Inventory policy, accruals quality and information risk

Abstract

This paper provides evidence consistent with firms with Last-in-first-out (LIFO) inventory policy being priced by the market as having lower information risk than First-in-first-out (FIFO) firms. Furthermore, the paper shows that this pricing differential is sustained after controlling for accruals quality, suggesting that the inventory policy signals some information risk characteristics that are not captured by accruals quality measure. We investigate the relation between inventory policy and accruals quality and find that accruals quality is systematically worse for FIFO firms than for LIFO firms after controlling for correlated omitted variables and known firm attributes. These findings complement the currently established relationship between the cost of capital, market pricing and accruals quality by focusing on the need for understanding the incremental effects of individual accounting policies.

Appendices

Appendix: Section 1: Non-discretionary accruals

In this section, we show that the accrual quality (AQ) as defined by McNichols (2002) will be higher for FIFO firms than for LIFO firms under the assumption that the LIFO layers are not used during that year.

We make the following simplifying assumptions:

• 1. The unit cost of purchased inventoriable resources follows a random walk as follows: Unit cost in year t = c _t . c _t+1 = c _t  + ɛ_t+1 where ɛ_t+1 is distributed with a mean of 0 and a constant variance $\sigma_\varepsilon^{2}.$ Further, Cov(ɛ _t , ɛ_t±k) = 0 ∀ k ≠ 0. It is easy to see that in this process, conditional variance $V(c_{t+s}|c_t)=s\sigma_{\varepsilon}^{2}.$

• 2. The unit price of the final product also follows a similar random walk as follows: Unit price in year t =  p _t ; p _t+1 = p _t + u _t+1 where u _t+1 is distributed with a mean of 0 and a constant variance ψ². Further, Cov(ψ _t , ψ_t±k) = 0 ∀ k ≠ 0. It is easy to see that in this process, conditional variance V(p_t+s|p_t) = sψ².

• 3. We suppress (without loss of generality) fixed production costs if any, and also other variable costs of labor and other non-inventoriable resources. Therefore, the unit gross margin = unit contribution margin = (p _t − c _t ).

• 4. The operating expenses are all-cash expenses and remain constant from year to year. Further, the sale quantity, the depreciation expense and the property, plant and equipment remain constant.

• 5. Other notations are as follows:

  • a. d _ar  = (Number of days of accounts receivable)/365

  • b. d _ap  = (Number of days of accounts payable)/365

  • c. d _inv  = (Number of days of inventory)/365

  • d. $\Updelta AR_{t}, \Updelta AP_{t}, \Updelta Inv_{t}$ =  changes in accounts receivable, accounts payable and reported inventory costs respectively from the beginning of year t to end of year t. $\Updelta Inv_{t\,\, LIFO}$ and $\Updelta Inv_{t\,\, FIFO}$ denote the expected inventory changes under LIFO and FIFO, respectively

  • e. TCA _t  = Total current accrual for year t. In our simplified setting, it is defined as $(\Updelta AR_{t} + \Updelta Inv_{t} - \Updelta AP_{t}).$

1.1 Step 1: Computation of changes in AR, AP and INV

AR _t = d _ar qp _t This gives ΔAR _t = [d _ar q(p _t − p_t−1)] = [d _ar qu _t ].

Similarly, ΔAP _t = [d _ap q(c _t − c _t−1)] = [d _ap qɛ _t ].

The change in inventory under LIFO, without dipping into the LIFO layers = 0 because the same level of physical inventory is expected at the end of both years (t − 1) and t and both the inventories will have the same LIFO layers with identical costs.

$$ \Updelta Inv_{t\, LIFO} = 0 $$

Assuming that the number of units taken out of inventory in year t is greater than the number of units in inventory at the end of year t − 1, the reported expected inventory level at the end of year (t − 1) under FIFO =  d _inv qc _t−1. At the end of year t, it is d _inv qc _t . The change in inventory under FIFO is therefore, d _inv q(c _t − c _t−1) = d _inv qɛ _t .

