3. A bond ABC is issued today at price $10000 with maturity 5 years. Its face value is $13000. (a) (1 point) Is this bond a discount bond or premium bond? Explain. (b) If this bond pays no coupon, i. (2 points) What is the YTM of this bond? ii. (1 point) The YTM is higher than the risk-free T-Bill at 1%, but not all investors would choose this bond over the T-Bill. Explain briefly. (c) Now this bond pays coupon, i. (2 points) With the same face value, this bond now pays annual coupon at coupon rate 5%. Therefore, the bond price should have changed. Should the change be an increase or decrease? Explain verbally without any mathematics. ii. (3 points) Find the new bond price, if the YTM does not change from part b(i). iii. (2 points) This part should be done using MS Excel. If the bond price is fixed at $10000, the YTM cannot be the same as part b(i). Fill in the new YTM of this bond. (d) Now this bond pays special coupons, i. (3 points) With the same face value, this bond now pays semi-annual coupon at coupon rate 8%, for the first two years (i.e. there are a total of 4 payments). What is the new bond price in this case? Given that the YTM does not change from part b(i). ii. (4 points) Find the duration of this special bond. 3c (1) Present Value Coupon Rate Face Value YTM Number of years = the cell that you can fill in = the