portfolio assignment 2 interest inventory valuation

Introduction to Computational Finance and Financial Econometrics with R

15.1 statistical analysis of portfolios: two assets.

Most of the issues involved with the statistical analysis of portfolios can be illustrated in the simple case of a two asset portfolio. Let \(R_{A}\) and \(R_{B}\) denote the simple returns on two risky assets and assume these returns are characterized by the CER model: \[\begin{equation} \left(\begin{array}{c} R_{A}\\ R_{B} \end{array}\right)\sim N\left(\left(\begin{array}{c} \mu_{A}\\ \mu_{B} \end{array}\right),\,\left(\begin{array}{cc} \sigma_{A}^{2} & \sigma_{AB}\\ \sigma_{AB} & \sigma_{B}^{2} \end{array}\right)\right)\tag{15.1} \end{equation}\] In matrix notation we have: \[ \mathbf{R}\sim N(\mu,\,\Sigma), \] where \[ \mathbf{R}=\left(\begin{array}{c} R_{A}\\ R_{B} \end{array}\right),\,\mu=\left(\begin{array}{c} \mu_{A}\\ \mu_{B} \end{array}\right),\,\Sigma=\left(\begin{array}{cc} \sigma_{A}^{2} & \sigma_{AB}\\ \sigma_{AB} & \sigma_{B}^{2} \end{array}\right) \] A portfolio with weight vector \(\mathbf{x}=(x_{A},x_{B})^{\prime}\) has return \(R_{p}=\mathbf{x}^{\prime}\mathbf{R}=x_{A}R_{A}+x_{B}R_{B}\) which is also described by the CER model \[\begin{eqnarray*} R_{p} & \sim & N(\mu_{p},\,\sigma_{p}^{2}),\\ \mu_{p} & = & \mathbf{x}^{\prime}\mu=x_{A}\mu_{A}+x_{B}\mu_{B},\\ \sigma_{p}^{2} & = & \mathbf{x}^{\prime}\mathbf{\varSigma}\mathbf{x}=x_{A}^{2}\sigma_{A}^{2}+x_{B}^{2}\sigma_{B}^{2}+2x_{A}x_{B}\sigma_{AB}. \end{eqnarray*}\] We observe a sample of asset returns of size \(T\) , \(\{r_{t}\}_{t=1}^{T}\) , where \(\mathbf{r}_{t}=(r_{At},r_{Bt})^{\prime}\) , that we assume is generated from the CER model (15.1) from which we create the sample portfolio returns \(r_{p,t}=\mathbf{x}^{\prime}\mathbf{r}_{t}=x_{A}r_{At}+x_{B}r_{Bt}\) .

The true CER model parameters are unknown in practice and must be estimated from the observed data. From chapter xxx, the CER model parameter estimates are the corresponding sample statistics: \[\begin{align} & \hat{\mu}_{i}=\frac{1}{T}\sum_{t=1}^{T}r_{it},\,\hat{\sigma}_{i}^{2}=\frac{1}{T-1}\sum_{t=1}^{T}(r_{it}-\hat{\mu}_{i})^{2}, \nonumber \\ & \hat{\sigma}_{i}=\sqrt{\hat{\sigma}_{i}^{2}},\,\hat{\sigma}_{ij}^{2}=\frac{1}{T-1}\sum_{t=1}^{T}(r_{it}-\hat{\mu}_{i})(r_{jt}-\hat{\mu}_{j}).\tag{15.2} \end{align}\] These estimates are unbiased, asymptotically normally distributed, and have estimation errors which can be quantified by standard errors and 95% confidence intervals. 94 For \(\hat{\mu}_{i}\) , \(\hat{\sigma}_{i}^{2}\) , \(\hat{\sigma}_{i}\) we have analytic standard error formulas: \[\begin{equation} \mathrm{se}(\hat{\mu}_{i})=\frac{\sigma_{i}}{\sqrt{T}},\,\mathrm{se}(\hat{\sigma}_{i}^{2})\approx\frac{\sigma_{i}^{2}}{\sqrt{T/2}},\,\mathrm{se}(\hat{\sigma}_{i})\approx\frac{\sigma_{i}}{\sqrt{2T}}.\tag{15.3} \end{equation}\] For \(\hat{\sigma}_{ij}^{2}\) there is no easy formula but we can use the bootstrap to compute a numerical estimate of the standard error. For 95% confidence intervals, we use the rule of thumb “estimate \(\pm\) 2 \(\times\) standard error” .

We can estimate the CER model parameters \(\mu_{p}\) , \(\sigma_{p}^{2}\) and \(\sigma_{p}\) for the portfolio return, \(R_{p}\) , using two equivalent methods. In the first method, we use the sample portfolio returns \(\{r_{p,t}\}_{t=1}^{T}\) and compute sample statistics: \[\begin{equation} \hat{\mu}_{p}=\frac{1}{T}\sum_{t=1}^{T}r_{p,t},\,\hat{\sigma}_{p}^{2}=\frac{1}{T-1}\sum_{t=1}^{T}(r_{p,t}-\hat{\mu}_{p})^{2},\,\hat{\sigma}_{p}=\sqrt{\hat{\sigma}_{p}^{2}}.\tag{15.4} \end{equation}\] These estimates are unbiased and asymptotically normal with standard errors: \[\begin{equation} \mathrm{se}(\hat{\mu}_{p})=\frac{\sigma_{p}}{\sqrt{T}},\,\mathrm{se}(\hat{\sigma}_{p}^{2})\approx\frac{\sigma_{p}^{2}}{\sqrt{T/2}},\,\mathrm{se}(\hat{\sigma}_{p})\approx\frac{\sigma_{p}}{\sqrt{2T}}.\tag{15.5} \end{equation}\] In the second method, we compute estimates of \(\mu_{p}\) and \(\sigma_{p}^{2}\) directly from the individual asset estimates in (15.2) : \[\begin{eqnarray} \hat{\mu}_{p} & = & \mathbf{x}^{\prime}\hat{\mu}=x_{A}\hat{\mu}_{A}+x_{B}\hat{\mu}_{B},\tag{15.6}\\ \hat{\sigma}_{p}^{2} & = & x^{\prime}\widehat{\Sigma}x=x_{A}^{2}\hat{\sigma}_{A}^{2}+x_{B}^{2}\hat{\sigma}_{B}^{2}+2x_{A}x_{B}\hat{\sigma}_{AB}.\tag{15.7} \end{eqnarray}\] The estimates of \(\mu_{p}\) and \(\sigma_{p}^{2}\) in (15.6) and (15.7) , respectively, are numerically identical to the estimates in (15.4) . To see this, consider the calculation of \(\hat{\mu}_{p}\) in (15.6) : \[\begin{eqnarray*} \hat{\mu}_{p} & = & x_{A}\hat{\mu}_{A}+x_{B}\hat{\mu}_{B}=x_{A}\left(\frac{1}{T}\sum_{t=1}^{T}r_{At}\right)+x_{B}\left(\frac{1}{T}\sum_{t=1}^{T}r_{Bt}\right)\\ & = & \frac{1}{T}\sum_{t=1}^{T}(x_{A}r_{At}+x_{B}r_{Bt})=\frac{1}{T}\sum_{t=1}^{T}r_{p,t}. \end{eqnarray*}\] The proof of the equivalence of \(\hat{\sigma}_{p}^{2}\) in (15.7) with \(\hat{\sigma}_{p}^{2}\) in (15.4) is left as an end-of-chapter exercise.

The standard errors of \(\hat{\mu}_{p}\) and \(\hat{\sigma}_{p}^{2}\) can also be directly calculated from (15.6) and (15.7) . Consider the calculation for \(\mathrm{se}(\hat{\mu}_{p})\) : \[\begin{equation} \mathrm{var}(\hat{\mu}_{p})=\mathrm{var}(x_{A}\hat{\mu}_{A}+x_{B}\hat{\mu}_{B})=x_{A}^{2}\mathrm{var}(\hat{\mu}_{A})+x_{B}^{2}\mathrm{var}(\hat{\mu}_{B})+2x_{A}x_{B}\mathrm{cov}(\hat{\mu}_{A},\hat{\mu}_{B}).\tag{15.8} \end{equation}\] Now, from chapter ?? , \[ \mathrm{var}(\hat{\mu}_{A})=\frac{\sigma_{A}^{2}}{T},\,\mathrm{var}(\hat{\mu}_{B})=\frac{\sigma_{B}^{2}}{T}. \] However, what is \(\mathrm{cov}(\hat{\mu}_{A},\hat{\mu}_{B})\) ? It can be shown that \[ \mathrm{cov}(\hat{\mu}_{A},\hat{\mu}_{B})=\frac{\sigma_{AB}}{T}. \] Then (15.8) can be rewritten as \[\begin{eqnarray*} \mathrm{var}(\hat{\mu}_{p}) & = & x_{A}\frac{\sigma_{A}^{2}}{T}+x_{B}\frac{\sigma_{B}^{2}}{T}+2x_{A}x_{B}\frac{\sigma_{AB}}{T}\\ & = & \frac{1}{T}\left(x_{A}^{2}\sigma_{A}^{2}+x_{B}^{2}\sigma_{B}^{2}+2x_{A}x_{B}\sigma_{AB}\right)\\ & = & \frac{\sigma_{p}^{2}}{T} \end{eqnarray*}\] Hence, \[ \mathrm{se}(\hat{\mu}_{p})=\sqrt{\mathrm{var}(\hat{\mu}_{p})}=\frac{\sigma_{p}}{\sqrt{T}} \] which is the same formula given in (15.5) .