1.2 Step 2: Total current accruals

Under LIFO,

$$ TCA_{t\, LIFO} =\left(\Updelta AR_t +\Updelta Inv_{t\, LIFO} -\Updelta AP_t\right)=d_{ar} q\left(p_t -p_{t-1}\right)-d_{ap} q\left(c_t -c_{t-1}\right)=d_{ar} qu_t -d_{ap} q\varepsilon_t $$

(A1-LIFO)

Under FIFO,

$$ \begin{aligned} TCA_{t\, FIFO} &=\left(\Updelta AR_t +\Updelta Inv_{t\,FIFO} -\Updelta AP_t \right)=d_{ar} q\left(p_t -p_{t-1} \right)+d_{inv} q\left(c_t -c_{t-1} \right)-d_{ap} q\left(c_t -c_{t-1} \right) \\ &=d_{ar} qu_t +d_{inv} q\varepsilon_t -d_{ap} q\varepsilon_t \end{aligned} $$

(A1-FIFO)

From the above two expressions,

$$ TCA_{t\, FIFO} =TCA_{t\, LIFO} +d_{inv} q\varepsilon_t. $$

(A1)

1.3 Step 3: Operating cash flows

In our setting, the cash flow in year t is the difference between the revenue and replacement cost for resources, less the operating cash expenses, adjusted for changes in accounts receivable and accounts payable. We can also view this as the earnings adjusted for the changes in accruals. The pre-tax earnings are given by

$$ Earnings_{tj} =qp_t -(qc_t -\Updelta Inv_{tj})-OE $$

where the subscript j = FIFO,LIFO; qp _t is the revenue and $qc_t -\Updelta Inv_{tj}$ is the cost of goods sold.

We assume that the effective tax rate is τ. Adjusting for the change in accruals, we get the following expressions for cash flow from operations after deducting the tax payments.

For FIFO firms,

$$ CFO_{FIFOs} =\left(1-\tau \right)\left[ q\left(p_s -c_s \right)-OE+\Updelta Inv_s \right]-d_{ar} qu_s +d_{ap} q\varepsilon_s -\Updelta Inv_s;\,\, s=(t-1),t,(t+1) $$

Substituting for $\Updelta Inv_s,$ we get

$$ CFO_{FIFOs} =\left(1-\tau \right)\left[ q\left(p_s -c_s \right)-OE \right]-d_{ar} qu_s +d_{ap} q\varepsilon_s -\tau d_{inv} q\varepsilon_s;\,\, s=(t-1),t,(t+1) $$

(A2-FIFO)

For LIFO firms,

$$ CFO_{LIFO,s} =\left(1-\tau \right)\left[ q\left(p_s -c_s \right)-OE \right]-d_{ar} qu_s +d_{ap} q\varepsilon_s; s=(t-1),t,(t+1) $$

We can write

$$ CFO_{FIFO\,s} =CFO_{LIFO,s} -\tau qd_{inv} \varepsilon_s\quad \hbox{where } \hbox{s}=\hbox{t}-1, \hbox{t or t}+1 $$

(A2-LIFO)

1.4 Step 4: Change in Sales

The sales quantity is constant and therefore, the change is sales revenue is purely driven by the change in price.

$$ \Updelta Sales=q(p_t -p_{t-1}) $$

1.5 Step 5: The McNichols (2002) Accrual Quality Regression and Estimation

In our setting, given that the PPE is assumed to be constant, the regression is:

$$ TCA_{j,i,t} =\beta_0 +\beta_1 CFO_{j,i,t-1} +\beta_2 CFO_{j,i,t} +\beta_3 CFO_{j,i,t+1} +\beta_4 \Updelta Sales_{i,t} +\xi_{it} $$

(A3)

where j denotes the inventory policy, j = FIFO, LIFO, i denotes the firm and t denotes the year. and ξ _it denotes the residual term.

