 |
|
|
|
|
| Unwind discount / Interest | 414.76 |
| 351.58 |
|
| 63.18 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 229.56 | 581.14 | 644.32 |
| 74.46 |
| 5 | balance carried forward | 12,265.13 |
| 9,815.66 |
|
| 2,449.47 |
|
|
|
|
| Unwind discount / Interest | 429.28 |
| 343.55 |
|
| 85.73 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 237.59 | 581.14 | 666.87 |
| 97.40 |
| 6 | balance carried forward | 12,694.41 |
| 9,578.07 |
|
| 3,116.34 |
|
|
|
|
| Unwind discount / Interest | 444.30 |
| 335.23 |
|
| 109.07 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 245.91 | 581.14 | 690.21 |
| 121.15 |
| 7 | balance carried forward | 13,138.71 |
| 9,332.16 |
|
| 3,806.56 |
|
|
|
|
| Unwind discount / Interest | 459.85 |
| 326.63 |
|
| 133.23 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 254.51 | 581.14 | 714.37 |
| 145.73 |
| 8 | balance carried forward | 13,598.57 |
| 9,077.64 |
|
| 4,520.92 |
|
|
|
|
| Unwind discount / Interest | 475.95 |
| 317.72 |
|
| 158.23 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 263.42 | 581.14 | 739.37 |
| 171.17 |
| 9 | balance carried forward | 14,074.52 |
| 8,814.22 |
|
| 5,260.30 |
|
|
|
|
| Unwind discount / Interest | 492.61 |
| 308.50 |
|
| 184.11 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 272.64 | 581.14 | 765.25 |
| 197.50 |
| 10 | balance carried forward | 14,567.13 |
| 8,541.58 |
|
| 6,025.55 |
|
|
|
|
| Unwind discount / Interest | 509.85 |
| 298.96 |
|
| 210.89 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 282.18 | 581.14 | 792.03 |
| 224.75 |
| 11 | balance carried forward | 15,076.98 |
| 8,259.40 |
|
| 6,817.58 |
|
|
|
|
| Unwind discount / Interest | 527.69 |
| 289.08 |
|
| 238.62 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 292.06 | 581.14 | 819.76 |
| 252.96 |
| balance carried forward | 15,604.67 |
| 7,967.33 |
|
| 7,637.34 |
|
|
| |
|
| Unwind discount / Interest | 546.16 |
| 278.86 |
|
| 267.31 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 302.28 | 581.14 | 848.45 |
| 282.15 |
| 13 | balance carried forward | 16,150.83 |
| 7,665.05 |
|
| 8,485.78 |
|
|
|
|
| Unwind discount / Interest | 565.28 |
| 2 68.28 |
|
| 297.00 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 312.86 | 581.14 | 878.14 |
| 312.37 |
| 14 | balance carried forward | 16,716.11 |
| 7,352.19 |
|
| 9,363.93 |
|
|
|
|
| Unwind discount / Interest | 585.06 |
| 257.33 |
|
| 327.74 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 323.81 | 581.14 | 908.88 |
| 343.64 |
| 15 | balance carried forward | 17,301.18 |
| 7,028.37 |
|
| 10,272.80 |
|
|
|
|
| Unwind discount / Interest | 6 05.54 |
| 2 45.99 |
|
| 359.55 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 335. 15 | 581.14 | 9 40.69 |
| 376.01 |
| 16 | balance carried forward | 17,906.72 |
| 6,693.23 |
|
| 11,213.49 |
|
|
|
|
| Unwind discount / Interest | 626.74 |
| 234.26 |
|
| 392.47 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 346.88 | 581.14 | 973.61 |
| 409.51 |
| 17 | balance carried forward | 18,533.45 |
| 6,346.35 |
|
| 12,187.10 |
|
|
|
|
| Unwind discount / Interest | 648.67 |
| 222.12 |
|
| 426.55 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 3 59.02 | 581.14 | 1,007.69 |