Unfortunately, the calculation of \(\mathrm{se}(\hat{\sigma}_{p}^{2})\) is a bit horrific and we only sketch out some of the details. Now, \[\begin{eqnarray} \mathrm{var}(\hat{\sigma}_{p}^{2}) & = & \mathrm{var}(x_{A}^{2}\hat{\sigma}_{A}^{2}+x_{B}^{2}\hat{\sigma}_{B}^{2}+2x_{A}x_{B}\hat{\sigma}_{AB})\tag{15.9}\\ & = & x_{A}^{4}\mathrm{var}(\hat{\sigma}_{A}^{2})+x_{B}^{4}\mathrm{var}(\hat{\sigma}_{B}^{2})+4x_{A}^{2}x_{B}^{2}\mathrm{var}(\hat{\sigma}_{AB})\nonumber \\ & & +2x_{A}^{2}x_{B}^{2}\mathrm{cov}(\hat{\sigma}_{A}^{2},\hat{\sigma}_{B}^{2})+4x_{A}^{3}x_{B}\mathrm{cov}(\hat{\sigma}_{A}^{2},\hat{\sigma}_{AB})\nonumber \\ & & +4x_{A}x_{B}^{3}\mathrm{cov}(\hat{\sigma}_{B}^{2},\hat{\sigma}_{AB})\nonumber \end{eqnarray}\] Unfortunately, there are no easy formulas for \(\mathrm{var}(\hat{\sigma}_{AB})\) , \(\mathrm{cov}(\hat{\sigma}_{A}^{2},\hat{\sigma}_{B}^{2})\) , \(\mathrm{cov}(\hat{\sigma}_{A}^{2},\hat{\sigma}_{AB})\) and \(\mathrm{cov}(\hat{\sigma}_{B}^{2},\hat{\sigma}_{AB})\) . With a CLT approximation and much tedious calculation it can be shown that (15.9) is approximately equal to the square of \(\mathrm{se}(\hat{\sigma}_{p}^{2})\) given in (15.5) . Obviously, the method of computing standard errors for \(\hat{\mu}_{p}\) and \(\hat{\sigma}_{p}^{2}\) directly from the CER model estimates computed from the sample portfolio returns is much easier than the indirect calculations based on the individual asset estimates.

To be completed… table example data

Table 11.1 gives annual return distribution parameters for two hypothetical assets \(A\) and \(B\) . We use this distribution but re-scale the values to represent a monthly return distribution. Asset \(A\) is the high risk asset with a monthly return of \(\mu_{A}=1.46\%\) and monthly standard deviation of \(\sigma_{A}=7.45\%\) . Asset B is a lower risk asset with monthly return \(\mu_{B}=0.458\%\) and monthly standard deviation of \(\sigma_{B}=3.32\%\) . The assets are assumed to be slightly negatively correlated with correlation coefficient \(\rho_{AB}=-0.164\) . Given the standard deviations and the correlation, the covariance can be determined from \(\sigma_{AB}=\rho_{AB}\sigma_{A}\sigma_{B}=-0.0004\) . In R, these CER model parameters are created using:

For portfolio analysis, we consider an equally weighted portfolio of assets A and B. The CER model parameters for this portfolio are:

We use the above CER model parameters to simulate \(T=60\) hypothetical returns for assets A and B and the equally weighted portfolio:

The estimates of the CER model parameters from the simulated returns for the individual assets are:

The estimated standard errors and 95% confidence intervals for \(\hat{\mu}_{i}\) and \(\hat{\sigma}_{i}\) \((i=A,\,B)\) are:

Here, we see that the means are not estimated as precisely as the volatilities and that all of the true values are contained in the 95% confidence intervals.

For the equally weighted portfolio, the CER model estimates computed directly from the simulated portfolio returns using (15.4) are:

The portfolio estimates computed from the asset estimates (15.6) and (15.7) are numerically equivalent:

The estimated standard errors for \(\hat{\mu}_{p}\) and \(\hat{\sigma}_{p}\) , and 95% confidence intervals for \(\mu_{p}\) and \(\sigma_{p}\) computed using (15.5) are:

As with the individual assets, the portfolio mean is estimated less precisely than the portfolio volatility and the true values are in the 95% confidence intervals.

\(\blacksquare\)

In our analysis of portfolios, we visualized the risk return trade-off between portfolios by plotting the volatility-expected return pairs \((\hat{\sigma}_{p},\,\hat{\mu}_{p})\) of different portfolios. We did this without considering estimation error in \(\hat{\sigma}_{p}\) and \(\hat{\mu}_{p}\) . Estimation error in \(\hat{\sigma}_{p}\) and \(\hat{\mu}_{p}\) creates uncertainty about the location of the true values \((\sigma_{p},\,\mu_{p})\) in the risk-return diagram.

Figure 15.1 shows the true values and sample estimates of the pairs \((\sigma_{A},\mu_{A}),\) \((\sigma_{B},\mu_{B})\) , and \((\sigma_{p},\mu_{p})\) for the equally weighted portfolio created using:

Figure 15.1: Risk-return diagram for example data. \(\mathrm{A}=(\sigma_{A},\mu_{A})\) , \(\mathrm{B}=(\sigma_{B},\mu_{B})\) , \(\mathrm{A~Hat}=(\hat{\sigma}_{A},~\hat{\mu}_{A})\) , \(\mathrm{B~Hat}=(\hat{\sigma}_{B},~\hat{\mu}_{B})\) .

We see that \((\hat{\sigma}_{B},\hat{\mu}_{B})\) is fairly close to \((\sigma_{B},\mu_{B})\) but that \((\hat{\sigma}_{A},\hat{\mu}_{A})\) is quite far above \((\sigma_{A},\mu_{A})\) and \((\hat{\sigma}_{P},\hat{\mu}_{P})\) is moderately far above \((\sigma_{P},\mu_{P})\) . The large positive estimation errors in \(\hat{\mu}_{P}\) and \(\hat{\mu}_{A}\) greatly overstate the risk-return characteristics of the equally weighted portfolio and asset A.

To illustrate estimation error in the risk return diagram, the individual 95% confidence intervals for \(\mu_{i}\) and \(\sigma_{i}\) could be superimposed on the plot as rectangles centered at the pairs \((\hat{\sigma}_{i},\hat{\mu}_{i})\) . However, the probability that these rectangles contain the true pairs \((\sigma_{i},\mu_{i})\) is not equal to 95% because the confidence intervals for \(\mu_{i}\) are created independently from the confidence intervals for \(\sigma_{i}\) . To create a joint confidence set that cover the pair \((\sigma_{i},\mu_{i})\) with probability 95% requires knowing the joint probability distribution of \((\hat{\sigma}_{i},\hat{\mu}_{i})\) . In chapter ?? , it was shown that in the CER model: \[\begin{equation} \left(\begin{array}{c} \hat{\sigma}_{i}\\ \hat{\mu}_{i} \end{array}\right)\sim N\left(\left(\begin{array}{c} \sigma_{i}\\ \mu_{i} \end{array}\right),\left(\begin{array}{cc} \mathrm{se}(\hat{\sigma}_{i})^{2} & 0\\ 0 & \mathrm{se}(\hat{\mu}_{i})^{2} \end{array}\right)\right)\tag{15.10} \end{equation}\] for large enough \(T\) . Hence, \(\hat{\sigma}_{i}\) and \(\hat{\mu}_{i}\) are (asymptotically) jointly normally distributed and \(\mathrm{cov}(\hat{\sigma}_{i},\hat{\mu}_{i})=0\) which implies that they are also independent. Let \(\theta=(\sigma_{i},\mu_{i})^{\prime},\,\) \(\hat{\theta}=(\hat{\sigma}_{i},\hat{\mu}_{i})^{\prime}\) and \(\mathbf{V}=\mathrm{diag}(\mathrm{se}(\hat{\sigma}_{i})^{2},\mathrm{se}(\hat{\mu}_{i})^{2})\) . Then (15.10) can be expressed as \(\hat{\theta}\sim N(\theta,\,\mathbf{V})\) . It follows that the quadratic form \(\left(\hat{\theta}-\theta\right)^{\prime}\mathbf{V}^{-1}\left(\hat{\theta}-\theta\right)\sim\chi^{2}(2),\) and so \[\begin{equation} Pr\left\{ \left(\hat{\theta}-\theta\right)^{\prime}\mathbf{V}^{-1}\left(\hat{\theta}-\theta\right)\leq q_{.95}^{\chi^{2}(2)}\right\} =0.95\tag{15.11} \end{equation}\] where \(q_{.95}^{\chi^{2}(2)}\) is the 95% quantile of the \(\chi^{2}(2)\) distribution. The equation \(\left(\hat{\theta}-\theta\right)^{\prime}\mathbf{V}^{-1}\left(\hat{\theta}-\theta\right)=q_{.95}^{\chi^{2}(2)}\) defines an un-tilted ellipse in \(\sigma_{i}-\mu_{i}\) space centered at \((\hat{\sigma}_{i},\hat{\mu}_{i})\) with axes proportional to \(\mathrm{se}(\hat{\sigma}_{i})\) and \(\mathrm{se}(\hat{\mu}_{i})\) , respectively. This ellipse is the joint 95% confidence set for \((\sigma_{i},\mu_{i})\) .

Figure 15.2 repeats Figure 15.1 with the addition of the joint confidence sets for \((\sigma_{A},\mu_{A}),\) \((\sigma_{B},\mu_{B})\) , and \((\sigma_{p},\mu_{p})\) , created using

Figure 15.2: Risk return tradeoff with 95% confidence ellipses

The ellipse() function from the R package ellipse is used to draw the 95% confidence sets. The confidence ellipses are longer in the \(\mu_{i}\) direction because \(\mathrm{se}(\hat{\mu}_{i})\) is larger than \(\mathrm{se}(\hat{\sigma}_{i})\) and indicate more uncertainty about the true values of \(\mu_{i}\) than the true values of \(\sigma_{i}.\) The ellipse for \((\sigma_{A},\mu_{A})\) is much bigger than the ellipses for \((\sigma_{B},\mu_{B})\) and \((\sigma_{p},\mu_{p})\) and indicates a wide range of possible values for \((\sigma_{A},\mu_{A})\) . For all pairs, the true values are inside the 95% confidence ellipses. 95

The estimation errors in the points \((\hat{\sigma}_{i},\hat{\mu}{}_{i})\) can also be illustrated using the bootstrap. We simply sample with replacement from the observed returns \(B\) times and compute estimates of \((\sigma_{i},\mu_{i})\) from each bootstrap sample. We can then plot the \(B\) bootstrap pairs \((\hat{\sigma}_{i}^{*},\hat{\mu}_{i}^{*})\) on the risk return diagram instead of the confidence ellipses.