1.6 Step 6: Vector Notation

Let n denote the number of firm-years.

We will express (A3) as Y = XB + S. In particular, for LIFO and FIFO firms, this expression becomes

$$ Y_{LIFO} =X\,\, B_{LIFO} +S_{LIFO} $$

(A3-LIFO)

and

$$ Y_{FIFO} =X_{FIFO} B_{FIFO} +S_{FIFO} $$

(A3-FIFO)

where Y is a n-dimensional vector of the corresponding TCA _it values,

$$ Y_{LIFO} =\left[ \begin{array}{c} TCA_{1tLIFO} \\ TCA_{2tLIFO} \\ TCA_{3tLIFO} \\.. \\ TCA_{ntLIFO} \\ \end{array} \right], \quad\quad Y_{FIFO} =\left[ \begin{array}{c} TCA_{1tFIFO} \\ TCA_{2tFIFO} \\ TCA_{3tFIFO} \\.. \\ TCA_{ntFIFO} \\ \end{array} \right] $$

$$ \hbox{X} =\left[ \begin{array}{ccccc} 1& CFO_{1jt-1} & CFO_{1jt} & CFO_{1jt+1} & \Updelta Sales_{1t} \\ 1& CFO_{2jt-1} & CFO_{2jt} & CFO_{2jt+1} & \Updelta Sales_{2t} \\ ..& ..& ..& ..& .. \\ ..& ..& ..& ..& .. \\ 1& CFO_{njt-1} & CFO_{njt} & CFO_{njt+1} & \Updelta Sales_{nt} \\ \end{array} \right];\quad j=FIFO,LIFO $$

B is the vector of estimated β’s:

$$ B_{LIFO} =\left[ \begin{array}{l} \hat{\beta}_{0LIFO} \\ \hat{\beta}_{1LIFO} \\ \hat{\beta}_{2LIFO} \\ \hat{\beta}_{3LIFO} \\ \hat{\beta}_{4LIFO} \\ \end{array} \right],\quad \hbox{and } B_{FIFO} =\left[ \begin{array}{l} \hat{\beta}_{0FIFO} \\ \hat{\beta}_{1FIFO} \\ \hat{\beta}_{2FIFO} \\ \hat{\beta}_{3FIFO} \\ \hat{\beta}_{4FIFO} \\ \end{array} \right] $$

$$ S_{LIFO} =\left[ \begin{array}{c} \xi_{1tLIFO} \\ \xi_{2tLIFO} \\ \xi_{3tLIFO} \\ .. \\ \xi_{ntLIFO} \\ \end{array} \right]\quad \hbox{and } S_{FIFO} =\left[ \begin{array}{c} \xi_{1tFIFO} \\ \xi_{2tFIFO} \\ \xi_{3tFIFO} \\ .. \\ \xi_{ntFIFO} \\ \end{array} \right]\quad \hbox{Further, we denote } \Upxi =\left[ \begin{array}{c} \varepsilon_{1 {\rm t}} \\ \vdots \\ \varepsilon_{{\rm n t}} \\ \end{array} \right] $$

(A4)

1.7 Step 7: Proof

We assume cov(ξ_t, ξ_s) = 0 s ≠ t

$$ \begin{aligned} \hbox{v}\left(\xi_{\rm t}\right) &=\hbox{v}\left(\xi_{\rm s}\right)=\sigma^{2}\\ \hbox{v}\left(\varepsilon_{\rm t} \right)&=\sigma_\varepsilon^{2} \end{aligned} $$

(A5)

The relationships are

$$ Y_{LIFO} =\left[ \begin{array}{c} TCA_{1t LIFO} \\ \vdots \\ TCA_{nt LIFO} \end{array} \right]=Y_{FIFO} -d_{inv} q\Upxi $$

