Question

Wolfrum Technology​ (WT) has no debt. Its assets will be worth ​$451 million one year from now if the economy is​ strong, but only ​$213 million in one year if the economy is weak. Both events are equally likely. The market value today of its assets is ​$258 million. a. What is the expected return of WT stock without​ leverage? b. Suppose the​ risk-free interest rate is 5 %. If WT borrows ​$104 million today at this rate and uses the proceeds to pay an immediate cash​ dividend, what will be the market value of its equity just after the dividend is​ paid, according to​ MM? c. What is the expected return of WT stock after the dividend is paid in part ​(b​)d

Answer 1

a.

Scenario	Net Asset	Probability	Weighted Net Asset
Economy is Strong	451	50%	225.5
Economy is weak	213	50%	106.5
Total			332

Expected Return = Change in net asset / net asset at start of the year * 100

= (332-258) / 258 * 100 = 28.68%

[Note : Since both the events are equally likely probability of both the events is considered 50% each (100%/2)]

b.

Assuming question is talking about start of the year.

Value of Net Asset = 258

Loan Taken = 104

Dividend paid = 104

Value of firm = 258 (258-104+104)

Value of Equity = 258-104 = 154 (Value of firm - value of debt)

c. Since the value of firm remains same, the profitability remains same and new return will be -

Interest on loan at 5% = 104*5% = 5.2 (net asset will be reduced by this amount)

Expected net asset = 332-5.2 = 326.8

Expected return = (326.8-258) / 154 * 100 = 44.68%

New equity is 154 and return will be calculated on that because interest on loan of 104 is already deducted from return.