The following R code creates \(B=500\) bootstrap estimates of \((\sigma_{i},\mu_{i})\) for \(i=A,B,P\) :

Figure 15.3 repeats Figure 15.2 and adds the bootstrap estimates of \((\sigma_{i},\mu_{i})\) for \(i=A,B,P\) . Notice that the bootstrap estimates for each asset produce a scatter that fills the 95% confidence ellipses with just a few estimates lying outside the ellipses. Hence, the bootstrap is an easy and effective way to illustrate estimation error in the risk-return diagram.

Figure 15.3: Risk return trade off with bootstrap estimates.

15.1.1 Estimation error in the portfolio frontier

In the case of two risky assets, the portfolio frontier is a plot of the risk-return characteristics of all feasible portfolios. From this frontier, we can readily determine the set of efficient portfolios which are those portfolios that have the highest expected return for a given risk level. If we construct the portfolio frontier from portfolio risk and return estimates from the CER model, then the estimation error in these estimates leads to estimation error in the entire portfolio frontier.

Using the example data, we can construct the true unobservable portfolio frontier as well as an estimate of this frontier from the simulated returns. For example, consider creating the true and estimated portfolio frontiers for the following portfolios:

The risk-return characteristics of the portfolios on the true portfolio frontier are:

The risk-return characteristics of the portfolios on the estimated frontier are:

The true and estimated portfolios are illustrated in Figure 15.4 , created with

Figure 15.4: True and estimated portfolio frontiers

Due to the large estimation error in \(\hat{\mu}_{A}\) , the estimated frontier is considerably higher than the true frontier. As a result, portfolios on the estimated frontier appear to have higher reward-to-risk properties than they actually do.

Sampling uncertainty about the estimated frontier can be easily computed using the bootstrap. The process is the same as in the case of a single asset. For each bootstrap sample, estimate the expected return and volatility of each portfolio on the frontier and then plot these bootstrap pairs on the plot showing the estimated frontier from the sample returns.

The R code to create \(B=1000\) bootstrap estimates of risk and return pairs for the frontier portfolios is

The true and estimated frontier together with the bootstrap risk-return pairs for each portfolio on the estimated frontier is illustrated in Figure 15.5 , create using

Figure 15.5: Estimated frontier with bootstrap estimates.

The true frontier portfolios are the black dots, the estimated frontier portfolios are the dark blue dots and the bootstrap risk-return pairs are the light blue dots. The bootstrap estimates form a light blue cloud around the estimated frontier. The bootstrap cloud can be interpreted as approximating a confidence interval around estimated frontier. From (15.11) , this confidence interval can be thought of the union of all of the confidence ellipses about the portfolios on the frontier. The true frontier of portfolios (black dots) is within the blue cloud.

15.1.2 Statistical properties of the global minimum variance portfolio

For portfolios of two risky assets, the global minimum variance portfolio weights satisfy \[\begin{equation} x_{A}^{\min}=\frac{\sigma_{B}^{2}-\sigma_{AB}}{\sigma_{A}^{2}+\sigma_{B}^{2}-2\sigma_{AB}},~x_{B}^{\min}=1-x_{A}^{\min}=\frac{\sigma_{A}^{2}-\sigma_{AB}}{\sigma_{A}^{2}+\sigma_{B}^{2}-2\sigma_{AB}}.\tag{15.12} \end{equation}\] The expected return and variance of the global minimum variance portfolio are \[\begin{eqnarray*} \mu_{p,\mathrm{min}} & = & x_{A}^{\mathrm{min}}\mu_{A}+x_{B}^{\mathrm{min}}\mu_{B},\\ \sigma_{p,\mathrm{min}}^{2} & = & \left(x_{A}^{\mathrm{min}}\right)^{2}\sigma_{A}^{2}+\left(x_{B}^{\mathrm{min}}\right)^{2}\sigma_{B}^{2}+2x_{A}^{\mathrm{min}}x_{B}^{\mathrm{min}}\sigma_{AB}. \end{eqnarray*}\]

The estimated global minimum variance portfolio weights are then \[\begin{equation} \hat{x}_{A}^{\min}=\frac{\hat{\sigma}_{B}^{2}-\hat{\sigma}_{AB}}{\hat{\sigma}_{A}^{2}+\hat{\sigma}{}_{B}^{2}-2\hat{\sigma}_{AB}},~x_{B}^{\min}=1-\hat{x}{}_{A}^{\min}=\frac{\hat{\sigma}{}_{A}^{2}-\hat{\sigma}{}_{AB}}{\hat{\sigma}_{A}^{2}+\hat{\sigma}_{B}^{2}-2\hat{\sigma}{}_{AB}}.\tag{15.13} \end{equation}\] From (15.13) we see that estimation error in the global minimum variance weights is related to estimation error in the asset variances and the covariance in a complicated nonlinear way. However, the estimation error does not depend on estimation error in the expected returns. The estimated expected returns and variance of the global minimum variance portfolio are \[\begin{eqnarray} \hat{\mu}_{p,\mathrm{min}} & = & \hat{x}{}_{A}^{\mathrm{min}}\hat{\mu}_{A}+\hat{x}{}_{B}^{\mathrm{min}}\hat{\mu}_{B},\tag{15.14}\\ \hat{\sigma}_{p,\mathrm{min}}^{2} & = & \left(\hat{x}{}_{A}^{\mathrm{min}}\right)^{2}\hat{\sigma}_{A}^{2}+\left(\hat{x}{}_{B}^{\mathrm{min}}\right)^{2}\hat{\sigma}_{B}^{2}+2\hat{x}{}_{A}^{\mathrm{min}}\hat{x}_{B}^{\mathrm{min}}\hat{\sigma}_{AB}\tag{15.15} \end{eqnarray}\] Here, estimation error in \(\hat{\mu}_{p,\mathrm{min}}\) depends on two sources: estimation error in the global minimum variance weights (which depend on estimation error in the asset variances and the covariance), and estimation error in the asset expected returns. However, estimation error in \(\hat{\sigma}_{p,\mathrm{min}}^{2}\) only depends on estimation error in the asset variances and the covariance. Because there is more estimation error in the asset expected returns than the asset variances \(\hat{\mu}_{p,\mathrm{min}}\) , will be estimated more imprecisely than \(\hat{\sigma}_{p,\mathrm{min}}^{2}\) .

For the example data, the true and estimated global minimum variance portfolio are:

The estimated weights are close to the true weights. The true and estimated expected return and volatility of the global minimum variance portfolio are:

The estimated volatility of the global minimum variance portfolio is close to the true volatility but the estimated expected return is much larger than the true expected return. These portfolios are illustrated in Figure 15.6 .

Figure 15.6: True and estimated global minimum variance portfolios.

The statistical properties of (15.13) , (15.14) and (15.15) are difficult to derive analytically. For example, suppose we would like to evaluate the bias in the global minimum variance weights. We would need to evaluate \[\begin{equation} E\left[\hat{x}_{A}^{\min}\right]=E\left[\frac{\hat{\sigma}_{B}^{2}-\hat{\sigma}_{AB}}{\hat{\sigma}_{A}^{2}+\hat{\sigma}{}_{B}^{2}-2\hat{\sigma}_{AB}}\right].\tag{15.16} \end{equation}\] Now, \[ E\left[\frac{\hat{\sigma}_{B}^{2}-\hat{\sigma}_{AB}}{\hat{\sigma}_{A}^{2}+\hat{\sigma}{}_{B}^{2}-2\hat{\sigma}_{AB}}\right]\neq\frac{E\left[\hat{\sigma}_{B}^{2}\right]-E\left[\hat{\sigma}_{AB}\right]}{E\left[\hat{\sigma}_{A}^{2}\right]+E\left[\hat{\sigma}{}_{B}^{2}\right]-2E\left[\hat{\sigma}_{AB}\right]} \] because \(E[g(X)]\neq g(E[X])\) for nonlinear functions \(g(\cdot)\) . Hence, (15.16) is extremely difficult to evaluate analytically. Similarly, suppose we would like to compute \(\mathrm{se}(\hat{x}_{A}^{\min}).\) We would need to compute \[ \mathrm{var}\left(\hat{x}_{A}^{\min}\right)=\mathrm{var}\left(\frac{\hat{\sigma}_{B}^{2}-\hat{\sigma}_{AB}}{\hat{\sigma}_{A}^{2}+\hat{\sigma}{}_{B}^{2}-2\hat{\sigma}_{AB}}\right), \] which is a difficult and tedious calculation and can only be approximated based on the CLT.

The computations are even more difficult for evaluating bias and computing standard errors for (15.14) and (15.15) . For example, to evaluate the bias of \(\hat{\mu}_{p,\mathrm{min}}\) we need to calculate \[\begin{equation} E\left[\hat{\mu}_{p,\mathrm{min}}\right]=E\left[\hat{x}{}_{A}^{\mathrm{min}}\hat{\mu}_{A}+\hat{x}{}_{B}^{\mathrm{min}}\hat{\mu}_{B}\right]=E\left[\hat{x}{}_{A}^{\mathrm{min}}\hat{\mu}_{A}\right]+E\left[\hat{x}{}_{B}^{\mathrm{min}}\hat{\mu}_{B}\right].\tag{15.17} \end{equation}\] Without knowing more about the joint distributions of the asset means and weights we cannot simplify (15.17) . To compute the standard error of \(\hat{\mu}_{p,\mathrm{min}}\) we need to calculate \[\begin{align*} \mathrm{var}\left(\hat{\mu}_{p,\mathrm{min}}\right)&=\mathrm{var}\left(\hat{x}{}_{A}^{\mathrm{min}}\hat{\mu}_{A}+\hat{x}{}_{B}^{\mathrm{min}}\hat{\mu}_{B}\right)\\ &=\mathrm{var}(\hat{x}{}_{A}^{\mathrm{min}}\hat{\mu}_{A})+\mathrm{var}(\hat{x}{}_{B}^{\mathrm{min}}\hat{\mu}_{B})+2\mathrm{cov}\left(\hat{x}{}_{A}^{\mathrm{min}}\hat{\mu}_{A},\,\hat{x}{}_{B}^{\mathrm{min}}\hat{\mu}_{B}\right). \end{align*}\]

Again, without knowing more about the joint distributions of the asset means and estimated weights we cannot simplify (15.17) .

