# Accounting for corporate finance: UK GAAP before 1 January 2005: lenders: mark to market: discounted securities

## Accounting for discounted securities

A discounted security is one acquired at a discount to its face value. The same accounting applies to a security issued at face value and redeemable at a premium (or any combination of discount/premium on acquisition and discount/premium on redemption). The return to the lender comprises the interest received on the bond plus the difference between the purchase price and the redemption price.

### Example

Wellbeach Bank plc issues a £100m bond paying interest at 2% for £80m. The bond is redeemable at face value after 5 years. The total return to the lender is equivalent to a fixed rate loan of £80m with an interest rate of 6.9% (assuming that all but £2m of the interest each year is rolled up into the balance outstanding).

At inception the company passes £80m to the borrower, i.e. purchases the loan.

Debit debtor | £80m |

Credit cash | £80m |

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

All the movements in the mark-to-market value of the loan will be recorded in the profit and loss account for the year. Assuming Wellbeach Bank plc’s initial transaction is at market value the market discount rate at inception is 6.9%. When this is applied to the future cash flows it gives a net present value of £80m as follows:

Market valuation at start of loan (simplified discounting):

Cash flow |

£m | Discount factor @ 6.9% | Present value |

£m | ||||

Interest at end of year 1 | 2 | 0.9358 | 1.87 | |

Interest at end of year 2 | 2 | 0.8757 | 1.75 | |

Interest at end of year 3 | 2 | 0.8195 | 1.64 | |

Interest at end of year 4 | 2 | 0.7669 | 1.53 | |

Interest at end of year 5 | 2 | 0.7177 | 1.44 | |

Repayment of loan | 100 | 0.7177 | 71.77 | |

80 |

Market valuation at the start of year 2 (simplified discounting):

Cash flow |

£m | Discount factor @ 6.9% | Present value |

£m | ||||

Interest at end of year 2 | 2 | 0.9358 | 1.87 | |

Interest at end of year 3 | 2 | 0.8757 | 1.75 | |

Interest at end of year 4 | 2 | 0.8195 | 1.64 | |

Interest at end of year 5 | 2 | 0.7669 | 1.53 | |

Repayment of loan | 100 | 0.7669 | 76.69 | |

83.48 |

The market value has risen by £3.5m giving a total return of £5.5m when the £2m interest received is included. This is the same as the result under an accruals basis because the simplified discounting assumes a constant rate of interest and this is the basis of the accruals method.

However, the discount factor to apply will in fact be dependent on the market expectations of future interest rates. This might show that the market rate for year 1 is 6% but that this is expected to rise to 6.5% in year 2, 7% in year 3, 7.5% in year 4 and 7.4% in year 5. The market value of the discounted security 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 | 2 | 0.9434 | 1.89 | |

Interest at end of year 2 | 2 | 0.8858 | 1.77 | |

Interest at end of year 3 | 2 | 0.8279 | 1.66 | |

Interest at end of year 4 | 2 | 0.7701 | 1.54 | |

Interest at end of year 5 | 2 | 0.7171 | 1.43 | |

Repayment of loan | 100 | 0.7171 | 71.71 | |

80 |

Again the market valuation is still £80m because the market’s anticipated profile of future interest rates equates to a constant rate of 6.9%.

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 | 2 | 0.9390 | 1.88 | |

Interest at end of year 3 | 2 | 0.8775 | 1.76 | |

Interest at end of year 4 | 2 | 0.8163 | 1.63 | |

Interest at end of year 5 | 2 | 0.7601 | 1.52 | |

Repayment of loan | 100 | 0.7601 | 76.01 | |

82.80 |

The market value has risen by £2.8m giving a total return of £4.8m. This is equivalent to a 6% return on the opening £80m. 6% was the anticipated market yield for the first year.

At the start of year 3 the market value is as follows:

Cash flow |

£m | Discount factor | Present value |

£m | ||||

Interest at end of year 3 | 2 | 0.9346 | 1.87 | |

Interest at end of year 4 | 2 | 0.8694 | 1.74 | |

Interest at end of year 5 | 2 | 0.8095 | 1.62 | |

Repayment of loan | 100 | 0.8095 | 80.95 | |

86.18 |

The market value has risen by a further £3.4m giving a total return of £5.4m. This is equivalent to a 6.5% return on the opening £82.8m. 6.5% was the anticipated market yield for the second year.

If the discount factor to be applied changes in a way unanticipated in the opening market future expectation then the market value of the loan will also change in an unanticipated manner. This will be either because the expectations themselves have changed or because the market assessment of the credit risk of the borrower has changed. If the discount factor increases (interest rates as derived from the rise in expectations or the credit rating falls) then the market value of the loan will fall and vice versa.

For example, if at the start of the second year the yield curve was anticipating interest rates of 6%, 6.5%, 7%, and 7.5% for the remaining four years respectively, interest rates have fallen and the market value will have risen as follows:

Cash flow |

£m | Discount factor | Present value |

£m | ||||

Interest at end of year 2 | 2 | 0.9434 | 1.89 | |

Interest at end of year 3 | 2 | 0.8858 | 1.77 | |

Interest at end of year 4 | 2 | 0.8279 | 1.66 | |

Interest at end of year 5 | 2 | 0.7701 | 1.54 | |

Repayment of loan | 100 | 0.7701 | 77.01 | |

83.87 |

The market value has risen by £3.9m. Of this £2.8m was anticipated because the yield in year one was expected to be 6% (£80m x 6% = £4.8m but interest received was £2m so market value expected to rise by £2.8m). The additional rise of £1.1m is due to the unanticipated change in future interest rates.