Abstract. The stochastic demand cost-volume-profit (CVP) modei has recently received coBsiderable attention. For this model, management must determine optimal production prior tc knowing the actual demand, a stochastic variable with known distribution. Managemeot must choose the production quantity to balance prospects for sales revenue against risks of losses from shortages and from unsold items. This paper develops an expected retam on investment criterion model for determining the optimal production quantity. Formulas and solution methods applicable to general demand distributions are obtained. A special solution technique for normally distributed demand is presented. The resulting choice criterion offers the advantages inherent in return rate methods. !n addition, compared to a profit maximization approach, the expected rate of return on investment criterion is more widely applicable.Resume. Le modele de demande stochastique cout-volume-profit (CVP). a recemment regu considerablement d'atteotion. Avec ce modele, la gestion doit determiner la production optimale avant de connaitre la demande actuelle. une variable stochastique ayant une distribution connue. La gestion doit choisir la quantite a produire afin d'equilibrer les perspectives de ventes et !es risques de pertes resultant des penuries et des unites non vendues., Cet article developpe un modele base sur le rendement espere du capital investi pour determifler la quantite optimale a produire. On obtient des formules et des methodes pouvant s'appliquer k des distributions de demande generale. Une technique de solution particuliere pour une demande distribuee selon une loi normale est presentee. Ce modele offre ies avantages inherents aux methodes du taux de rendement. De plus, comparativement a i'approche de la maximisation du profit, !e critere du taux de rendement espere du capital investi, est applicable dans beaucoup plus de situations.
Portfolio models of the Markowitz-Tobin type implicitly assume that the investor does not have to liquidate any part of his portfolio to meet some exogenous cash demand. Since liquidity needs can be an important factor in portfolio management, Chen, Jen, and Zionts [3] in a recent paper developed a model assuming stochastic demand for cash and the possibility of meeting the cash demand by liquidating one or more assets. However, borrowing is an important alternative t o liquidating assets. This paper considers that possibility. Unlike Chen, Jen, and Zionts, this paper also considers the more difficult question of liquidation costs being partly fixed and partly variable. In order to make the consideration of borrowing and fixed transfer costs mathematically tractable, the problem is first cast in a framework different from that of [3].Whalen [lo] extended the Baurnol-Tobin [ I ] [7] model for the transaction demand for money by allowing firms or individuals to borrow in order t o meet their scheduled disbursements. However, like Baumol and Tobin, Whalen assumed that the expenditure stream planned by the individual concerned is certain. On the other hand, Chen, Jen and Zionts [3] (hereafter CJZ) developed a model assuming stochastic demand for cash and, unlike Baumol-Tobin-Whalen, they considered the possibility of liquidating one or more assets (depending on the quantum of cash demand) to meet the cash demand. However, CJZ did not consider the possibility of borrowing as an alternative to liquidating the assets to meet the cash demand. CJZ assumed the liquidation cost to be completely variable and indicated that fixed transfer costs cannot be considered in their framework. Tsiang [9], who developed a model very similar to that of CJZ, recognized borrowing as an alternative to liquidating the assets,' but did not explicitly introduce borrowing in his model.
According to conventional wisdom, the use of debt financing offsets the negative effect of historical cost depreciation on the firm's real cash flows. This effect derives from the following: According to tax law, the debtor firm can claim the entire nominal interest payment as a tax deduction notwithstanding the fact that the nominal interest payment includes a component which represents the return of real capital to the firm's bondholders.Maher and Nantell (Journal of Accounting Research, Spring 1983, pp. 329-340) claim to show that, given Miller's equilibrium tax rates, the use of debt financing does not ameliorate but rather aggravates the deleterious effect of historical cost depreciation. The aim of this paper is to criticize their conclusion. It is shown that their result derives, not from Miller's equilibrium tax rates, but rather from their implicit assumption regarding the behaviour of bond interest rates in the presence of inflation. They assume that bondholders are fully compensated on a postpersonal tax basis for the effect of inflation. We argue that it is implausible to assume that bondholders are completely insulated from the effects of inflation while shareholders suffer wealth losses due to inflation. A more plausible assumption is that both groups of investors are affected by inflation. Consistent with the theoretical result of Nielsen (Journal of Monetary Economics, 1981, pp. 261-2701, we assume that the real post-personal tax rate of return on the firm's bonds declines in the presence of inflation. Given this stipulation. we show that traditional wisdom is upheld, e. debt financing ameliorates the negative effect of historical cost depreciation.
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