Fortunately, statistical properties of (15.13) , (15.14) and (15.15) can be easily quantified using the bootstrap. For each bootstrap sample we calculate these statisticss and from the bootstrap distributions we can then evaluate bias and compute standard errors and confidence intervals.

To compute \(B=1000\) bootstrap estimates of (15.13) , (15.14) and (15.15) use:

The bootstrap bias estimates for the global minimum variance portfolio weights are:

These values are close to zero suggesting that the estimated weights are unbiased. Notice that the estimates are identical but opposite in sign. This arises because the bootstrap estimates are perfectly negatively correlated:

The bootstrap standard error estimates for the weights are:

The standard errors estimates are identical and close to 0.05 which is not too large. Figure 15.7 shows histograms and normal QQ-plots for the bootstrap estimates of the weights. These distributions are centered at the sample estimates (white vertical lines) and look slightly asymmetric.

Figure 15.7: Empirical distribution of bootstrap estimates of global minimum variance portfolio weights.

The bootstrap estimates of bias for the estimated expected return and volatility of the global minimum variance portfolio are:

These small values indicate that the estimates are roughly unbiased. The bootstrap standard error estimates are:

Here, the bootstrap standard error estimate for \(\hat{\mu}_{p,\mathrm{min}}\) is larger than the estimate for \(\hat{\sigma}_{p,\mathrm{min}}\) indicating more uncertainty about the mean of the global minimum variance portfolio than the volatility of the portfolio. Interestingly, the bootstrap standard error estimates are close to the naive analytical standard error formulas based on the CLT that ignore estimation error in the weights:

That is, \[ \mathrm{se_{boot}}(\hat{\mu}_{p,\mathrm{min}})\approx\frac{\hat{\sigma}_{p,\mathrm{min}}}{\sqrt{T}},\,\mathrm{se_{boot}}\left(\hat{\sigma}_{p,\mathrm{min}}\right)\approx\frac{\hat{\sigma}_{p,\mathrm{min}}}{\sqrt{2\cdot T}}. \] The histograms and normal QQ-plots of the bootstrap estimates of \(\mu_{p,min}\) and \(\sigma_{p,min}\) are illustrated in Figure 15.8 , and look like normal distributions.

Figure 15.8: Empirical distribution of bootstrap estimates of \(\mu_{p,min}\) and \(\sigma_{p,min}\) .

The sampling uncertainty in \(\hat{\mu}_{p,\mathrm{min}}\) and \(\hat{\sigma}_{p,\mathrm{min}}\) can be visualized by plotting the bootstrap estimates of \(\mu_{p,min}\) and \(\sigma_{p,min}\) on the risk return diagram, as shown in Figure 15.9 . Clearly there is much more uncertainty about the location of \(\mu_{p,min}\) than the location of \(\sigma_{p,min}\) .

To sum up, for the global minimum variance portfolio we have roughly unbiased estimates of the weights, expected return and variance. We have a fairly precise estimate of volatility but an imprecise estimate of expected return.

Figure 15.9: Estimation error in estimates of the global minimum variance portfolio.

15.1.3 Statistical properties of the Sharpe ratio and the tangency portfolio

Let \(r_{f}\) denote the rate of return on a risk free asset with maturity equal to the investment horizon of the return \(R_{i}\) on risky asset \(i\) . Recall from chapter 11 , the Shapre ratio of asset \(i\) is defined as \[ \mathrm{S}\mathrm{R}_{i}=\frac{\mu_{i}-r_{f}}{\sigma_{i}}, \] and is a measure of risk-adjusted expected return. Graphically in the risk-return diagram, \(\mathrm{S}\mathrm{R}_{i}\) is the slope of a straight line from the risk-free rate that passes through the point \((\sigma_{i},\mu_{i})\) and represents the risk-return tradeoff of portfolios of the risk-free asset and the risky asset. The estimated Sharpe ratio is \[ \widehat{\mathrm{SR}}_{i}=\frac{\hat{\mu}_{i}-r_{f}}{\hat{\sigma}_{i}}, \] which inherits estimation error from \(\hat{\mu}_{i}\) and \(\hat{\sigma}_{i}\) in a nonlinear way. As a result, analytically computing the bias and standard error for \(\widehat{\mathrm{SR}}_{i}\) is complicated and typically involves approximations based on the CLT. However, computing numerical estimates of the bias and the standard error for \(\widehat{\mathrm{SR}}_{i}\) using the bootstrap is simple.

For the example data, assume a monthly risk-free rate of \(r_{f}=0.03/12=0.0025.\) The true Sharpe ratios are:

Here, asset A has a much higher Sharpe ratio than asset B. For the simulated data, the estimated Sharpe ratios are:

For both assets the estimated Sharpe ratios are quite different from the true Sharpe ratios and are highly misleading. The estimated Sharpe ratio for asset A is more than two times larger than the true Sharpe ratio and indicates a much higher risk adjusted preformance than is actually available. For asset B, the estimated Sharpe ratio is slightly negative when, in fact, the true Sharpe ratio is slightly positive. The true and estimated Sharpe ratios are illustrated in Figure 15.10 . The slopes of the black lines are the true Sharpe ratios, and the slopes of the blues lines are the estimated Sharpe ratios.

Figure 15.10: True and estimated Sharpe ratios.

To illustrate the magnitude of the estimation errors in the estimated Sharpe ratios, Figure 15.11 shows 500 bootstrap estimates of the risk-return pairs \((\sigma_{A},\mu_{A})\) and \((\sigma_{B},\mu_{B})\) along with the maximum and minimum bootstrap Sharpe ratio estimates for each asset. The bootstrap Sharpe ratio estimates are computed using:

Figure 15.11: Bootstrap risk-return estimates with maximum and minimum Sharpe ratios.

The maximum and minimum bootstrap Sharpe ratio estimates for asset B are the two grey straight lines from the risk-free rate that have the highest and lowest slopes, respectively. The maximum and minimum bootstrap Sharpe ratio estimates for asset A are the two light blue lines with the highest and lowest slopes, respectively. These maximum and minimum estimates are:

For each asset the difference in the maximum and minimum slopes is substantial and indicates a large about of estimation error in the estimated Sharpe ratios.

The statistical properties of the estimated Sharpe ratios can be estimated from the bootstrap samples. The bootstrap estimates of bias are:

Here we see there is a substantial upward bias in \(\widehat{\mathrm{SR}}_{A}\) (bias relative to true Sharpe ratio is 141%) and a substantial downward bias in \(\widehat{\mathrm{SR}}_{B}\) (bias relative to true Sharpe ratio is -105%). A crude bias adjusted Sharpe ratio estimate, which substracts the estimated bias from the sample estimate, gives results much closer to the true Sharpe ratios:

The bootstrap estimated standard errors for both assets are big and indicate that the Sharpe ratios are not estimated well:

Figure 15.12 shows the histograms and normal QQ-plots of the bootstrap distributions for the estimated Sharpe ratios. The histograms for both assets show the wide dispersion of the bootstrap Sharpe ratio estimates that was illustrated in Figure 15.11 . The histogram and QQ-plot for asset A shows a positive skewness whereas the histogram and QQ-plot for asset B show a more symmetric distribution. The quantile-based 95% confidence intervals for the true Sharpe ratios are:

These intervals are quite large and indicate much uncertainty about the true Sharpe ratio values.

Figure 15.12: Bootstrap distributions of estimated Sharpe ratios.

\(\hat{\sigma}_{i}\) is asymptotically unbiased and the bias for finite \(T\) is typically very small so that it is essentially unbiased for moderately sized \(T\) . ↩︎

Notice, however, that the pair \((\sigma_{p},\mu_{p})\) is inside the confidence ellipse for \((\sigma_{B},\mu_{B})\) but that \((\sigma_{B},\mu_{B})\) is not in the confidence ellipse for \((\sigma_{p},\mu_{p})\) . ↩︎

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How to Choose the Best Stock Valuation Method

Pete Rathburn is a copy editor and fact-checker with expertise in economics and personal finance and over twenty years of experience in the classroom.

When deciding which valuation method to use to value a stock for the first time, it's easy to become overwhelmed by the number of valuation techniques available to investors. There are valuation methods that are fairly straightforward, while others are more involved and complicated. 

Unfortunately, there's no one method that's best suited for every situation. Each stock is different, and each industry or sector has unique characteristics that may require multiple valuation methods . In this article, we'll explore the most common valuation methods and when to use them.

Key Takeaways

• There are several methods for valuing a company or its stock, each with its own strengths and weaknesses.
• Some models try to pin down a company's intrinsic value based on its own financial statements and projects, while others look to relative valuation against peers.
• For companies that pay dividends, a discount model like the Gordon growth model is often simple and fairly reliable — but many companies do not pay dividends.
• Often, a multiples approach may be employed to make comparative evaluations of a company's value in the market against its competitors or broader market.
• When choosing a valuation method, make sure it is appropriate for the firm you're analyzing, and if more than one is suitable use both to arrive at a better estimate.

Two Categories of Valuation Models

Valuation methods typically fall into two main categories: absolute valuation and relative valuation.

Absolute Valuation

Absolute valuation models attempt to find the intrinsic or "true" value of an investment based only on fundamentals. Looking at fundamentals simply means you would only focus on such things as dividends, cash flow, and the growth rate for a single company—and not worry about any other companies. Valuation models that fall into this category include the dividend discount model, discounted cash flow model, residual income model, and asset-based model.

