Several major companies (like Disney and AT&T) have issued "Century Bonds." These bonds pay regular semi-annual coupons, but do not mature until 100 years after they are issued. Some critics have stated that there is huge risk that you won't get the principal (face value) repaid because you just can't predict what will happen to the company in 100 years. For this question assume that the company has just issued a $1000 face value, 8% coupon bond with semi-annual payments.

a) If currently the yield to maturity for these bonds is 8%, what is the current price of the bond?

b) What is the present value of the face value alone? What proportion of the bond's price does the principal payment make up? (Hint: calculate the PV of the $1,000 face value to be paid in 100 years; divide it by the price you calculated in part a)

c) What is the present value of the first 40 years of coupon payments? What proportion of the bond's price does the first 40 years coupon payments make up?

d) Suppose 40 years after the bonds issuance, by which time, due to the monetary policy of the Fed, the yield to maturity of the same bond will be 20% at that time. How much will the bond be worth at that time?