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

Answer:

The answer is "0.85 "

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

$Unlevered \ beta= \frac{levered \ beta}{(1+((1- tax rate)\times(\frac{Debt}{Equity})))}$

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

   $Unlevered \ beta \ for \ UPS= \frac{0.8}{1+(1-0)\times (0.1099)}$

                                            $= \frac{0.8}{1+(1)\times (0.1099)}\\\\= \frac{0.8}{1+(0.1099)}\\\\= \frac{0.8}{1.1099}\\\\=0.72$

$Unlevered \ beta \ for \ FedEx= \frac{1.1}{1+(1-0)\times (0.2182)}$

                                            $= \frac{1.1}{1+(1)\times (0.2182)}\\\\= \frac{1.1}{1+(0.2182)}\\\\= \frac{1.1}{1.2182}\\\\=0.90$

$Average \ Unlevered \ beta = \frac{0.72+0.90}{2}$

                                       $= \frac{1.62}{2}\\\\=0.81$

$\text{levered beta of the delivery service firm }= unlevered \ beta \times(1+(1-taxes) \times (\frac{debt}{equity}))$

                                                              $= 0.81 \times (1+(1-0)\times (\frac{20}{450})\\\\= 0.81 \times (1+(1)\times (0.04)\\\\= 0.81 \times (1+(0.04)\\\\= 0.81 \times (1.04)\\\\=0.85$