(A6)

$$ X_{LIFO} =X_{FIFO} +\tau d_{inv} q\left[ \begin{array}{ccccc} 0 &\varepsilon_{1 t-1} &\varepsilon_{1 t} &\varepsilon_{1 t+1} &0 \\ \vdots &\vdots &\vdots &\vdots &\vdots \\ 0 &\varepsilon_{n t-1} &\varepsilon_{n t} &\varepsilon_{nt+1} &0 \\ \end{array}\right] $$

(A7)

Denoting the second term in (A6) as Z, we have X _LIFO = X _FIFO + Z

From the regression Eq. A3,

$$ \begin{array}{c} \hbox{Sum of squares of error}\\ SSE \\ \end{array} = \begin{array}{c} \hbox{Sum of squares} \left(\hbox{Total} \right)\\ SST \\ \end{array} - \begin{array}{c} \hbox{Sum of squares regression} \\ SSR\\ \end{array} $$

(A8)

$$ \begin{array}{l} SST=Y^{\prime} Y-n\bar{y}^{2}\quad\quad SSR= B^{\prime} X^{\prime} Y-n\bar{y}^{2} \\ SSE=Y^{\prime} Y-B^{\prime} X^{\prime}Y \end{array} $$

(A9)

Separately, for FIFO and LIFO firms,

$$ \begin{array}{l} SSE_{FIFO} =Y^{\prime}Y_{FIFO} -B_{FIFO}^{\prime} X_{FIFO}^{\prime} Y_{FIFO}\\ SSE_{LIFO} =Y^{\prime}Y_{LIFO} -B^{\prime}_{LIFO} X_{LIFO}^{\prime} Y_{LIFO} \end{array} $$

(A10)

From (A6), we know that Y _FIFO = Y _LIFO + d _inv qΞ

Substituting in (A10), we get

$$ Y^{\prime}Y_{FIFO} =\left({Y^{\prime}_{LIFO} +d_{inv} q\Upxi } \right)\left({Y_{LIFO} +d_{inv} q\Upxi } \right) $$

Noting that Cov(ɛ _t , ɛ _s ) = 0 ∀ s ≠ t,

$$ Y^{\prime}Y_{FIFO} =Y^{\prime}Y_{LIFO} +d_{inv}^2 q^{2} (n\varepsilon^{2}) $$

In expectation,

$$ Y^{\prime}Y_{FIFO} =Y^{\prime}Y_{LIFO} +nd_{inv}^2 q^{2}\sigma_\varepsilon^{2} $$

(A11)

$$ \begin{array}{l} SSE_{LIFO} =SST_{LIFO} -SSR_{LIFO}\\ SSE_{LIFO} =Y^{\prime}Y_{LIFO} -B^{\prime}_{LIFO} X_{LIFO}^{\prime} Y_{LIFO} \end{array} $$

(A12)

We note that

$$ SSE_{LIFO} \leq Y^{\prime}Y_{LIFO} -B_{FIFO}^{\prime} X_{LIFO}^{\prime} Y_{LIFO} $$

(A13)

In the expression $B_{FIFO}^{\prime} X_{LIFO}^{\prime} Y_{LIFO}$ in (A13), we use B _FIFO to determine the sum of squares. By definition, it is not optimal. Hence the inequality.

Now consider the expression $B_{FIFO}^{\prime} X_{LIFO}^{\prime} Y_{LIFO}$

We can write it as

$$ \begin{array}{l} B_{FIFO}^{\prime} \left[ X_{FIFO}^{\prime} +Z^{\prime} \right] \left[ Y_{FIFO} -d_{inv} q\Upxi \right] \\ \quad = \underset{\left(\hbox{i} \right)}{B_{FIFO}^{\prime} X_{FIFO}^{\prime} Y_{FIFO}} + \underset{\left(\hbox{ii} \right)}{B_{FIFO}^{\prime} Z^{\prime} Y_{FIFO}} - \underset{\left(\hbox{iii} \right)}{d_{inv} qB_{FIFO}^{\prime} X_{FIFO}^{\prime} \Upxi} - \underset{\left(\hbox{iv} \right)}{d_{inv} qB_{FIFO}^{\prime} Z^{\prime} \Upxi} \end{array} $$

