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## Book Debt-to-Equity Ratios

*Firm 1: Tesco.*

*Firm 2: Sainsbury’s.*

## Asset Beta of Tesco

## Equity Beta of Sainsbury

β_{A} = 0.43 Same as that of Tesco.

β_{D} = 0

V/E = 3.28

β_{E} = (0.43 – 0 ) x 3.28 = 1.41

## A Word on Assumptions

The asset beta of Tesco has been determined by time-series of using stock returns in 2006. this beta is assumed to inlcide the effects of leverage, hence this is the asset-beta.

Both tesco and Sainsbury are in food and drug retailing business. Although they are industry peers, they have significantly different debt-to-equity ratios. High D/E ratio definitely alters the risk profile of a company and hence it does increases the overall riskiness of the firm. We see above that D/E ratio of Tesco is much lower (1.4) compared to that of Sainsbury (2.28). Hence assuming here that both firms would have same asset-beta for they are in same industry does not justify. This assumption is not realistic although supported by theory.

At the same time, assuming that debt betas are zero also bear little factual ground. Debt is never risk free when a firm of this scale goes into such high debt ratio.

## Sainsbury’s Beta using Time-series of Stock-returns

βA = 0.64

βE = (0.64) x 3.28 = 2.1

## Explaining the Difference

Now, based on its stock returns, Sainsbury’s equity beta comes out to be 2.1, much higher than 1.41 that was estimated using Tesco’s asset-beta. This estimate seems more realistic, considering the high debt ratio of Sainsbury.

This difference also again questions the assumtion that asset beta of botht the firms is equal. Earlier the beta of 1.41 for Sainbury was estimated on the basis of asset beta of Tesco. Now the beta of 2.1 has been determined by the time-series of stock returns of Sainsbury itself. The difference is significant, that signifies the fact that covariance of Sainbury stock with market is greater. In other words, Sainsbury’s market risk is greater than that of Tesco. This fact is both verified by the higher debt ratio of Sainsbury and also more variance of its stock returns. This is imperative also to note that if debt betas of firms are not considered to be zero, this difference might even become larger. As disscussed above, assuming debt betas to be zero is far from realistic.

## Bibliography

Jonathan B. Berk, Peter M. DeMarzo. Corporate Finance. Pearson Addison Wesley, 2006.

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