Exactly eight years ago, just before the bankruptcy of the Lehman Brother and th
ID: 2733003 • Letter: E
Question
Exactly eight years ago, just before the bankruptcy of the Lehman Brother and the precipitation of the financial crisis. Sigma Inc. was a strong firm: market value of its assets was more than €100 million. At the moment, Sigma consolidated its debt and issued an 11-year zero-coupon bond with face value of €15 million (i.e. no other debt was outstanding after issue). Total market value of Sigma assets is now only €20 million. The risk free rate is 2% per year and the standard deviation of the assets value sigma is 25% per year. The shareholders of Sigma are faced with an intriguing investment opportunity: Project R has a NPV of €1 million, but if it were accepted, it would cause the standard deviation of total assets value (old asset plus Project R) to increase to 40% per year.
a. The current total market value of equity for Sigma is €6,73 million. What would the equity value be if the shareholders accept project R?
b. Should the shareholders accept Project R? Why?
c. How does your answer (b) fit with the NPV rule?
Explanation / Answer
a)
b) The value of the equity increased from €6.73 million to €8.10 million by accepting R, which shall increase the shareholder wealth therefore yes shareholders should accept Project R.
c) The Answer b fits correctly in line with the NPV rule,NPV rule also indicates that the shareholder wealth shall increase with the acceptance of project thus accept the project from shareholders perspective as NPV>0 similar conclusion as provided by the answer to part b.
Merton model(mkt value of equity before accepting R) current value of the company’s assets S0 20 standard deviation of the return on assets sigma 25.00% effective annual risk-free rate r 2% Exercise Price X 15 Time to Maturity(yrs) T 3 Dividend Yield q 0.00% d1 d1=[ln(So/X)+(r-q+.5*sigma^2)*T]/[sigma*sqrt(T)] 1.02 d2 d2=[ln(So/X)+(r-q-.5*sigma^2)*T]/[sigma*sqrt(T)] 0.59 N(d1) N(d1)=NORM.S.DIST(d1,TRUE) 0.85 N(d2) N(d2)=NORM.S.DIST(d2,TRUE) 0.72 call option value on Firm's Assets($ mn) c=S0*exp(-qT)*N(d1)-X*exp(-rT)*N(d2) $ 6.73 (=Value of Equity) Merton model(mkt value of equity after accepting R) current value of the company’s assets S0 20 standard deviation of the return on assets sigma 40.00% effective annual risk-free rate r 2% Exercise Price X 15 Time to Maturity(yrs) T 3 Dividend Yield q 0.00% d1 d1=[ln(So/X)+(r-q+.5*sigma^2)*T]/[sigma*sqrt(T)] 0.85 d2 d2=[ln(So/X)+(r-q-.5*sigma^2)*T]/[sigma*sqrt(T)] 0.16 N(d1) N(d1)=NORM.S.DIST(d1,TRUE) 0.80 N(d2) N(d2)=NORM.S.DIST(d2,TRUE) 0.56 call option value on Firm's Assets($ mn) c=S0*exp(-qT)*N(d1)-X*exp(-rT)*N(d2) $ 8.10 (=Value of Equity)Related Questions
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