ABC Corp is a levered company with a market value of debt of $$20$ million. The

company has had consistently stable unlevered free cash flow of $$20$ million each

year. The company faces a marginal tax rate of $35\%.$ The firm management is

considering to permanently increase its leverage to benefit from unexploited tax

shields. The proceeds of any new debt issuance will be used to repurchase stock. The

current number of outstanding shares is $5$ million. According to the management$$s

estimations, the present value of the direct default costs is $20\%$ of the firm$$s unlevered

value of assets. The probability of bankruptcy increases with leverage according to the

following schedule:

Debt $($million$)$ Default probability

$$200\%$

$$405\%$

$$6010\%$

$$8030\%$

$$10060\%$

All investors of the company are risk$-$neutral. The long$-$term treasury bill rate is $10\%,$

and the expected market risk premium is $8\%.$ The beta of the assets is currently $1\mathrm{.}5.$

a$)$ Estimate the optimal level of debt for the firm based on the Trade$-$off Theory.

Explain your calculations, and summarize the tax shields, default costs, and

market value of the firm for each debt level in a table.

$(10$ marks$)$

b$)$ At what price will the firm be able to repurchase the stock if the firm

implements the optimal debt level? Motivate assumptions used in your

calculations.

$(4$ marks$)$

c$)$ Show and compare the initial market value balance sheet and the market

value balance sheets at different stages of the leverage recapitalization

$($announcement$,$ debt issuance, stock repurchase$).$ Explain all required

calculations.

$(5$ marks$)$

d$)$ After estimating the optimal level of debt, management realises it has not

taken into account the fact that the company is fast growing and has many

investment opportunities. How would this change the decision of management

on optimal capital structure?

$(4$ marks$)$

e$)$ Assume the firm has implemented the leverage recapitalization based on the

optimal debt level determined in the question $($a$),$ and the company faces a

Page $5$ of $6$

positive NPV investment opportunity requiring investment of $$30$ million. The

management cannot find external financing for this project, and current

debtholders also refuse to fund it$.$ What should the equity holders$$ expected

payoff be to motivate them to fund this investment? What can be done if the

actual equity holders$$ expected payoff is lower than the one you have

calculated. Discuss one possible solution for this situation $($Hint: propose a

deal in which both equity holders and debtholders have a mutual interest to

support this investment$).$