Relative Valuation

Relative valuation models , in contrast, operate by comparing the company in question to other similar companies. These methods involve calculating multiples and ratios, such as the price-to-earnings (P/E) ratio, and comparing them to the multiples of similar companies. For example, if the P/E of a company is lower than the P/E of a comparable company, the original company might be considered undervalued. Typically, the relative valuation model is a lot easier and quicker to calculate than the absolute valuation model, which is why many investors and analysts begin their analysis with this model.

Let's take a look at some of the more popular valuation methods available to investors, and see when it's appropriate to use each model. 

The dividend discount model (DDM) is one of the most basic of the absolute valuation models. The dividend discount model calculates the "true" value of a firm based on the dividends the company pays its shareholders. The justification for using dividends to value a company is that dividends represent the actual cash flows going to the shareholder, so valuing the present value of these cash flows should give you a value for how much the shares should be worth.

The first step is to determine if the company pays a dividend.

The second step is to determine whether the dividend is stable and predictable since it's not enough for the company to just pay a dividend. The companies that pay stable and predictable dividends are typically mature blue chip companies in well-developed industries. These types of companies are often best suited for the DDM valuation model. For instance, review the dividends and earnings of company XYZ below and determine if the DDM model would be appropriate for the company:

In the above example, the earnings per share (EPS) is consistently growing at an average rate of 5%, and the dividends are also growing at the same rate. The company's dividend is consistent with its earnings trend, which should make it easy to predict dividends for future periods. Also, you should check the payout ratio to make sure the ratio is consistent. In this case, the ratio is 0.125 for all six years, which makes this company an ideal candidate for the dividend discount model. 

The Gordon Growth Model (GGM) is widely used to determine the intrinsic value of a stock based on a future series of dividends that grow at a constant rate. It is a popular and straightforward variant of a dividend discount mode (DDM).

What if the company doesn't pay a dividend or its dividend pattern is irregular? In this case, move on to check if the company fits the criteria to use the  discounted cash flow (DCF) model . Instead of looking at dividends, the DCF model uses a firm's discounted future cash flows to value the business. The big advantage of this approach is that it can be used with a wide variety of firms that don't pay dividends, and even for companies that do pay dividends, such as company XYZ in the previous example.

The DCF model has several variations, but the most commonly used form is the Two-Stage DCF model. In this variation, the free cash flows are generally forecasted for five to 10 years, and then a terminal value is calculated to account for all the cash flows beyond the forecasted period. The first requirement for using this model is for the company to have positive and predictable free cash flows. Based on this requirement alone, you will find that many small high-growth companies and non-mature firms will be excluded due to the large capital expenditures these companies typically encounter.

For example, let's take a look at the cash flows of the following firm:

In this snapshot, the firm has produced an increasing positive operating cash flow , which is good. However, you can see by the large amounts of capital expenditures that the company is still investing much of its cash back into the business in order to grow. As a result, the company has negative free cash flows for four of the six years, which makes it extremely difficult or nearly impossible to predict the cash flows for the next five to 10 years.

To use the DCF model most effectively, the target company should generally have stable, positive, and predictable free cash flows. Companies that have the ideal cash flows suited for the DCF model are typically  mature firms that are past the growth stages. 

Discounted Cash Flow (DCF)

The last model is sort of a catch-all model that can be used if you are unable to value the company using any of the other models, or if you simply don't want to spend the time crunching the numbers. This model doesn't attempt to find an intrinsic value for the stock like the previous two valuation models. Instead, it compares the stock's price multiples to a benchmark to determine if the stock is relatively undervalued or overvalued. The rationale for this is based on the Law of One Price , which states that two similar assets should sell for similar prices. The intuitive nature of this model is one of the reasons it is so popular.

The reason why the comparables model can be used in almost all circumstances is due to the vast number of multiples that can be used, such as the price-to-earnings (P/E), price-to-book (P/B), price-to-sales (P/S), price-to-cash flow (P/CF), and many others. Of these ratios, the P/E ratio is the most commonly used because it focuses on the earnings of the company, which is one of the primary drivers of an investment's value.

When can you use the P/E multiple for a comparison? You can typically use it if the company is publicly traded since you'll need both the stock price and the earnings of the company. Secondly, the company should be generating positive earnings because a comparison using a negative P/E multiple would be meaningless. Lastly, the earnings quality should be strong. That is, earnings should not be too volatile, and the accounting practices used by management should not distort the reported earnings drastically.

These are just some of the main criteria investors should look at when choosing which ratio or multiples to use. If the P/E multiple cannot be used, choose a different ratio, such as the price-to-sales or price-to-cash flow multiples.

No single valuation model fits every situation, but by knowing the characteristics of the company, you can select a valuation model that best suits the situation. Additionally, investors are not limited to just using one model. Often, investors will perform several valuations to create a range of possible values or average all of the valuations into one. With stock analysis, sometimes it's not a question of the right tool for the job but rather how many tools you employ to obtain varying insights from the numbers.

The Stern School of Business, New York University. " Dividend Discount Models ."

• Valuing a Company: Business Valuation Defined With 6 Methods 1 of 37
• What Is Valuation? 2 of 37
• Valuation Analysis: Meaning, Examples and Use Cases 3 of 37
• Financial Statements: List of Types and How to Read Them 4 of 37
• Balance Sheet: Explanation, Components, and Examples 5 of 37
• Cash Flow Statement: How to Read and Understand It 6 of 37
• 6 Basic Financial Ratios and What They Reveal 7 of 37
• 5 Must-Have Metrics for Value Investors 8 of 37
• Earnings Per Share (EPS): What It Means and How to Calculate It 9 of 37
• P/E Ratio Definition: Price-to-Earnings Ratio Formula and Examples 10 of 37
• Price-to-Book (PB) Ratio: Meaning, Formula, and Example 11 of 37
• Price/Earnings-to-Growth (PEG) Ratio: What It Is and the Formula 12 of 37
• Fundamental Analysis: Principles, Types, and How to Use It 13 of 37
• Absolute Value: Definition, Calculation Methods, Example 14 of 37
• Relative Valuation Model: Definition, Steps, and Types of Models 15 of 37
• Intrinsic Value of a Stock: What It Is and Formulas to Calculate It 16 of 37
• Intrinsic Value vs. Current Market Value: What's the Difference? 17 of 37
• The Comparables Approach to Equity Valuation 18 of 37
• The 4 Basic Elements of Stock Value 19 of 37
• How to Become Your Own Stock Analyst 20 of 37
• Due Diligence in 10 Easy Steps 21 of 37
• Determining the Value of a Preferred Stock 22 of 37
• Qualitative Analysis 23 of 37
• How to Choose the Best Stock Valuation Method 24 of 37
• Bottom-Up Investing: Definition, Example, Vs. Top-Down 25 of 37
• Financial Ratio Analysis: Definition, Types, Examples, and How to Use 26 of 37
• What Book Value Means to Investors 27 of 37
• Liquidation Value: Definition, What's Excluded, and Example 28 of 37
• Market Capitalization: What It Means for Investors 29 of 37
• Discounted Cash Flow (DCF) Explained With Formula and Examples 30 of 37
• Enterprise Value (EV) Formula and What It Means 31 of 37
• How to Use Enterprise Value to Compare Companies 32 of 37
• How to Analyze Corporate Profit Margins 33 of 37
• Return on Equity (ROE) Calculation and What It Means 34 of 37
• Decoding DuPont Analysis 35 of 37
• How to Value Private Companies 36 of 37
• Valuing Startup Ventures 37 of 37

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portfolio assignment 2 interest inventory valuation

10.1 Describe and Demonstrate the Basic Inventory Valuation Methods and Their Cost Flow Assumptions

Accounting for inventory is a critical function of management. Inventory accounting is significantly complicated by the fact that it is an ongoing process of constant change, in part because (1) most companies offer a large variety of products for sale, (2) product purchases occur at irregular times, (3) products are acquired for differing prices, and (4) inventory acquisitions are based on sales projections, which are always uncertain and often sporadic. Merchandising companies must meticulously account for every individual product that they sell, equipping them with essential information, for decisions such as these:

• What is the quantity of each product that is available to customers?
• When should inventory of each product item be replenished and at what quantity?
• How much should the company charge customers for each product to cover all costs plus profit margin?
• How much of the inventory cost should be allocated toward the units sold (cost of goods sold) during the period?
• How much of the inventory cost should be allocated toward the remaining units (ending inventory) at the end of the period?
• Is each product moving robustly or have some individual inventory items’ activity decreased?
• Are some inventory items obsolete?

The company’s financial statements report the combined cost of all items sold as an offset to the proceeds from those sales, producing the net number referred to as gross margin (or gross profit). This is presented in the first part of the results of operations for the period on the multi-step income statement. The unsold inventory at period end is an asset to the company and is therefore included in the company’s financial statements, on the balance sheet, as shown in Figure 10.2 . The total cost of all the inventory that remains at period end, reported as merchandise inventory on the balance sheet, plus the total cost of the inventory that was sold or otherwise removed (through shrinkage, theft, or other loss), reported as cost of goods sold on the income statement (see Figure 10.2 ), represent the entirety of the inventory that the company had to work with during the period, or goods available for sale.

Fundamentals of Inventory

Although our discussion will consider inventory issues from the perspective of a retail company, using a resale or merchandising operation, inventory accounting also encompasses recording and reporting of manufacturing operations. In the manufacturing environment, there would be separate inventory calculations for the various process levels of inventory, such as raw materials, work in process, and finished goods. The manufacturer’s finished goods inventory is equivalent to the merchandiser’s inventory account in that it includes finished goods that are available for sale.

