Problem 21-4 APV Model with Constant Growth An unlevered firm has a value of $85

Question

Problem 21-4
APV Model with Constant Growth

An unlevered firm has a value of $850 million. An otherwise identical but levered firm has $40 million in debt at a 5% interest rate. Its cost of debt is 5% and its unlevered cost of equity is 10%. After Year 1, free cash flows and tax savings are expected to grow at a constant rate of 3%. Assuming the corporate tax rate is 30%, use the compressed adjusted present value model to determine the value of the levered firm. (Hint: The interest expense at Year 1 is based on the current level of debt.) Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Do not round intermediate calculations. Round your answer to two decimal places.

$   million

Explanation / Answer

Step 1: Computation of value of Free cash Flow

Value of Unlevered Firm=

where FCFF0 is the current after-tax operating cash flow to the firm,

ru is the unlevered cost of equity ,and

g is the expected growth rate.

850= FCFF(1+g)/ .10-.03

FCFF= $57.76m

Step 2: Computation of post tax interest rate

Kd= rate of debt(1-tax rate)

      = 5*.95  

= 4.75%
Step 3:

Value of levered Firm= [Value of unlevered firm+[( rate of debt)/rate of equity- growth)]]tax rate

                                    = 850+ [[4.57/ .10-.03)].30]

=$870m

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