Text Book: Financial Management Theory and Practice 13e, Brigham Ehrhardt Proble

Question

Text Book: Financial Management Theory and Practice 13e, Brigham Ehrhardt

Problem: (26-8)
Schwarzentraub Industries expected free cash flow for the year is $500,000; in the future, free cash flow is expected to grow at t a rate of 9%. The company currently has no debt, and its cost of equity is 13%. Its tax rate is 40%. a. Find Vu. b. Find VL and rsL if Schwarzentraub uses $5 million in debt with a cost of 7%. c. Use the extension of the MM model that allows for growth. d. Based on Vu from part a, find VL and rsL using the MM model (with taxes) if Schwarzentraub uses $5million in 7% debt
d. Explain the difference between your answers to parts b and c.

Explanation / Answer

a) Vu = $500,000 / (Ru - g)           = $500,000 / (0.13 - 0.09)           = $12,500,000 b) Vl = $12.5 million + [(0.07 * 0.40 * $5,000,000) / (0.13 - 0.09)]          = $12.5 million + $3.5 million          = $16 million Since the value of Debt is $5,000,000     S = $16,000,000 - $5,000,000        = $11,000,000 Rl = Ru + (Ru - Rd) * (Debt / Equity)       = 0.13 + (0.13 - 0.07) * 5/11      = 0.157 or 15.7% c) Under M&M          Vl = Vu + T * D              = $12,500,000 + 0.40 * $5,000,000             = $12,500,000 + $2,000,000             = $14,500,000     S = $14,500,000 - $5,000,000        = $9,500,000 Rl = Ru + (Ru - Rd) * (1 - Tax rate) * (Debt / Equity)     = 0.13 + (0.13 - 0.07) * (1 - 0.40) * ($5,000,000 / $9,500,000)     = 0.149 or 14.9% d) Vl is greater under the extension that incorporates growth than under M&M because M&M assumes zero growth. A positive growth rate gives a larger value to the tax shield. In this case the value of tax shied under M&M is $2,000,000 and is $3,500,000 if growth is included. The cost of capital when growth is included is higher because the relative weight of equity is higher and the relative weight of debt is lower when the growth is ignored.

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