# Accounting for corporate finance: key concepts: amortised cost: examples

## Effective interest rate

The effective interest rate is the rate of return that provides a level yield on a financial asset through to maturity date (or the next re-pricing date). To look at it another way, it is the rate that exactly discounts the cash flows associated with the financial instrument through to maturity (or the next re-pricing date) to the net carrying amount at initial recognition, i.e. a constant rate on the carrying amount.

This is easiest to see if you consider a zero coupon bond.

### Example 1

A company pays £100,000 for a zero coupon bond that matures in a year’s time. The bond has an effective interest rate of 10%. It is readily apparent that it will pay £110,000 on maturity. If you know it will pay £110,000 on maturity, it is equally straightforward to work backwards. If r is the interest rate at which you must invest £100,000 to produce £110,000,

100,000 x (1 + r) = 110,000,

So, r must be (110,000 - 100,000)/100,000 or 0.1, i.e. 10%

Suppose that the bond has an effective interest rate of 10%, but matures in 2 years’ time. Its carrying value at the end of year 1 will be £100,000 x (1 + 0.1) = £110,000. At the end of year 2, its maturity value will be

£110,000 x (1 + 0.1) = £121,000

In other words, if you use a discount rate of 10%, the net present value of a cash flow of £121,000 due in 2 years’ time is equal to the initial outlay of £100,000.

It is still possible, in this example, to work backwards and compute that, in order for the return to be £121,000 in two years, you require a discount rate of 10%. However, in more complicated cases an exact algebraic solution is not possible, and various approximation methods have been developed.

In practice, the worksheet function IRR (internal rate of return) in Microsoft Excel can be used to calculate the effective interest rate where a financial asset gives rise to cash flows at regular intervals. The Excel Help file gives details of how IRR is used.

### Example 2

A company buys a bond with a maturity value of £100,000 and an interest coupon of 5%, payable annually in arrears. The bond has exactly 5 years to maturity. The company buys the bond at a discount of £4,212, in other words it pays £95,788.

The cash flows from this bond are:

Period | Cash flow |

- 95,788 | |

1 | 5,000 |

2 | 5,000 |

3 | 5,000 |

4 | 5,000 |

5 | 105,000 |

Putting these figures into the IRR function gives an effective interest rate of 6%.

This means that, in the first year, the company’s accounts will show a return of £5,747 (£95,788 x 6%) on the investment. £5,000 of this represents the coupon interest received: the remaining £747 represents amortisation of the purchase discount. Thus at the end of year 1, the bond will - on an amortised cost basis - be shown in the balance sheet at £96,535 (95,788 + 747).

Over the 5-year period, the position will be:

Period | Credit to P&L | Amortisation amount | Carrying value |

95,788 | |||

1 | 5,747 | 747 | 96,535 |

2 | 5,792 | 792 | 97,327 |

3 | 5,840 | 840 | 98,167 |

4 | 5,890 | 890 | 99,057 |

5 | 5,943 | 943 | 100,000 |

The computation of effective interest rate must take into account all the contractual terms of the instrument, including such things as prepayment options. It will include fees and costs where these are integral to the loan. But it does not take into account any expected credit losses. Amortisation will often be over the period to maturity, but in some cases a shorter period may be appropriate, for example if a bond can be redeemed early and it is likely that this will happen.

Sometimes estimates of future cash flows will change, for example where the expected maturity date of a financial asset changes. In such cases the effective interest rate is recalculated, and there is a cumulative catch-up through profit and loss account.