Investing in Zero-coupon Bonds
Charles is considering zero-coupon bonds issued by Nationwide Company. These bonds were issued on January 1, 2011 with a maturity of 5 years and mature on December 31, 2015. The face value of each bond is $1000. He plans to buy these bonds on January 1, 2012 and sell on December 31, 2014. His friend, who is a finance professor, explains to him that the bond price on December 31, 2014 can be calculated by using the forward rate calculated from the zero-coupon yield curve seen on January 1, 2012.
The zero coupon yield curve on January 1, 2012 is shown below: Maturity Date Yield
December 31, 2012 7.2%
December 31, 2013 7.4%
December 31, 2014 7.6%
December 31, 2015 8.0%
(a)Calculate the forward rate for one-year investment starting on January 1, 2015. (4marks)
(b) Calculate the bond price on January 1, 2012. (4 marks)
(c) Calculate the bond price on December 31, 2014. (4 marks)
(d) Calculate the expected annual return on the bond investment. (4 marks)
You are interested in buying the shares of Goldproducer Inc. You would buy these shares only if the company undertakes the new mining operations. If the company does not undertake the operations, you would not buy the shares. This is equivalent to buying a call option on the shares. The shares are currently selling at $50. If mining operations are undertaken, the share price will increase by 8% and if it is not undertaken, share price will drop by 5% in 30 days. The exercise price of the option is $52. Assume 360 days in a year.
Calculate the price of call option if the risk-free rate is 4%.