It is April, Farmers, Inc. will issue $10 million in 5-year bonds at par in August. Coupon payments are made every six months and mature value is $1,000 per bond. Current interest rate is 6% for the 5-year issue. But given the recent increases in
Federal Reserve rates, IFI is worried interest rate will increase by 0.50% by August. Currently, August T-bond (semi-annual coupon rate is 5%) futures are 108'18.
(a) At an interest rate of 6.50%, how much will the $10 million worth of 5-year 6% semi-annual coupon bonds be worth?
(b) If interest rate will be 0.50% higher in August and FI did not hedge against the interest rate risk, how much more money they will pay in forms of coupon payments and principal payments over the lifespan of the bonds (not considering time value of money), assuming they will raise $10 million in bonds?
(c) If FI decides to hedge against the interest rate risk using T-bond futures, how many future contracts they need to sell, in order to hedge the entire $10 million?
(d) What is the current discount rate for the T-bonds?
(e) What is the price of the T-bond in August if interest rate (discount rate) is 0.50% higher?
(f) In August, how much profit will FI make on the future contracts?
(g) How much money would FI have in August if they did not issue more bonds as planned and they hedged against the interest rate risk?