What do accruals tell us about future cash flows?

Abstract

Our model, which is adapted from Feltham and Ohlson (Contemp Account Res 11:689–731, 1995) and Ohlson (Contemp Account Res 11:661–687, 1995) and extends Dechow and Dichev (Account Rev 77:35–59, 2002), characterizes the information about future cash flows reflected in accruals. It reveals investors can extract from accruals information about next period’s economic factor and the transitory part of one component of next period’s cash flow. The extent to which each accrual provides this information depends on whether the accrual aligns future or past cash flows and current period economics and whether it relates to the current or prior period. Thus each type of accrual has a different coefficient in valuation and forecasting cash flows or earnings. Each coefficient combines an information weight reflecting the information that accrual type provides and a multiple reflecting how that information is used in valuation and cash flow and earnings forecasting. The empirical evidence supports our main insight, namely that partitioning accruals based on their role in cash-flow alignment increases their ability to forecast future cash flows and earnings and explain firm value.

Appendices

Appendix 1: Proofs

Proposition 1 (Sect. 3.3)

Because investors are risk neutral, the value of the firm at time $t$ equals the expected present value of future dividends given information available to investors at $t$ . Because $Cash_{t}$ , i.e., the firm’s cash at $t$ , satisfies clean surplus, i.e., $Cash_{t} = RCash_{t - 1} + CFO_{t} - \, Div_{t}$ , dividends can be replaced in the dividend valuation expression using the clean surplus expression to yield:

$$P_{t} = Cash_{t} + {\text{E}}_{t} \left[ {\sum\limits_{\tau = 1}^{\infty } {\frac{{CFO_{t + \tau } }}{{R^{\tau } }}} } \right].$$

That is, the value of the firm at time $t$ equals current cash plus the expected present value of future operating cash flows. Using Eq. ( 4 ) from Sect. 3.2 , it is straightforward to determine that

$$\begin{aligned} {\text{E}}_{t} (CFO_{t + 1} ) & = \lambda^{A} \theta_{t} + (\lambda^{C} + \gamma \lambda^{B} ){\text{E}}_{t} (\theta_{t + 1} ) + {\text{E}}_{t} (e_{t + 1}^{A} ),\quad {\text{and}} \\ {\text{E}}_{t} (CFO_{t + \tau } ) & = \gamma^{\tau - 1} (\gamma^{ - 1} \lambda^{A} + \lambda^{C} + \gamma \lambda^{B} ){\text{E}}_{t} (\theta_{t + 1} ),{\text{ for }}\tau > 1. \\ \end{aligned}$$

Using these in the expression for $P_{t}$ above, together with standard expressions for the sum of an infinite series, yields Proposition 1.

Lemma (Sect. 4.1)

Given the definitions in Eq. ( 7 ) from Sect. 4.1 and assuming $\theta_{t}$ is known, it is straightforward to calculate the following:

$$\begin{aligned} Var(z1_{t} ) & = \sigma_{\theta }^{2} + \frac{1}{{(\lambda^{B} )^{2} }}\left( {\sigma_{{e^{A} }}^{2} + \sigma_{{e^{C} }}^{2} + \sigma_{{e^{B} }}^{2} } \right) \\ Var(z2_{t} ) & = \sigma_{\theta }^{2} + \frac{1}{{(\lambda^{B} )^{2} }}\left( {\sigma_{{e^{B} }}^{2} + \sigma_{{v^{B} }}^{2} } \right) \\ Var(z3_{t} ) & = \frac{1}{{(\lambda^{B} )^{2} }}\left( {\sigma_{{e^{A} }}^{2} + \sigma_{{v^{A} }}^{2} } \right) \\ Var(z4_{t} ) & = \left( {\sigma_{{e^{A} }}^{2} + \sigma_{{v^{A} }}^{2} } \right) \\ Cov(\theta_{t + 1} ,z1_{t} ) & = Cov(\theta_{t + 1} ,z2_{t} ) = \sigma_{\theta }^{2} \\ Cov(\theta_{t + 1} ,z3_{t} ) & = 0 \\ Cov(e_{t + 1}^{A} ,z4_{t} ) & = \sigma_{{e^{A} }}^{2} \\ Cov(z1_{t} ,z2_{t} ) & = \sigma_{\theta }^{2} + \frac{{\sigma_{{e^{B} }}^{2} }}{{(\lambda^{B} )^{2} }} \\ Cov(z1_{t} ,z3_{t} ) & = \frac{{\sigma_{{e^{B} }}^{2} }}{{(\lambda^{B} )^{2} }} \\ Cov(z2_{t} ,z3_{t} ) & = 0. \\ \end{aligned}$$