In merchandising companies, inventory is a company asset that includes beginning inventory plus purchases , which include all additions to inventory during the period. Every time the company sells products to customers, they dispose of a portion of the company’s inventory asset. Goods available for sale refers to the total cost of all inventory that the company had on hand at any time during the period, including beginning inventory and all inventory purchases. These goods were normally either sold to customers during the period (occasionally lost due to spoilage, theft, damage, or other types of shrinkages) and thus reported as cost of goods sold, an expense account on the income statement, or these goods are still in inventory at the end of the period and reported as ending merchandise inventory, an asset account on the balance sheet. As an example, assume that Harry’s Auto Parts Store sells oil filters. Suppose that at the end of January 31, 2018, they had 50 oil filters on hand at a cost of $7 per unit. This means that at the beginning of February, they had 50 units in inventory at a total cost of $350 (50 × $7). During the month, they purchased 20 filters at a cost of $7, for a total cost of $140 (20 × $7). At the end of the month, there were 18 units left in inventory. Therefore, during the month of February, they sold 52 units. Figure 10.3 illustrates how to calculate the goods available for sale and the cost of goods sold.

Inventory costing is accomplished by one of four specific costing methods: (1) specific identification, (2) first-in, first-out, (3) last-in, first-out, and (4) weighted-average cost methods. All four methods are techniques that allow management to distribute the costs of inventory in a logical and consistent manner, to facilitate matching of costs to offset the related revenue item that is recognized during the period, in accordance with GAAP expense recognition and matching concepts. Note that a company’s cost allocation process represents management’s chosen method for expensing product costs, based strictly on estimates of the flow of inventory costs, which is unrelated to the actual flow of the physical inventory. Use of a cost allocation strategy eliminates the need for often cost-prohibitive individual tracking of costs of each specific inventory item, for which purchase prices may vary greatly. In this chapter, you will be provided with some background concepts and explanations of terms associated with inventory as well as a basic demonstration of each of the four allocation methods, and then further delineation of the application and nuances of the costing methods.

A critical issue for inventory accounting is the frequency for which inventory values are updated. There are two primary methods used to account for inventory balance timing changes: the periodic inventory method and the perpetual inventory method. These two methods were addressed in depth in Merchandising Transactions ).

Periodic Inventory Method

A periodic inventory system updates the inventory balances at the end of the reporting period, typically the end of a month, quarter, or year. At that point, a journal entry is made to adjust the merchandise inventory asset balance to agree with the physical count of inventory, with the corresponding adjustment to the expense account, cost of goods sold. This adjustment shifts the costs of all inventory items that are no longer held by the company to the income statement, where the costs offset the revenue from inventory sales, as reflected by the gross margin. As sales transactions occur throughout the period, the periodic system requires that only the sales entry be recorded because costs will only be updated during end-of-period adjustments when financial statements are prepared. However, any additional goods for sale acquired during the month are recorded as purchases. Following are examples of typical journal entries for periodic transactions. The first is an example entry for an inventory sales transaction when using periodic inventory, and the second records the purchase of additional inventory when using the periodic method. Note: Periodic requires no corresponding cost entry at the time of sale, since the inventory is adjusted only at period end.

A purchase of inventory for sale by a company under the periodic inventory method would necessitate the following journal entry. (This is discussed in more depth in Merchandising Transactions .)

Perpetual Inventory Method

A perpetual inventory system updates the inventory account balance on an ongoing basis, at the time of each individual sale. This is normally accomplished by use of auto-ID technology, such as optical-scan barcode or radio frequency identification (RFIF) labels. As transactions occur, the perpetual system requires that every sale is recorded with two entries, first recording the sales transaction as an increase to Accounts Receivable and a decrease to Sales Revenue, and then recording the cost associated with the sale as an increase to Cost of Goods Sold and a decrease to Merchandise Inventory. The journal entries made at the time of sale immediately shift the costs relating to the goods being sold from the merchandise inventory account on the balance sheet to the cost of goods sold account on the income statement. Little or no adjustment is needed to inventory at period end because changes in the inventory balances are recorded as both the sales and purchase transactions occur. Any necessary adjustments to the ending inventory account balances would typically be caused by one of the types of shrinkage you’ve learned about. These are example entries for an inventory sales transaction when using perpetual inventory updating:

A purchase of inventory for sale by a company under the perpetual inventory method would necessitate the following journal entry. (Greater detail is provided in Merchandising Transactions .)

Continuing Application

As previously discussed, Gearhead Outfitters is a retail chain selling outdoor gear and accessories. As such, the company is faced with many possible questions related to inventory. How much inventory should be carried? What products are the most profitable? Which products have the most sales? Which products are obsolete? What timeframe should the company allow for inventory to be replenished? Which products are the most in demand at each location?

In addition to questions related to type, volume, obsolescence, and lead time, there are many issues related to accounting for inventory and the flow of goods. As one of the biggest assets of the company, the way inventory is tracked can have an effect on profit. Which method of accounting—first-in first-out, last-in first out, specific identification, weighted average— provides the most accurate reflection of inventory and cost of goods sold is important in determining gross profit and net income. The method selected affects profits, taxes, and can even change the opinion of potential lenders concerning the financial strength of the company. In choosing a method of accounting for inventory, management should consider many factors, including the accurate reflection of costs, taxes on profits, decision-making about purchases, and what effect a point-of-sale (POS) system may have on tracking inventory.

Gearhead exists to provide a positive shopping experience for its customers. Offering a clear picture of its goods, and maintaining an appealing, timely supply at competitive prices is one way to keep the shopping experience positive. Thus, accounting for inventory plays an instrumental role in management’s ability to successfully run a company and deliver the company’s promise to customers.

Data for Demonstration of the Four Basic Inventory Valuation Methods

The following dataset will be used to demonstrate the application and analysis of the four methods of inventory accounting .

Company: Spy Who Loves You Corporation

Product: Global Positioning System (GPS) Tracking Device

Description: This product is an economical real-time GPS tracking device, designed for individuals who wish to monitor others’ whereabouts. It is marketed to parents of middle school and high school students as a safety measure. Parents benefit by being apprised of the child’s location, and the student benefits by not having to constantly check in with parents. Demand for the product has spiked during the current fiscal period, while supply is limited, causing the selling price to escalate rapidly.

Specific Identification Method

The specific identification method refers to tracking the actual cost of the item being sold and is generally used only on expensive items that are highly customized (such as tracking detailed costs for each individual car in automobiles sales) or inherently distinctive (such as tracking origin and cost for each unique stone in diamond sales). This method is too cumbersome for goods of large quantity, especially if there are not significant feature differences in the various inventory items of each product type. However, for purposes of this demonstration, assume that the company sold one specific identifiable unit, which was purchased in the second lot of products, at a cost of $27.

Three separate lots of goods are purchased:

First-in, First-out (FIFO) Method

The first-in, first-out method (FIFO) records costs relating to a sale as if the earliest purchased item would be sold first. However, the physical flow of the units sold under both the periodic and perpetual methods would be the same. Due to the mechanics of the determination of costs of goods sold under the perpetual method, based on the timing of additional purchases of inventory during the accounting period, it is possible that the costs of goods sold might be slightly different for an accounting period. Since FIFO assumes that the first items purchased are sold first, the latest acquisitions would be the items that remain in inventory at the end of the period and would constitute ending inventory.

Last-in, First-out (LIFO) Method

The last-in, first out method (LIFO) records costs relating to a sale as if the latest purchased item would be sold first. As a result, the earliest acquisitions would be the items that remain in inventory at the end of the period.

IFRS Connection

For many companies, inventory is a significant portion of the company’s assets. In 2018, the inventory of Walmart , the world’s largest international retailer, was 70% of current assets and 21% of total assets. Because inventory also affects income as it is sold through the cost of goods sold account, inventory plays a significant role in the analysis and evaluation of many companies. Ending inventory affects both the balance sheet and the income statement. As you’ve learned, the ending inventory balance is reflected as a current asset on the balance sheet and the ending inventory balance is used in the calculation of costs of goods sold. Understanding how companies report inventory under US GAAP versus under IFRS is important when comparing companies reporting under the two methods, particularly because of a significant difference between the two methods.

Similarities

• When inventory is purchased, it is accounted for at historical cost and then evaluated at each balance sheet date to adjust to the lower of cost or net realizable value.
• Both IFRS and US GAAP allow FIFO and weighted-average cost flow assumptions as well as specific identification where appropriate and applicable.

Differences

• IFRS does not permit the use of LIFO. This is a major difference between US GAAP and IFRS. The AICPA estimates that roughly 35–40% of all US companies use LIFO, and in some industries, such as oil and gas, the use of LIFO is more prevalent. Because LIFO generates lower taxable income during times of rising prices, it is estimated that eliminating LIFO would generate an estimated $102 billion in tax revenues in the US for the period 2017–2026. In creating IFRS, the IASB chose to eliminate LIFO, arguing that FIFO more closely matches the flow of goods. In the US, FASB believes the choice between LIFO and FIFO is a business model decision that should be left up to each company. In addition, there was significant pressure by some companies and industries to retain LIFO because of the significant tax liability that would arise for many companies from the elimination of LIFO.

Weighted-Average Cost Method

The weighted-average cost method (sometimes referred to as the average cost method ) requires a calculation of the average cost of all units of each particular inventory items. The average is obtained by multiplying the number of units by the cost paid per unit for each lot of goods, then adding the calculated total value of all lots together, and finally dividing the total cost by the total number of units for that product. As a caveat relating to the average cost method, note that a new average cost must be calculated after every change in inventory to reassess the per-unit weighted-average value of the goods. This laborious requirement might make use of the average method cost-prohibitive.

Comparing the various costing methods for the sale of one unit in this simple example reveals a significant difference that the choice of cost allocation method can make. Note that the sales price is not affected by the cost assumptions; only the cost amount varies, depending on which method is chosen. Figure 10.4 depicts the different outcomes that the four methods produced.

Once the methods of costing are determined for the company, that methodology would typically be applied repeatedly over the remainder of the company’s history to accomplish the generally accepted accounting principle of consistency from one period to another. It is possible to change methods if the company finds that a different method more accurately reflects results of operations, but the change requires disclosure in the company’s notes to the financial statements, which alerts financial statement users of the impact of the change in methodology. Also, it is important to realize that although the Internal Revenue Service generally allows differing methods of accounting treatment for tax purposes than for financial statement purposes, an exception exists that prohibits the use of LIFO inventory costing on the company tax return unless LIFO is also used for the financial statement costing calculations.

