# Accounting for corporate finance: UK GAAP before 1 January 2005: lenders: mark to market accounting and fixed rate loans

## Accounting for fixed rate loans

A fixed rate loan pays interest at an amount that is fixed for the duration of the loan or is fixed for a period of the loan. For example a bank lends £100m at 8% for five years. Typically the lender will acquire (give money to the borrower) such a loan at face value. The return to the lender is the interest receivable on the loan.

### Example

Wellbeach Bank plc lends £100m at 8% for 5 years.

At inception the bank advances £100m to the borrower, i.e. purchases the loan.

Debit debtor £100m

Credit cash £100m

How does Wellbeach Bank plc then account for this £100m fixed rate loan?

Assuming Wellbeach Bank plc has negotiated the correct terms for the loan, the market value of the loan at inception will be £100m. This is because the market will discount the future cash flows at the same rate as the interest rate payable on the loan, i.e. 8% overall.

Market valuation at start of loan (simplified discounting):

Cash flow |

£m | Discount factor @ 8% | Present value |

£m | ||||

Interest at end of year 1 | 8 | 0.9259 | 7.41 | |

Interest at end of year 2 | 8 | 0.8573 | 6.86 | |

Interest at end of year 3 | 8 | 0.7938 | 6.35 | |

Interest at end of year 4 | 8 | 0.7350 | 5.88 | |

Interest at end of year 5 | 8 | 0.6806 | 5.44 | |

Repayment of loan | 100 | 0.6806 | 68.06 | |

100 |

This is a simplification and the discount factor to apply will in fact be dependent on the yield curve. This might show that the market rate for year 1 is 6% but that this is expected to rise to 7% in year 2, 8% in year 3, 9% in year 4 and 11% in year 5. The market value of the fixed rate loan at the start of the loan is now derived as follows:

Cash flow |

£m | Discount factor | Present value |

£m | ||||

Interest at end of year 1 | 8 | 0.9434 (1/(1.06) | 7.55 | |

Interest at end of year 2 | 8 | 0.8817 (1/(1.06 x 1.07) | 7.05 | |

Interest at end of year 3 | 8 | 0.8164 | 6.53 | |

Interest at end of year 4 | 8 | 0.7490 | 5.99 | |

Interest at end of year 5 | 8 | 0.6748 | 5.40 | |

Repayment of loan | 100 | 0.6748 | 67.48 | |

100 |

Again the market valuation is £100m because the markets anticipated profile of future interest rates equates to a fixed rate of 8%.

At the start of year 2 the market value is as follows:

Cash flow |

£m | Discount factor | Present value |

£m | ||||

Interest at end of year 2 | 8 | 0.9346 (1/(1.07)) | 7.48 | |

Interest at end of year 3 | 8 | 0.8654 (1/(1.07 x 1.08)) | 6.92 | |

Interest at end of year 4 | 8 | 0.7939 | 6.35 | |

Interest at end of year 5 | 8 | 0.7152 | 5.72 | |

Repayment of loan | 100 | 0.7152 | 71.52 | |

98 |

The market value has fallen by £2m. This loss is included in the results for the year along with the £8m interest received. The total result for the year is £6m, which is the same as the market return for year 1 of 6%.

Note the market value has changed despite the fact that interest rates have behaved exactly as anticipated when the loan was advanced. This is because the yield curve is not a flat line and the expected return achieved on a mark to market basis will be based on the yield curve rather than the fixed rate payable on the loan.

At the start of year 3 the market value will be derived as follows:

Cash flow |

£m | Discount factor | Present value |

£m | ||||

Interest at end of year 3 | 8 | 0.9259 (1/(1.07 x 1.08)) | 7.41 | |

Interest at end of year 4 | 8 | 0.8495 (1/(1.07 x 1.08 x 1.09)) | 6.80 | |

Interest at end of year 5 | 8 | 0.7653 | 6.12 | |

Repayment of loan | 100 | 0.7653 | 76.53 | |

96.86 |

The market value has fallen by a further £1.14m. This loss is included in the results for the year along with the £8m interest received. The total result for the year is £6.86m, which is the same as the market return for year 1 of 7% on the opening book value of £98m.

If the discount factor to be applied changes in a way unanticipated in the opening yield curve, then the market value of the loan will also change in an unanticipated manner. This will be either because the yield curve itself has moved or because the market assessment of the credit risk of the borrower has changed. If the discount factor increases because interest rates as derived from the yield curve rise or the credit rating falls, then the market value of the loan will fall and vice versa.

For example, if at the start of year 2 the yield curve was anticipating interest rates of 8%, 9%, 10%, 11% for the remaining 4 years. Interest rates have risen and the market value will have fallen as follows:

Cash flow |

£m | Discount factor | Present value |

£m | ||||

Interest at end of year 2 | 8 | 0.9259 | 7.41 | |

Interest at end of year 3 | 8 | 0.8495 | 6.80 | |

Interest at end of year 4 | 8 | 0.7722 | 6.18 | |

Interest at end of year 5 | 8 | 0.6957 | 5.57 | |

Repayment of loan | 100 | 0.6957 | 69.57 | |

95.53 |

The market value has fallen by £4.47m. Of this £2m was anticipated because the yield in year 1 was 6% (£100m @ 6% = £6m) but interest received was £8m so market value expected to fall by £2m). The additional fall of £2.47m is due to the unanticipated change in future interest rates.

Note that whatever the interest rate, the loan will have a market value of £100m after 5 years, immediately prior to redemption. At this point the discount rate becomes irrelevant as there is no time over which to apply it.