Question

Question 3 7.0/8 points (graded) The market value of asset of Company XYZ is currently $15,000,000. The capital structure of XYZ has two elements: debt with face value $10,000,000, which matures in one year from now, and common equity, with 100,000 shares outstanding. Currently, the total market value of XYZ's debt is $8,000,000, and the market value of its equity is $7,000,000. (a) Complete the table below entering XYZ's equity and debt values (in millions) conditional on the value of its assets a year from now. Assets Total Equity Total Debt $5 mln 0 $ million 5 $ million $15 min 5 $ million ✓ 10 $ million ✓ $25 min 15 $ million ✓ 10 $ million ✓

Answer 1

3.a) As the equity holders get the residual value, and debt of $10 million matures 1 year from now

i) In case value of assets = $5 million, Debtholders get $5 million and Shareholders get remaining 0 million

So, Total Equity = $0 & Total Debt = $5 million

ii) In case value of assets = $15 million, Debtholders get $10 million and Shareholders get remaining $5 million

So, Total Equity = $5 million & Total Debt = $10 million

iii) In case value of assets = $25 million, Debtholders get $10 million and Shareholders get remaining $15 million

So, Total Equity = $15 million & Total Debt = $10 million

b)

value of stock price today = $7 million / 100000 = $70 per share

After one year, if asset value = $5 million , equity value = 0 and so Value of share =0

After one year, if asset value = $25 million , equity value = $15 million and so Value of share =$15 million/100000 = $150 per share

So, value of option in upside = max(150-50,0) = 100

value of option in downside = max(0-50,0) = 0

The current value of Bond = $8 million which will mature to $10 million in a year

So, riskfree rate (although the bond has some default risk)

= $10 million/$8 million -1 = 0.25 or 25%

u = 150/70 = 2.1428

d= 0/70 =0

So, risk neutral probability = (1+risk free rate - d)/(u-d)

=(1.25-0)/(2.1428-0) = 0.58333

So, value of call option today = (p*value of option in upside +(1-p) * value of option in downside)/1.25

c =(0.583333*100 + 0.41666*0)/1.25 = $46.67

From put- call parity

c + K/(1+riskfree rate) = p + S

where c and p are the values of call and put options , S is the spot price today and K is the strike price   

46.67+ 50/1.25 = p + 70

=> p = $16.667