Ethical Considerations

Auditors look for inventory fraud.

Inventory fraud can be used to book false revenue or to increase the amount of assets to obtain additional lending from a bank or other sources. In the typical chain of accounting events, inventory ultimately becomes an expense item known as cost of goods sold. 1 In a manipulated accounting system, a trail of fraudulent transactions can point to accounting misrepresentation in the sales cycle, which may include

• recording fictitious and nonexistent inventory,
• manipulation of inventory counts during a facility audit,
• recording of sales but no recording of purchases, and/or
• fraudulent inventory capitalization,

to list a few. 2 All these elaborate schemes have the same goal: to improperly manipulate inventory values to support the creation of a fraudulent financial statement. Accountants have an ethical, moral, and legal duty to not commit accounting and financial statement fraud. Auditors have a duty to look for such inventory fraud.

Auditors follow the Statement on Auditing Standards (SAS) No. 99 and AU Section 316 Consideration of Fraud in a Financial Statement Audit when auditing a company’s books. Auditors are outside accountants hired to “obtain reasonable assurance about whether the financial statements are free of material misstatement, whether caused by error or fraud.” 3 Ultimately, an auditor will prepare an audit report based on the testing of the balances in a company’s books, and a review of the company’s accounting system. The auditor is to perform “procedures at locations on a surprise or unannounced basis, for example, observing inventory on unexpected dates or at unexpected locations or counting cash on a surprise basis.” 4 Such testing of a company’s inventory system is used to catch accounting fraud. It is the responsibility of the accountant to present accurate accounting records to the auditor, and for the auditor to create auditing procedures that reasonably ensure that the inventory balances are free of material misstatements in the accounting balances.

Additional Inventory Issues

Various other issues that affect inventory accounting include consignment sales, transportation and ownership issues, inventory estimation tools, and the effects of inflationary versus deflationary cycles on various methods.

Consignment

Consigned goods refer to merchandise inventory that belongs to a third party but which is displayed for sale by the company. These goods are not owned by the company and thus must not be included on the company’s balance sheet nor be used in the company’s inventory calculations. The company’s profit relating to consigned goods is normally limited to a percentage of the sales proceeds at the time of sale.

For example, assume that you sell your office and your current furniture doesn’t match your new building. One way to dispose of the furniture would be to have a consignment shop sell it. The shop would keep a percentage of the sales revenue and pay you the remaining balance. Assume in this example that the shop will keep one-third of the sales proceeds and pay you the remaining two-thirds balance. If the furniture sells for $15,000, you would receive $10,000 and the shop would keep the remaining $5,000 as its sales commission. A key point to remember is that until the inventory, in this case your office furniture, is sold, you still own it, and it is reported as an asset on your balance sheet and not an asset for the consignment shop. After the sale, the buyer is the owner, so the consignment shop is never the property’s owner.

Free on Board (FOB) Shipping and Destination

Transportation costs are commonly assigned to either the buyer or the seller based on the free on board (FOB) terms, as the terms relate to the seller. Transportation costs are part of the responsibilities of the owner of the product, so determining the owner at the shipping point identifies who should pay for the shipping costs. The seller’s responsibility and ownership of the goods ends at the point that is listed after the FOB designation. Thus, FOB shipping point means that the seller transfers title and responsibility to the buyer at the shipping point, so the buyer would owe the shipping costs. The purchased goods would be recorded on the buyer’s balance sheet at this point.

Similarly, FOB destination means the seller transfers title and responsibility to the buyer at the destination, so the seller would owe the shipping costs. Ownership of the product is the trigger that mandates that the asset be included on the company’s balance sheet. In summary, the goods belong to the seller until they transition to the location following the term FOB, making the seller responsible for everything about the goods to that point, including recording purchased goods on the balance sheet . If something happens to damage or destroy the goods before they reach the FOB location, the seller would be required to replace the product or reverse the sales transaction.

Lower-of-Cost-or-Market (LCM)

Reporting inventory values on the balance sheet using the accounting concept of conservatism (which discourages overstatement of net assets and net income) requires inventory to be calculated and adjusted to a value that is the lower of the cost calculated using the company’s chosen valuation method or the market value based on the market or replacement value of the inventory items. Thus, if traditional cost calculations produce inventory values that are overstated, the lower-of-cost-or-market (LCM) concept requires that the balance in the inventory account should be decreased to the more conservative replacement value rather than be overstated on the balance sheet.

Estimating Inventory Costs: Gross Profit Method and Retail Inventory Method

Sometimes companies have a need to estimate inventory values. These estimates could be needed for interim reports, when physical counts are not taken. The need could be result from a natural disaster that destroys part or all of the inventory or from an error that causes inventory counts to be compromised or omitted. Some specific industries (such as select retail businesses) also regularly use these estimation tools to determine cost of goods sold. Although the method is predictable and simple, it is also less accurate since it is based on estimates rather than actual cost figures.

The gross profit method is used to estimate inventory values by applying a standard gross profit percentage to the company’s sales totals when a physical count is not possible. The resulting gross profit can then be subtracted from sales, leaving an estimated cost of goods sold. Then the ending inventory can be calculated by subtracting cost of goods sold from the total goods available for sale. Likewise, the retail inventory method estimates the cost of goods sold, much like the gross profit method does, but uses the retail value of the portions of inventory rather than the cost figures used in the gross profit method.

Inflationary Versus Deflationary Cycles

As prices rise (inflationary times), FIFO ending inventory account balances grow larger even when inventory unit counts are constant, while the income statement reflects lower cost of goods sold than the current prices for those goods, which produces higher profits than if the goods were costed with current inventory prices. Conversely, when prices fall (deflationary times), FIFO ending inventory account balances decrease and the income statement reflects higher cost of goods sold and lower profits than if goods were costed at current inventory prices. The effect of inflationary and deflationary cycles on LIFO inventory valuation are the exact opposite of their effects on FIFO inventory valuation.

Link to Learning

Accounting Coach does a great job in explaining inventory issues (and so many other accounting topics too): Learn more about inventory and cost of goods sold on their website.

Think It Through

First-in, first-out (fifo).

Suppose you are the assistant controller for a retail establishment that is an independent bookseller. The company uses manual, periodic inventory updating, using physical counts at year end, and the FIFO method for inventory costing. How would you approach the subject of whether the company should consider switching to computerized perpetual inventory updating? Can you present a persuasive argument for the benefits of perpetual? Explain.

• 1 “Inventory Fraud: Knowledge Is Your First Line of Defense.” Weaver. Mar. 27, 2015. https://weaver.com/blog/inventory-fraud-knowledge-your-first-line-defense
• 2 Wells, Joseph T. “Ghost Goods: How to Spot Phantom Inventory.” Journal of Accountancy . June 1, 2001. https://www.journalofaccountancy.com/issues/2001/jun/ghostgoodshowtospotphantominventory.html
• 3 American Institute of Certified Public Accountants (AICPA). Consideration of Fraud in a Financial Statement Audit (AU Section 316). https://www.aicpa.org/Research/Standards/AuditAttest/DownloadableDocuments/AU-00316.pdf
• 4 American Institute of Certified Public Accountants (AICPA). Consideration of Fraud in a Financial Statement Audit (AU Section 316). https://www.aicpa.org/Research/Standards/AuditAttest/DownloadableDocuments/AU-00316.pdf

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Bond Valuation – Excel Template

Bond valuation is based on the time value of money principle. In fact, bond pricing is simply an application of discounted cash flow analysis—all you must do is solve a time value of money problem. The bond price identifies the present value of all future cash flows until maturity, discounted by the yield to maturity (YTM). You can use the template to determine the theoretical fair value of a bond.

This open-access Excel template is a useful tool for bankers, investment professionals, corporate finance practitioners, portfolio managers, and anyone preparing a corporate presentation.

Bond Valuation is among the topics included in the Fixed Income module of the CFA Level 1 Curriculum. Gain valuable insights into the subject with our Fixed Income Investments course.

You can also explore other related templates such as— Yield to Maturity , Current Yield of a Bond , and Coupon Rate of Bond .

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Module 8: Inventory Valuation Methods

Assignment: inventory valuation methods.

This assignment can be found in Google Docs: Financial Accounting Assignment: Inventory Valuation Methods

To make your own copy to edit:

• If you want a Google Doc : in the file menu of the open document, click “Make a copy.” This will give you your own Google Doc to work from.
• If you want a PDF or Word file : in the file menu of the open document, click “Download” and select the file type you would like to have (note: depending on the file type you select, the formatting could get jumbled).
• Assignment: Inventory Valuation Methods. Authored by : Cindy Moore. Provided by : Lumen Learning. License : CC BY: Attribution

Inventory Valuation: How to Measure and Manage Your Stock Value

• 20 Feb 2024

If your business deals with physical goods, then learning everything you can about inventory valuation is of critical importance. It can affect your cash flow and many other aspects of your business, even its overall financial health. In this article, we will guide you through it all, including what inventory evaluation is, why it is important, what the main methods are of inventory valuation, what the challenges and considerations are, and how to choose the valuation method best suited to your business. Lastly, we will delve into how inventory management software can make inventory valuation and management so much easier for you.

What is Inventory Valuation?

All goods that businesses stock, whether they are put up for sale or used within the production process, are known as inventory. At the end of an accounting period, a monetary value is assigned to the inventory that a business has in stock. This is called inventory valuation. This valuation will directly affect the balance sheet and income statement of the business. It will ascertain the cost of goods sold (COGS), which is the cost of all inventory sold during the accounting period. The inventory valuation will also ascertain the value of any remaining unsold inventory, which will show as an asset on the balance sheet, also known as closing inventory .

Why is Inventory Valuation Important?

