Question

Weston Enterprises is an all-equity firm with two divisions. The soft drink division has an asset beta of 0.55, expects to generate free cash flow of $ 40 million this year, and anticipates a 3 % perpetual growth rate. The industrial chemicals division has an asset beta of 1.06, expects to generate free cash flow of $ 56 million this year, and anticipates a 2 % perpetual growth rate. Suppose the risk-free rate is 4 % and the market risk premium is 5 %. a. Estimate the value of each division. b. Estimate Weston's current equity beta c. Estimate Weston's current cost of capital. Is this cost of capital useful for valuing Weston's projects? How is Weston's equity beta likely to change over time? a. Estimate the value of each division.

Answer 1

(a)

Compute the required rate on soft drink, using the equation as shown below:

Required rate = Risk-free rate + (Beta*Market premium)

                       = 4% + (0.55*5%)

                       = 6.75%

Hence, the required rate on soft drinks is 6.75%.

Compute the value of soft drink division, using the equation as shown below:

Value of soft drink = Free cash flow/ (Required rate – Growth rate)

                               = $40 million/ (6.75% - 3%)

                               = $1,066.67 million

Hence, the value of a soft drinks is $1,066.67 million.

Compute the required rate on soft drink, using the equation as shown below:

Required rate = Risk-free rate + (Beta*Market premium)

                       = 4% + (1.06*5%)

                       = 9.30%

Hence, the required rate on soft drinks is 9.30%.

Compute the value of chemical division, using the equation as shown below:

Value of chemical = Free cash flow/ (Required rate – Growth rate)

                               = $56 million/ (9.30% - 2%)

                               = $767.12 million

Hence, the value of the chemical division is $767.12 million.

b.

Compute the weight of soft drink, using the equation as shown below:

Weight = Value of soft drink/ (Value of soft drink + Value of chemical division)

             = $1,066.67 million/ ($1,066.67 million + $767.12 million)

             = 0.58

Hence, the weight of the soft drinks is 0.58.    

Compute the weight of chemical division, using the equation as shown below:

Weight = 1 – Weight of soft drink

             = 1 – 0.58

           = 0.42

Hence, the weight of the chemical division is 0.42.

Compute the equity beta of the company, using the equation as shown below:

Equity beta = (Soft drink beta*Weight) + (Chemical division beta*Weight)

                   = (0.55*0.58) + (1.06*0.42)

                   = 0.319 + 0.4452

                   = 0.7642

Hence, the equity beta is 0.7642.

c.

Compute the current cost of capital, using the equation as shown below:

Cost of capital = Risk free rate + (Beta*Market premium)

                        = 4% + (0.7642*5%)

                        = 7.821%

Hence, the cost of capital is 7.821%.

This is not useful in evaluation because both the division has a different level of risk and the different cost of capital. Therefore using the average cost of capital will result in the selection of low risky projects and this will result in acceptance of high-risk projects.

The increase in the level of debt due to growth in the company, the beta of the company will change over time.