The IASB and FASB stumble over the annuity method of depreciation
Stephen Zeff
Rice University
Annuity method of depreciation
The annuity method, or compound interest method, of depreciation has been discussed and
illustrated in US accounting textbooks and handbooks for almost one hundred years. Typically, it
gives rise to an increasing periodic depreciation charge, and it is compatible with capital
budgeting methods for evaluating investment decisions. Let me give an example of how the
interest method would produce accounting results post hoc that would enable an assessment of
an investment decision.
Suppose a company purchases a depreciable asset on January 1, Year 1 at a cost of $15,850. It
has a useful life of four years and no estimated salvage value. When making the purchase
decision, the company anticipated that the use of the asset would generate a revenue (cash)
inflow of $5,000 each year, assumed to occur at the end of the year. The cost of the asset was
found by discounting the four annual cash flows at 10%. Assume that depreciation is the
company’s only expense for the year.
If the company were to record straight-line depreciation, its four years’ income statements would
appear as follows:
1
2
3
4
$5,000
$5,000
$5,000
$5,000
3,963
3,963
3,963
3,961
Net income (A)
$1,037
$1,037
$1,037
$1,039
Initial investment (B)
$15,850
$11,887
$7,924
$3,961
3,963
3,963
3,963
3,961
Revenue
Depreciation expense
Less: deprecation expense
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Ending investment balance
Return on investment (A ÷ B)
$11,887
$7,924
6.5%
8.7%
$3,961
13.1%
$
0
26.2%
Clearly, the rising annual return on investment is an illusion, created by the use of an arbitrary
method of depreciation. In this example, with straight-line depreciation, a constant numerator
(Net income) is divided by a declining denominator (Initial investment) to produce a rising
annual return on investment, which is a counter-intuitive result. Why should the annual return on
investment be rising when the actual cash inflow each year was precisely as anticipated? Each
year, in these circumstances, the return should be 10%.
Suppose, instead, that the company records depreciation by a method that actually implies a 10%
annual return, sometimes called the “annuity method” or “compound interest method.” This
method yields an annual return on investment of 10% in the income statement so long as the
actual cash flows coincide with the anticipated cash flows. If the actual cash flows were to
exceed, or fall short of, the anticipated cash flows, the annual return on investment would be
correspondingly higher or lower. The annual net income is set at 10% of the investment at the
beginning of the year, and the depreciation expense becomes the difference between the Revenue
and the Net income. Here is how the four years’ income statements would appear:
1
2
3
4
$5,000
$5,000
$5,000
$5,000
3,415
3,756
4,132
4,545
Net income (A)
$1,585
$1,244
$ 868
$ 455
Initial investment (B)
$15,850
$12,435
$8,679
$4,547
Less: depreciation expense
3,415
3,756
4,132
4,545
Ending investment balance
$12,435
$8,679
$4,547
Revenue
Depreciation expense
$
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Return on investment (A ÷ B)
10%
10%
10%
10%
By this method, the amount of the annual depreciation rises each year; thus, the declining
numerator (Net income) is divided by a correspondingly declining denominator (Initial
investment). The use of this method enables a reader of the income statement to determine
whether, and to what extent, the company achieved its required 10% return on investment.
Another way of looking at the “annuity method” is that the depreciation expense each year
represents the implicit depreciation when one calculates the present value of the stream of annual
cash flows. This present value becomes the cost the company is willing to pay for the asset in
order to achieve the required return on investment.
The “annuity method” is not an acceptable method in U.S. financial reporting, primarily because
it is too subjective. Yet all depreciation methods are subjective. It may, however, be used by
companies for internal reporting purposes, especially when one seeks to evaluate the
performance of divisions and subsidiaries. The foregoing examples also highlight the conceptual
weakness of straight-line depreciation.
