Question

We run a delivery service, and we believe our firm has market risk equally between that of UPS and FedEx. We know the following about these 2 firms:______.

Stock Price per share # shares outstanding Market Value of Debt
UPS $65 0.7 billion $ 5 billion
FedEx $55 250 million $ 3 billion
We also have the following data on the securities of these firms:_______.
Beta E Beta D
UPS 0.8 0
FedEx 1.1 0.1
Assume that our firm has risk-free debt with market value $20 million and equity with market value $450 million. Assume that taxes are not relevant. Please estimate our firm’s equity beta

Answer 1

The answer is "0.85 "

Step-by-step explanation:

In order to locate a beta of the company, we must find the average beta of unlevered UPS and FedEx and find a levered beta of the company.

Price Outstanding shares(Billion) Market valu of equity(Billion) Market value of debt(billions) D/E Ratio

UPS 65 0.7 45.5 5 0.1099

FedEx 55 0.25 13.75 3 0.2182

`Unlevered \ beta= (levered \ beta)/((1+((1- tax rate)*((Debt)/(Equity)))))`

taxes desn't matter , given in the question so, assumed to be 0

`Unlevered \ beta \ for \ UPS= (0.8)/(1+(1-0)* (0.1099))`

`= (0.8)/(1+(1)* (0.1099))\\\\= (0.8)/(1+(0.1099))\\\\= (0.8)/(1.1099)\\\\=0.72`

`Unlevered \ beta \ for \ FedEx= (1.1)/(1+(1-0)* (0.2182))`

`= (1.1)/(1+(1)* (0.2182))\\\\= (1.1)/(1+(0.2182))\\\\= (1.1)/(1.2182)\\\\=0.90`

`Average \ Unlevered \ beta = (0.72+0.90)/(2)`

`= (1.62)/(2)\\\\=0.81`

`\text{levered beta of the delivery service firm }= unlevered \ beta *(1+(1-taxes) * ((debt)/(equity)))`

`= 0.81 * (1+(1-0)* ((20)/(450))\\\\= 0.81 * (1+(1)* (0.04)\\\\= 0.81 * (1+(0.04)\\\\= 0.81 * (1.04)\\\\=0.85`