(A14)

In expectation, expressions (ii) and (iii) in (A14) are zeros because in (ii) Z′ consists of ɛ which do not co-vary with Y _FIFO and in (iii), Ξ consists of ɛ which do not co-vary with X. Therefore,

$$ B_{FIFO}^{\prime} X_{LIFO}^{\prime} Y_{LIFO} =B_{FIFO}^{\prime} X_{FIFO}^{\prime} Y_{FIFO} -d_{inv} qB_{FIFO}^{\prime} Z^{\prime} \Upxi $$

(A15)

However, we can expand

$$ B^{\prime}Z^{\prime} \Upxi =\left[ \begin{array}{lllll} \beta_0 & \beta_1 & \beta_2 & \beta_3 & \beta_4 \\ \end{array} \right]\left[ \begin{array}{l} 0 \cdots \cdots 0 \\ \varepsilon_{1 t-1} \cdots \cdots \varepsilon_{n t-1} \\ \varepsilon_{1 t} \cdots \cdots \varepsilon_{n t} \\ \varepsilon_{1 t+1} \cdots \cdots \varepsilon_{n t+1} \\ 0 \cdots \cdots 0 \end{array} \right] \left[ \begin{array}{l} \varepsilon_{1 t} \\ \varepsilon_{2 t} \\ \vdots \\ \varepsilon_{n t} \\ \end{array} \right]\tau q^{2}d_{inv}^2 $$

In expectation, this will reduce to

$$ B^{\prime}Z^{\prime} \Upxi =n\beta_{2FIFO} \tau q^{2}d_{inv}^2 \sigma_\in^{2} $$

(A16)

From (A13) and (A16),

$$ SSE_{LIFO} \leq Y^{\prime}Y_{LIFO} +n\beta_{2FIFO} \tau q^{2}d_{inv}^2 \sigma_\varepsilon^{2}-B_{FIFO}^{\prime} X_{FIFO}^{\prime} Y_{FIFO} $$

From (A11),

$$ SSE_{LIFO} \leq [Y^{\prime}Y_{FIFO} -B_{FIFO}^{\prime} X_{FIFO}^{\prime} Y_{FIFO} ]-nq^{2}d_{inv}^2 \sigma_\varepsilon^{2}\left(1-\tau \beta_{2FIFO} \right),\quad \tau < 1 $$

The expression in [..] is SSE _FIFO.

From the expressions A1-FIFO, A2-FIFO and A3-FIFO, we can write

$$ \begin{aligned} \beta_{2FIFO} =&\frac{Cov(CFO_{FIFOt}, TCA_{FIFOt})}{Var(CFO_{FIFOt})} = \frac{-d_{ar}^{2}\psi^{2}-d_{ap}^{2}\sigma_\varepsilon^{2}-\tau d_{inv}^{2}\sigma_\varepsilon^{2}}{d_{ar}^{2}\psi^{2}+d_{ap}^{2}\sigma_\varepsilon^{2} + \tau^{2}d_{inv}^{2}\sigma_\varepsilon^{2}}\\ =&-1-\frac{\tau (1-\tau)d_{inv}^{2}\sigma_\varepsilon^{2}} {d_{ar}^{2}\psi^{2}+d_{ap}^{2}\sigma_\varepsilon^{2} +\tau^{2}d_{inv}^{2}\sigma_\varepsilon^{2}} < 0 \end{aligned} $$

$$ SSE_{LIFO} =SSE_{FIFO} -nq^{2}d_{inv}^2 \sigma_\varepsilon^{2} \left(1-\tau \beta_{2FIFO}\right) $$

(A17)

Given that τ < 1 and β₂ < 0, SSE _LIFO < SSE _FIFO

From this inequality, it is clear that the expected variance of the residuals in McNichols (2002) regression using FIFO is higher than the expected variance of the residuals in the regression using LIFO. In other words, the AQ for FIFO firms is expected to be higher than the AQ for LIFO firms.

