Question

ABC company has the following expected cash flows for three scenarios that could occur:

              Recession     Expected      Expansion

              (prob. = .2)  (prob. = .5)        (prob. =.3)

EBIT            $10,000      $20,000      $30,000

MV Assets          ______       ______     ______

(a) Complete the table above if the company is 100% equity financed and the non-levered return on equity is expected to be 12%

(b) If the company pays tax at a 30% rate and it wants to recapitalize (debt for equity swap) to save on taxes, what is the most debt the company can add (at a 6% rate) so that it will never go bankrupt under the above scenarios? (Assume the company goes bankrupty if EBIT < Interest owed)

(c) Calculate the WACC for the unlevered case and for the result in part (b).

(d) What is the market value of the assets if the firm chooses the debt level in part (b)?

(e) If further analysis suggests that the following can be used to predict the cash flows of the company:   EBIT = $1500 x random number chosen from 1 to 20

What is the optimal deb/equity ratio if the company wants to limit the probability of bankruptcy to 5% or less?

Answer 1

	Recession	Expected (Most Likely)	Expansion
Probability	0.2	0.5	0.3
EBIT	$10,000	$20,000	$30,000

Answer to part (a)
Non-levered return on equity (ROE) is expected to be 12%
ROE = EBIT (1-taxes) / Assets,
Thus, Assets = EBIT (1-taxes) / ROE

Total Assets (book value) = $20,000 (1-30%) /12% = $116,666.67
Since, expected ROE is 12%, market value of asset (MV assets) in case of expected EBIT will be same as the book value of assets = $116,666.67

In the case of recession,
ROE = $10,000 (1-30%) / $116,666,67 = 6%
Thus, market value of assets will be half the book value (6% / 12%)
MV assets (recession) = $58,333.33

In case of expansion,
ROE = $30,000 (1-30%) / $116,666,67 = 18%
Thus, market value of assets will be half the book value (18% / 12%)
MV assets (recession) = $175,000

	Recession	Expected (Most Likely)	Expansion
Probability	0.2	0.5	0.3
EBIT	$10,000	$20,000	$30,000
MV Assets Market Value of Assets	$58,333.33	$116,666.67	$175,000.00

Answer part (b)
We need to calculate the maximum debt that the company can take in the above scenarios so that the company can never go bankrupt.
Interest Rate = 6%
Since, Interest Outgo <= EBIT, the maximum permissible debt EBIT/interest rate.

Using the above formula, we recalculate the above table

	Recession	Expected (Most Likely)	Expansion
Probability	0.2	0.5	0.3
EBIT	$10,000	$20,000	$30,000
MV Assets Market Value of Assets	$58,333.33	$116,666.67	$175,000.00
Maximum Debt	$166,666.67	$333,333.33	$500,000.00
Calculation Step	$10,000/6%	$20,000/6%	$30,000/6%

However, since we do not want the firm to go bankrupt under any circumstances, and especially since one cannot predict whether the next year will be as expected or a recession/expansion year, one should assume the worst and not take a loan greater than $166,666.67. This will ensure that even in a recession, the firm will be able to pay interest on its debt.


Answer (c) - Calculation of WACC
For the non-levered case, WACC is
ROE (recession) X Probability (recession) + ROE (expected) X Probability (expected) + ROE (expansion) X Probability (expansion) = 0.2 X 6% + 0.5 X 12% + 0.3 X 18% = 12.6%

Answer (d)
The debt level in part (b) is $166,666.67
Interest outgo = 6% * $166,666.67. = $10,000
Using probability theory, the expected EBIT of the firm is
EBIT (recession) X Probability (recession) + EBIT (expected) X Probability (expected) + EBIT (expansion) X Probability (expansion)

EBIT =0.2 * $10,000 + 0.5 * $20,000 + 0.3 * $30,000 = $21,000
Enterprise Value = MV of Assets + Debt = EBIT / ROE
EV = $21,000 /12% = $175,000

Thus, MV of assets = EV - Total Debt = $175,000 - $166,666.67 = $ 8333.33