| 444. 18 |
| 18 | balance carried forward | 19,182.12 |
| 5,987.33 |
|
| 13,194.79 |
|
|
|
|
| Unwind discount / Interest | 671.37 |
| 209.56 |
|
| 461.82 |
|
|
|
|
| Repayment |
|
| -£581.14 |
| 371.58 | 581.14 | 1,042.96 |
| 480. 07 |
| 19 | balance carried forward | 19,853.50 |
| 5,615.75 |
|
| 14,237.75 |
|
|
|
|
| Unwind discount / Interest | 694.87 |
| 196.55 |
|
| 498.32 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 384.59 | 581.14 | 1,079.46 |
| 517.21 |
| 20 | balance carried forward | 20,548.37 |
| 5,231.16 |
|
| 15,317.21 |
|
|
|
|
| Unwind discount / Interest | 719.19 |
| 183.09 |
|
| 536.10 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 398.05 | 581.14 | 1,117.24 |
| 555.65 |
| 21 | balance carried forward | 21,267.56 |
| 4,833.11 |
|
| 16,434.45 |
|
|
|
|
| Unwind discount / Interest | 744.36 |
| 169.16 |
|
| 575.21 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 41.98 | 581.14 | 1,156.35 |
| 595.44 |
| 22 | balance carried forward | 22,011.93 |
| 4,421.13 |
|
| 17,590.80 |
|
|
|
|
| Unwind discount / Interest | 770.42 |
| 154.74 |
|
| 615.68 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 4 26.40 | 581.14 | 1,196.82 |
| 636.62 |
| 23 | balance carried forward | 22,782.35 |
| 3,994.73 |
|
| 18,787.62 |
|
|
|
|
| Unwind discount / Interest | 797.38 |
| 139.82 |
|
| 657.57 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 4 41.32 | 581.14 | 1,238.71 |
| 679.24 |
| 24 | balance carried forward | 23,579.73 |
| 3,553.41 |
|
| 20,026.32 |
|
|
|
|
| Unwind discount / Interest | 825.29 |
| 124.37 |
|
| 700.92 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 456.77 | 581.14 | 1,282.06 |
| 723.36 |
| 25 | balance carried forward | 24,405.02 |
| 3,096.64 |
|
| 21,308.38 |
|
|
|
|
| Unwind discount / Interest | 854.18 |
| 108.38 |
|
| 745.79 |
|
|
|
|
| Repayment |
|
| -£581.14 |
| 472.76 | 581.14 | 1,326.93 |
| 769.01 |
| 26 | balance carried forward | 25,259.20 |
| 2,623.88 |
|
| 22,635.32 |
|
|
|
|
| Unwind discount / Interest | 8 84.07 |
| 9 1.84 |
|
| 792.24 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 489.30 | 581.14 | 1,373.38 |
| 816.27 |
| 27 | balance carried forward | 26,143.27 |
| 2,134.57 |
|
| 24,008.69 |
|
|
|
|
| Unwind discount / Interest | 915.01 |
| 74.71 |
|
| 840.30 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 506.43 | 581.14 | 1,421.44 |
| 865.18 |
| 28 | balance carried forward | 27,058.28 |
| 1,628.14 |
|
| 25,430.14 |
|
|
|
|
| Unwind discount / Interest | 947.04 |
| 56.99 |
|
| 890.05 |
|
|
|
|
| Repayment |
|
| -£581.14 | - | 524.15 | 581.14 | 1,471.19 |
| 915.80 |
| 29 | balance carried forward | 28,005.32 |
| 1,103.99 |
|
| 26,901.33 |
|
|
|
|
| Unwind discount / Interest | 9 80.19 |
| 3 8.64 |
|
| 941.55 |
|
|
|
|
| Repayment |
|
| -£581.14 |
| 542.50 | 581.14 | 1,522.69 |
| 968.19 |
| 30 | balance carried forward | 28,985.51 |
| 561.49 |
|
| 28,424.02 |
|
|
|
|
| Unwind discount | 1,014.49 |
| 19.65 |
|
| 994.84 |
|
|
|
|
|
|
|
| -£581.14 |
| 561.49 | 581.14 | 1,575.98 |
| 1,022.42 |
|
| Closing balance | 30,000.00 |
| - 0.00 | - |
| 30,000.00 |
|
|
|
|
| Totals |
|
|
|
| 10,688.35 |
| 30,000.00 |
|
|