16-1.

Gladstone Corporation is about to launch a new product. Depending on the success of the new product, Gladstone may have one of four values next year: $150 million, $135 million, $95 million, and $80 million. These outcomes are all equally likely, and this risk is diversifiable. Gladstone will not make any payouts to investors during the year. Suppose the risk-free interest rate is 5% and assume perfect capital markets.

a.

What is the initial value of Gladstone’s equity without leverage?

Now suppose Gladstone has zero-coupon debt with a $100 million face value due next year. b.

What is the initial value of Gladstone’s debt?

c.

What is the yield-to-maturity of the debt? What is its expected return?

d.

What is the initial value of Gladstone’s equity? What is Gladstone’s total value with leverage?

a.

0.25 ×

150 + 135 + 95 + 80

=

$109.52 million

1.05

b.

0.25 ×

100 + 100 + 95 + 80

=

$89.28 million

1.05

c.

YTM =

100

– 1= 12%

89.29

expected return = 5%

d.

16-8.

equity = 0.25 ×

50 + 35 + 0 + 0

= total value = 89.28 +20.24 = $109.52 million

$20.24 million

1.05

As in Problem 1, Gladstone Corporation is about to launch a new product. Depending on the success of the new product, Gladstone may have one of four values next year: $150 million, $135 million, $95 million, and $80 million. These outcomes are all equally likely, and this risk is diversifiable. Suppose the risk-free interest rate is 5% and that, in the event of default, 25% of the value of Gladstone’s assets will be lost to bankruptcy costs. (Ignore all other market imperfections, such as taxes.)

a.

What is the initial value of Gladstone’s equity without leverage?

Now suppose Gladstone has zero-coupon debt with a $100 million face value due next year. b.

What is the initial value of Gladstone’s debt?

c.

What is the yield-to-maturity of the debt? What is its expected return?

d.

What is the initial value of Gladstone’s equity? What is Gladstone’s total value with leverage?

Suppose Gladstone has 10 million shares outstanding and no debt at the start of the year. e.

If Gladstone does not issue debt, what is its share price?

f.

If Gladstone issues debt of $100 million due next year and uses the proceeds to repurchase shares, what will its share price be? Why does your answer differ from that in part (e)?

a.

0.25 ×

150 + 135 + 95 + 80

=

$109.52 million

1.05

©2011 Pearson Education, Inc. Publishing as Prentice Hall

Berk/DeMarzo • Corporate Finance, Second Edition

203

100 + 100 + 95 × 0.75 + 80 × 0.75

=

$78.87 million

1.05

b.

0.25 ×

c.

YTM

=

100

= 26.79%

−1

78.87

expected return = 5%

d.

50 + 35 + 0 + 0

equity =

0.25 ×

= illion total value

$20.24 m

1.05

150 + 135 + 95 × 0.75 + 80 × 0.75

=

=

0.25 ×

$99.11 million

1.05

(or 78.87 + 20.24 = $99.11 million)

e.

109.52

= $10.95 / share

10

f.

99.11

= $9.91 / share Bankruptcy cost lowers share price.

10

Note that Gladstone will raise $78.87 million from the debt, and repurchase 78.87

= 7.96 million shares . Its equity will be worth $20.24 million, for a share price of 9.91

20.24

= $9.91 after the transaction is completed.

10 − 7.96

16-9.

Kohwe Corporation plans to issue equity to raise $50 million to finance a new investment. After making the investment, Kohwe expects to earn free cash flows of $10 million each year. Kohwe currently has 5 million shares outstanding, and it has no other assets or opportunities. Suppose the appropriate discount rate for Kohwe’s future free cash flows is 8%, and the only capital market imperfections are corporate taxes and financial distress costs. a.

What is the NPV of Kohwe’s investment?

b.

What is Kohwe’s share price today?

Suppose Kohwe borrows the $50 million instead. The firm will pay interest only on this loan each year, and it will maintain an outstanding balance of $50...