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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 拢100,000 for a zero coupon bond that matures in a year鈥檚 time. The bond has an effective interest rate of 10%. It is readily apparent that it will pay 拢110,000 on maturity. If you know it will pay 拢110,000 on maturity, it is equally straightforward to work backwards. If r is the interest rate at which you must invest 拢100,000 to produce 拢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鈥� time. Its carrying value at the end of year 1 will be 拢100,000 x (1 + 0.1) = 拢110,000. At the end of year 2, its maturity value will be

拢110,000 x (1 + 0.1) = 拢121,000

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

It is still possible, in this example, to work backwards and compute that, in order for the return to be 拢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 拢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 拢4,212, in other words it pays 拢95,788.

The cash flows from this bond are:

Period	Cash flow
0	- 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鈥檚 accounts will show a return of 拢5,747 (拢95,788 x 6%) on the investment. 拢5,000 of this represents the coupon interest received: the remaining 拢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 拢96,535 (95,788 + 747).

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

Period	Credit to P&L	Amortisation amount	Carrying value
0	-	-	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.