S07Assg4soln

S07Assg4soln - FIN 2200 CORPORATION FINANCE Sum 2007...

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FIN 2200 – CORPORATION FINANCE Sum 2007 Instructors: A. Dua Assignment #4 key 1. Spot rates of interest for zero-coupon Government of Canada bonds are observed for different terms to maturity as follows: Term to maturity Rate (r i ) 1 year from today 5.75% 2 years from today 6.25% 3 years from today 6.35% 4 years from today 6.25% 5 years from today 6.40% a) What is the forward rate of interest from year 2 to year 3, i.e., what is f 3 ? % 550282 . 6 1 ) 0625 . 1 ( ) 0635 . 1 ( 1 ) r 1 ( ) r 1 ( f 2 3 2 2 3 3 3 = - = - + + = b) What is the forward rate of interest from year 3 to year 4, i.e., what is f 4 ? % 950564 . 5 1 ) 0635 . 1 ( ) 0625 . 1 ( 1 ) r 1 ( ) r 1 ( f 3 4 3 3 4 4 4 = - = - + + = c) If you believe in the pure expectations theory, what does your answer to (a) imply about E[ 2 r 3 ]? If you believe in the augmented expectations theory, what does your answer to (a) imply about E[ 2 r 3 ]? pure expectations: E[ 2 r 3 ] = f 3 = 6.550282%; i.e., same 1 year rate 2 years from now. augmented expectations: E[ 2 r 3 ] < f 3 or < 6.550282%; i.e., lower 1 year rate 2 years from now. d) If you believe in the pure expectations theory, what does your answer to (b) imply about E[ 3 r 4 ]? If you believe in the augmented expectations theory, what does your answer to (b) imply about E[ 3 r 4 ]? pure expectations: E[ 3 r 4 ] = f 4 = 5.950564%; i.e., same 1 year rate 3 years from now. augmented expectations: E[ 3 r 4 ] < f 4 or < 5.25352388%; i.e., lower 1 year rate 3 years from now. e) Suppose a zero-coupon bond has a face value of $1,000 and matures 5 years from today. i) What is its price today? 32 . 733 $ ) 064 . 1 ( 000 , 1 ) r 1 ( FV PV price 5 T flows cash future = = + = =
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FIN 2200 – CORPORATION FINANCE Sum 2007 Instructors: A. Dua Assignment #4 key ii) If you believe in the pure expectations theory, then what do you expect its price to be four years from today? 56 . 934 $ 0700212064 . 1 000 , 1 ] price [ E % 00212064 . 7 ) 0625 . 1 ) 064 . 1 ( ) r 1 ( ) r 1 ( f f rate at year 1 discounted $1,000 equal should price 4 5 4 4 5 5 5 5 = = = = + + = = f) Suppose a bond has a 6% annual coupon, a face value of $1,000 and matures in 2
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S07Assg4soln - FIN 2200 CORPORATION FINANCE Sum 2007...

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