Question

It is January 1st 2020, on the day before, December 31st 2019, Alamo Co. reported a net income
of 4,009,000 dollars. To this date the company is unlevered and its real EBITDA is constant.
The company acquired the year before (on January 1st 2019) a new plant for 36,000,000
dollars, that the fiscal law allowed to depreciate straight line either in 3 (Plan 1) or 6 years
(Plan 2). All other assets are fully depreciated. Today, the company announces a
recapitalization in which it will issue risky debt and retire equity for an amount of 65,000,000
dollars. The company then plans to keep a constant debt level. Before the announcement, the
unlevered equity return is 7.65%. Assume that the inflation rate is 2.5%, that the debt beta is
0, that the expected market return is 8.00%, that the risk free rate is 4.50% and that the tax
rate is 30%. Finally assume that the depreciation tax shield is as risky as the company’s debt.
a) What is the depreciation plan chosen by the firm? Why?
b) What is the return experienced by the shareholders immediately after the
recapitalization announcement (but before the recapitalization is carried out)?
c) What is the beta of levered equity?

Answer 1

a) The firm would choose the accelerated depreciation plan, i.e. Plan 1 with useful life of plant = 3 years.

This is because the discounted value of tax savings due to depreciation will be higher when higher amounts are depreciated sooner than later.

b) As the firm announces the plans for raising debt to retire equity, the return demanded by equity holders would increase as additional debt increases the financial risk of the firm. This is reflected in the increased value of β for the firm.

We will first compute the Equity Value of the firm, which is also equal to the Unlevered enterprise value of the firm before recapitalization.

Cost of Plant	36000000
Useful life	3
Depreciation	12000000
Tax rate	30%
Unlevered Cost of Capital (ρ)	7.65%
Inflation rate	2.50%

NOTE: Interest expense is zero as we are first computing the unlevered enterprise value of the firm.

	0	1	2	3
EBITDA	17727143	18170321	18624579	19090194
(Dep)	12000000	12000000	12000000	0
EBIT	5727143	6170321	6624579	19090194
(Interest)	0	0	0	0
PBT	5727143	6170321	6624579	19090194
(Tax)	1718143	1851096	1987374	5727058
Net Income	4009000	4319225	4637206	13363136
Cash flow	16009000	16319225	16637206	13363136
Terminal Value				265965323
Equity Value	253425936

Hence, the equity value of the firm is $253,425,936.

As the company raises debt to the tune of $65,000,000 to retire the same proportion of equity, the new value of equity and debt in the firm are:

Equity Value = $253,425,936 - $65,000,000 = $188,425,936

Debt Value = $65,000,000

Debt/Equity ratio = 0.345

CAPM: Ke = Rf + βl*(Rm - Rf) = 8.41%

(c) Unlevered cost of capital (ρ) = Rf + βul*(Rm-Rf)

Substituting the value of other parameters, βul = 0.90.

βl = 0.9*[1+(1-30%)*(0.345)] = 1.12