The IASB/FASB’s leases exposure draft of May 2013
In the IASB/FASB’s basis for conclusions of the leases ED, paragraph BC36(a), the boards
describe the annuity method of depreciation and then say that they have rejected its use. One
reason for this rejection, they say, is that it “is currently prohibited in US GAAP.” In fact, prior
to the FASB’s Accounting Standards Codification (ASC), the annuity method of depreciation
was mentioned only once in all of the US authoritative literature: in paragraph 37 in Statement of
Financial Accounting Standards 92, “Regulated Enterprises – Accounting for Phase-in Plans,”
issued in 1987. Reference to the annuity method did not appear in the standard itself or in the
basis for conclusions but was tucked away in a nondescript paragraph in an illustrative appendix,
very much as an aside: “(annuity methods of depreciation are not acceptable under generally
accepted accounting principles applicable to enterprises in general).” Nothing more was said
about it than this, and a statement about the non-acceptability of the annuity method under
GAAP was not even germane to the subject of the standard. This was, in my view, a dubious
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basis for concluding that the annuity method was prohibited by US GAAP. Yet ASC 360-10-3510 currently states, “Annuity methods of depreciation are not acceptable for entities in general.”
Let us accept that the annuity method is contrary to US GAAP. And the IASB/ FASB inform us
that they have rejected the method. But they have not rejected the use of the method. They have
actually used the annuity method, whether they admit to it or not, when accounting for Type B
leases. The total expense to be shown by the lessee is the “single lease cost,” which, under
paragraph 42(b), combines “the unwinding of the discount on the lease liability with the
amortization of the right-of-use asset, calculated so that the remaining cost of the lease (as
described in paragraphs B15-B16) is allocated over the remaining lease term on a straight line
basis.” In the boards’ separately issued “Snapshot: Lease,” page 7, the total lease expense for the
Type B lease is 231 in each period. But there is only one conceptual underpinning for this
constant annual lease expense: the addition of the periodic unwinding of the discount on the
lease liability to the periodic amortisation of the right-of-use asset by use of the annuity method.
This total periodic expense for a lease where the payments are the same every year could not be
obtained any other way. As the periodic unwinding of the lease liability declines, the periodic
amortisation of the leased asset increases correspondingly, dollar per dollar, just as the boards
explain in paragraph B36(a), when discussing the effect of the annuity method: “Consequently,
the amortisation charge would typically increase over the lease term.”
So why do the boards announce that they will not use the annuity method of depreciation
(amortisation) when, in effect, they use precisely that method when accounting for amortisation
of the right-of-use asset for Type B leases? The boards’ explanation of their derivation of the
total lease expense is disingenuous and is not explained in terms of its conceptual underpinning.
It is made to look like a plug figure, but a plug figure is called for only when the figure cannot be
independently derived. But here it can be independently derived.
Prior to the issue of SFAS 92 in 1987, there was substantial support in the US authoritative
literature for the use of the annuity method when amortising the leased asset. In October 1958,
Gordon Shillinglaw, a long-time accounting professor at MIT and Columbia University and an
acknowledged authority on accounting for leases, wrote a widely cited article, “Leasing and
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Financial Statements,” in The Accounting Review. There he advocated the use of the “constant
yield” method (the “annuity method” by another name) to amortise both the leased asset and the
lease liability, the effect of which was to produce an equal periodic lease expense for the lessee
over the course of the lease term for leases with constant payment terms. Shillinglaw argued
explicitly in favour of amortising the leased asset by the “constant yield” method, yet the IASB
and the FASB, which go to pains to disavow the annuity method in the leases ED, come to the
same result, albeit without mentioning that they have actually made use of the annuity method.
Shillinglaw wrote, “If the constant yield method of amortization is used on both the asset and the
liability, the same total will be charged annually to expense” (1958, 587)
Why have the boards engaged in this deception? Discerning readers of the ED will realize that
the boards implicitly used the annuity method to amortise the right-of-use asset even though they
say they have rejected the method because it is contrary to US GAAP.
REFERENCE
Shillinglaw, G. 1958. Leasing and financial statements. The Accounting Review 33 (4): 581-592.
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