Please answer the following finance questions. PLEASE SHOW AND EXPLAIN ALL WORK!
ID: 2622108 • Letter: P
Question
Please answer the following finance questions. PLEASE SHOW AND EXPLAIN ALL WORK!
1. Morse Corporation stock sells at a price of $77.50 a share and the riskless rate is 3.5%. Calculate the price of a 6-month call option on Morse stock with an exercise price of $80. The sigma of Morse is 0.45.
2. Sterling Company common stock has a market price of $179 per share and its sigma is 0.33. Find the value of a European put option, with an exercise price of $180 and expiring after 62 days, on the Sterling stock. The riskless rate is 4.2%
3. Stratton Company has $56 million in face value zero-coupon bonds due in 6.5 years, and its sigma is 0.52. The total market value of Stratton Company is $82 million and the riskless rate is 2.9%. The company has 1.02 million shares outstanding. Find its price per share.
4. Dartmouth Company has a total value of $55 million. Its debt is in the form of zero-coupon bonds, which will mature in 6 years. The face value of the bonds is $20 million. The riskless rate is 3.41% at present. The sigma of Dartmouth is 0.36. Find the debt/assets ratio of Dartmouth.
Explanation / Answer
1)
Black scholes model,
according to black scholes model
value of call option, = S*N(d1)-K*(e^-rt)*N(d2)
where, S = 77.5
K = strike price = $80
now, d1 and d2 can be calculated as follows
d1 = ln(S/K)+(r+(sigma^2)/2)*t]/[sigma*t^.5]
d1 = (ln(77.5/80)+(.035+(.45^2)/2)*.5)/(.45*.5^.5) = .114319
d2 = d1-sigma*t^.5 = .1143-.45*.5^.5 = -.2038
call price = 77.5*N(.1143)-80*e^(-.035*.5)*N(-.2038) = 77.5*.545-80*(e^(-.035*.5))*.41925 = $9.3
2).
Sterling Company common stock has a market price of $179 per share and its sigma is 0.33. Find the value of a European put option, with an exercise price of $180 and expiring after 62 days, on the Sterling stock. The riskless rate is 4.2%
here also we have to calculate d1 and d2
d1 = ln(S/K)+(r+(sigma^2)/2)*t]/[sigma*t^.5]
d1 = (ln(179/180)+(.042+(.33^2)/2)*(62/365))/(.33*(62/365)^.5) = .079497
d2 = d1-sigma*t^.5 = .079497-.33*(62/365)^.5 = -.056510
Price of Put = 180*e^(-.042*(62/365))*N(-d2)-179*N(-d1)
Price of Put = 180*e^(-.042*(62/365))*N(.056510)-179*N(-.079497)=180*e^(-.042*(62/365))*0.52253-179*.46832 = 9.558