Using these expressions and the standard expression for conditional expectations in a multivariate normal distribution yields the following:

$${\text{E}}_{t} (\theta_{t + 1} ) = (1 - \beta_{1} - \beta_{2} )\gamma \theta_{t} + \beta_{1} z1_{t} + \beta_{2} z2_{t} + \beta_{3} z3_{t} ,$$

where $\beta_{1} = \frac{1}{D}(\sigma_{\varepsilon }^{2} \sigma_{{v^{B} }}^{2} (\sigma_{{e^{A} }}^{2} + \sigma_{{v^{A} }}^{2} )),\beta_{2} = \frac{1}{D}\sigma_{\varepsilon }^{2} (\sigma_{{e^{A} }}^{2} \sigma_{{e^{C} }}^{2} + (\sigma_{{e^{A} }}^{2} + \sigma_{{e^{C} }}^{2} )\sigma_{{v^{A} }}^{2} ),$ $\beta_{3} = - \frac{1}{D}(\sigma_{\varepsilon }^{2} \sigma_{{e^{A} }}^{2} \sigma_{{v^{B} }}^{2} ),D = \left( {\sigma_{\varepsilon }^{2} + \frac{{\sigma_{{e^{B} }}^{2} + \sigma_{{v^{B} }}^{2} }}{{(\lambda^{B} )^{2} }}} \right)\left( {\sigma_{{e^{A} }}^{2} \sigma_{{e^{C} }}^{2} + (\sigma_{{e^{A} }}^{2} + \sigma_{{e^{C} }}^{2} )\sigma_{{v^{A} }}^{2} } \right) + \left( {\sigma_{\varepsilon }^{2} + \frac{{\sigma_{{e^{B} }}^{2} }}{{(\lambda^{B} )^{2} }}} \right)\sigma_{{v^{B} }}^{2} \left( {\sigma_{{e^{A} }}^{2} + \sigma_{{v^{A} }}^{2} } \right)$, and

$$\begin{aligned} {\text{E}}_{t} (e_{t + 1}^{A} ) & = \beta_{4} z4_{t}, \quad {\text{where}} \quad \\ \beta_{4} & = \tfrac{{\sigma_{{e^{A} }}^{2} }}{{\sigma_{{e^{A} }}^{2} + \sigma_{{v^{A} }}^{2} }}. \\ \end{aligned}$$

Appendix 2: Variable definitions

MVE	market value of equity
CFO	cash flow from operations from the statement of cash flows plus after tax net interest paid
OPEARN	net income before extraordinary items plus after tax net interest expense
REV	total revenue
BVE	book value of equity
NI	net income before extraordinary items and discontinued operations
ACC	NI minus CFO
SFP A	total receivables plus deferred tax assets minus the sum of accounts payable, accrued expenses, pension liability, income taxes payable, and deferred tax liability
SFP B	the sum of inventories, prepaid expenses, income tax refund, property, plant, and equipment, intangible assets, deferred charges, investments and advances-equity, and long-term pension assets minus deferred revenues
OACC	ACC minus the sum of ΔSFP A and ΔSFP B

1. All variables are measured as of the firm’s fiscal year-end and deflated by average total assets. Δ denotes annual change