Inventory valuation may seem like a straightforward topic, but it plays a significant role in every business. Firstly, its importance is held in the fact that the valuation of inventory is used to calculate the COGS. This is crucial because COGS is used to determine the gross profit, which is the key indicator of the efficiency and profitability of a business. Secondly, it is important to know the inventory valuation because it affects the presentation of current assets on the balance sheet. One needs to know the current assets in order to calculate the working capital, which is the measure of the liquidity and solvency of the business. Furthermore, it is necessary for calculating the financial ratios of a business. The inventory valuation helps you determine your inventory turnover ratio . This ratio demonstrates how efficient a business is in managing its inventory. Another financial ratio would be the debt-to-equity ratio, which conveys how much a business is relying on debt to fund its operations. This ratio is vital as it influences the perception held by potential lenders, investors, and stakeholders. Finally, whichever method of inventory valuation a business chooses will impact how much tax it is liable for. Keep on reading to familiarize yourself with the extent of this impact.

Inventory Valuation Methods

Let’s discuss the four main methods of inventory valuation. Keep in mind that each method has advantages and disadvantages, which differ depending on the characteristics and nature of each business and its respective inventory, so consider this when valuing inventory as this will also affect inventory valuation accounting.

First In, First Out (FIFO)

The FIFO method works on the assumption that the oldest inventory purchased or produced gets sold before the newest inventory. Quite literally, the first piece of inventory arriving, should be the first to be sold. This method reflects the actual flow of inventory in the majority of businesses, in particular businesses that deal with fast-moving or perishable goods. With the FIFO method, COGS is calculated using the cost of the old inventory, which is generally lower than the cost of the newer inventory. However, the inventory value is calculated on the cost of the newer inventory, which is most often higher than that of the old inventory. The lower COGS means the gross profit is higher, while the higher inventory value means the working capital is higher than it would be using other methods. Due to the lower COGS, the taxable income is higher, resulting in higher taxes. Financial ratios, like the inventory turnover ratio, also tend to be higher due to the value of the equity and inventory being higher.

Last In, First Out (LIFO)

The LIFO method gives a very different picture to FIFO as it works on the assumption that the newer inventory is sold before the older inventory. This results in a more market-related valuation of the inventory, but an inaccurate reflection of the actual flow of inventory in the average business. In complete contrast to the FIFO method, the LIFO method calculates COGS using the cost of the new inventory, which is generally higher than the cost of the old inventory, and the inventory value is calculated on the cost of the old inventory, which is most often lower than the new inventory.  Higher COGS results in a lower gross profit, and a lower inventory value means a lower working capital. Due to the higher COGS, the taxable income is lower, resulting in lower taxes. Financial ratios, such as the debt-to-equity ratio, are lower with LIFO because the value of the equity and inventory is lower.

Weighted Average Cost (WAC)

The WAC method takes the total cost of the inventory and divides it by the number of inventory units. This calculates the average cost of each unit regardless of when it was purchased or how much it cost at the time of purchase. This simple method works well when the inventory is made up of similar items. The COGS is based on the average cost of the old and new inventory, which results in a more moderate COGS and moderate gross profit. The inventory value is also based on the average which means a moderate value and a moderate working capital. This results in a moderate income, moderate taxes, and a moderate financial ratio due to the moderate value of the inventory and equity.

Specific Identification Method

The specific identification method is exactly what it says, specific. It assigns the actual cost of each individual inventory item to that specific item. This method works well on unique inventory items such as jewelry or artwork. With this method, the COGS is based on the actual cost of the inventory that was sold. This leaves room for manipulation as the business can pick and choose its highest or lowest costing units to suit whichever outcome it wants to achieve. This also leaves the gross profit open to manipulation. Depending on the desired outcome, the highest or lowest-costing units can be selected to manipulate the value of the inventory when calculating the actual cost of the inventory. This allows the business to manipulate the working capital too. This method results in extremely variable taxes since the taxable income is so easily manipulated by the cost of the units you choose. The cost of the units you choose also results in variable financial ratios, as the inventory turnover ratio and debt-to-equity ratio are affected by the value of the inventory. Remember, the closing inventory is equivalent to the opening inventory of the next fiscal period.

Challenges and Considerations in Inventory Valuation

Inventory valuation is not as simple as selecting a method and applying it. There are several common challenges that can impact inventory valuation. It is therefore necessary for us to identify these problems and pinpoint strategies to mitigate them moving forward. Inventory shrinkage is the first challenge. This is when there is a loss of inventory which results in reduced inventory values and profitability. Inventory shrinkage, or inventory write-down , can be attributed to incidents such as theft, spoilage, damage, or monitoring errors. The best strategy to minimize the influence of inventory shrinkage involves utilizing effective tracking methods, like inventory controlling , quality control, and improving security measures. The second challenge comes in the form of inventory obsolescence. This is when inventory loses its value due to innovations in technology or changes in customer preferences and market conditions. When inventory becomes obsolete, a business is left with outdated products that can only be sold at a reduced price. Thankfully, one can avoid this issue by regularly conducting market research and updating their product mix. The last challenge that arises concerns changes in inventory valuation methods. Method changes will result in different taxable incomes. Also, if a business switches methods from one period to another, the comparability and consistency of its financial statements are affected. As these are indicators of performance, it is important to disclose and justify any changes within the financial statement.

Aside from these challenges, one must also consider three accounting principles when selecting a valuation method. Firstly, the lower cost or market rule dictates that a business must value its inventory at either its cost or market value (aka, the current replacement cost), according to which one has the lower value. This is done for two reasons: to recognize inventory shrinkage in the income statement and to avoid overstating one’s inventory on the balance sheets. Secondly, the matching principle is used to ensure that the true profitability of a business is shown in the income statement. The principle states that expenses must match the revenue generated within the same period. To apply this principle, a business should select a valuation method that allows COGS to accurately reflect the revenue generated by inventory, as well as the current market conditions. Lastly, the consistency principle is applied to prevent frequent and arbitrary changes in inventory valuation methods. This principle states that accounting methods must be consistent over time so that financial statements are reliable and comparable.

Choosing the Appropriate Valuation Method

When selecting an inventory valuation method for your business there are several factors and objectives that must be considered, as they can help you to make your choice. With so much responsibility riding on the accuracy of inventory valuation, it is imperative that you select the most appropriate valuation method for your company’s wants, needs, and goals. The first step is to analyze the objectives of the business, which are the goals you put in place to help your business achieve its vision. Because different valuation methods have different impacts on the financial performance of a business, your business objectives can be used to guide your decision. For example, if your goal is to attract investors then you should select a method that results in higher equity and financial ratios, such as the FIFO method. In contrast, LIFO will lead to lower tax liability which is useful if your objective is to minimize the taxes incurred by your business.

The next step is to examine the tax rules and regulations put in place by the government wherever you are conducting business. This will inform you of what tax requirements you must comply with. For example, countries like the UK forbid the use of LIFO for tax purposes, meaning you will have to choose between FIFO and WAC. However, in countries like the USA, LIFO can be used for tax purposes but not for financial statements. Thus, you could utilize it for taxes, but you would have to reconcile any discrepancies that occur as a result of needing to use a different method in your financial statement. The last step is to consider the impact your decision will have on your inventory forecasting . Inventory forecasting is important for planning and managing inventory, as it is used to estimate the future demand and supply of inventory. Your choice of inventory valuation can change how accurate your forecasting is. If the prices are increasing then FIFO, which provides more realistic inventory values, will improve inventory forecasting accuracy. In contrast, using LIFO in an environment where inventory prices are unstable will distort the forecasting, because LIFO provides unrealistic inventory values. Now that you are aware of what to consider in order to make your decision, we can discuss how to manage your decision thereafter.

Using Software in Inventory Valuation Management

Once you have chosen your inventory valuation method, you will engage in the process of applying and maintaining it. This is called inventory valuation management. It includes adjusting inventory accounts, as well as tracking, recording, and reporting the movement of inventory and transactions. In our modern world, it should come as no surprise that the technology industry has created inventory management software, which can be used to aid a business with managing and controlling its inventory, allowing for a more accurate and data-driven inventory valuation system. There are three distinct features that this kind of software offers.

Inventory tracking is a feature that a business can use to monitor movements in its inventory. Examples of movements include sales, returns, transfers, and purchases. This feature can accurately record inventory quantities, statuses, and locations, thereby reducing potential errors and discrepancies. The inventory costing feature uses a business’ chosen valuation method to calculate and assign costs to its inventory. It saves the business a lot of time by calculating the COGS, gross profit, and inventory value without much need for human labor. The lack of human error makes this feature particularly useful for helping a business comply with accounting and tax standards. Another feature offered by this software would be inventory reporting. This allows a business to generate inventory reports, like the inventory turnover report, inventory aging report, and inventory valuation report. With these reports, a business can evaluate the inventory performance and analyze where they can make improvements. It is important to note, that while inventory management software is incredibly beneficial, it is not a substitute for the intuition and expertise of people. This is because it still requires human selection of valuation methods and verification of results. When choosing an inventory management software, you should also consider AI-driven software, capable of optimizing your inventory. Take a look at Intuendi’s inventory optimization software.

Request a Demo

In this article, you have been made aware of how the process of inventory valuation can affect your business, both financially and operationally. For this reason, it is crucial to make sound decisions when selecting a valuation method that considers your business objectives, tax requirements, and forecasting tools. We explained that it is a process that faces several challenges (such as shrinkage and obsolescence) and that one must strictly adhere to the three accounting principles that regulate it. You have also learned that it does not simply end by selecting a method, but requires continual monitoring and maintenance. We then explained the features of inventory valuation management software that can assist you with this maintenance. We hope that you have found this article to be informative and that you will be able to take your new insights and apply them to your own business in the future.

A young South African with a passion for writing, social media management, and content creation. I graduated with a Bachelor of Arts in Film and Television majoring in Producing and a Bachelor of Arts Honours Degree in Political Communication. You'll be able to find me in 3 places: behind a laptop, behind a camera, or behind a makeup brush - creating in my favourite ways.

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