1.8 Generalization arguments

Most of those assumptions made in the derivation above are meant to simplify the model. However, they do not typically affect the findings. The main assumptions made to simplify the model are (i) constant sales volume; (ii) efficient factor and product markets and (iii) no drift in prices and costs.

Now consider the assumption of constant sales volume. Any increase or decrease in sales quantity in the current year could change the quantity of physical inventory. In so far as this does not necessitate dipping into LIFO layers, all the arguments in the derivation above are valid. If the sales volume is increasing or decreasing, the expected future cash flow and inventory introduce an additional noise but this noise is independent of the additional variance that we have shown in (A17).

If we relax the efficient factor and product markets assumption, we will no longer be able to model the effect using random walk model. However, as long as in expectation, the variability over a longer period is more than the variability over shorter periods for costs, the model yields the correct predictions.

Any drift in costs and prices also does not affect the effect very much because the effect is in the second rather than in the first moment.

Section 2: Discretionary accruals

In this section, we address the decision of a manager acting opportunistically to insert a discretionary accrual amount (that is not likely to get reflected in cash flow) into a financial statement account that is audited. Let the accrual amount be x and the distribution of the account in which he inserts the amount be described by f(y) where y is a random variable representing the amount in the account before the insertion of the accrual. We will assume that f(y) is a normal distribution with mean μ and variance $\sigma_y^{2}.$ We will also assume, without loss of generality, that overstatement of y is costly and that the auditor will investigate the account if the realized value of y exceeds the expected amount, μ.

The incremental probability of investigation by the auditor, P, after inserting an accrual x in the account is given by the following expression:

$$ P=N(\mu)-N(\mu -x)=\int\limits_{\mu -x}^{\mu_c } \frac{1}{\sigma_y \sqrt{2\pi}} \exp \left[ -\frac{(y-\mu)^{2}}{2\sigma_y^{2}} \right]dy $$

where N(·) denotes the cumulative normal distribution.

We will evaluate P using Taylor’s series for the first three terms around x = 0 (which also implies y = μ).

$$ P(x,\sigma_y)\approx P(0,\sigma_y)+xP{\prime} (0,\sigma_y) + \frac{x^{2}}{2}P^{\prime\prime}(0,\sigma_y) $$

where P(0, σ _y ), P′(0, σ _y ) and P′′(0, σ _y ) are the function, the first and the second derivatives evaluated at x = 0.

It is easy to see that $P(0,\sigma_y) =0, P^{\prime} (0, \sigma_y) = (\frac{1}{\sigma_y \sqrt{2\pi}})$ and P′′ (0, σ _y ) = 0

This gives

$$ P\approx x \left(\frac{1}{\sigma_y \sqrt{2\pi}}\right) $$

(A18)

Differentiating P with σ _y , we get:

$$ \frac{{\rm d}P}{{\rm d}\sigma_y} = -x\left(\frac{1}{\sigma_y^{2}\sqrt{2\pi}}\right) < 0 $$

(A19)

The above result shows that the incremental probability of investigation resulting from the insertion of the accrual into an asset account is reduced when the standard deviation of the account is high. In Sect. 1 of the appendix, we showed that the standard deviation of the cost of goods using FIFO is higher than that using LIFO. Therefore, inserting the accrual into a FIFO account is less likely to trigger an investigation by the auditor into the veracity of the accrual than when it is inserted into a similar LIFO account. If the manager is acting opportunistically and wants to reduce the probability of investigation, it is more likely that discretionary accruals are embedded in the FIFO account than in the LIFO account.