Consider a situation on October 16, 2007 in which a company lost a lawsuit and had to pay $100 million within nine months. However, they decided to sell one piece of equipment because they did not have enough money to pay for it now. The facility could cost up to $150 million. The company cannot afford to pay at the moment, so it will take much less to pay for the lawsuit. In response, the buyer offered to purchase the equipment at a significant discount and pay in six months. The company's CFO will determine that the deal will work if they sign a futures contract or a forward contract.

(a) If an entity decides to enter into a future contract using only the information available on 16 October 2007, what is the minimum that the entity should accept?

(b) If an entity decides to enter into a forward contract using only the information available on 16 October 2007, what is the minimum quantity that the entity should accept?

Consider the data in Table 3, where pfut(t,T) is the price of a 90-day Eurodollar futures contract expiring on April 14, 2008; f(t,T1, T2) is the time t forward rate for 90-day LIBOR at April 14, 2008; Z(t,T) is the LIBOR discount from t to April 14, 2008; and Z(t, t + dt) is the overnight LIBOR discount (where dt =1 day). Date 16-Oct-07 pfut (t.1) f(t, Ti,T2) 95.6400 4.6877% Zt, T1) Z(t,t + dt) 0.9908 0.9998 17-Oct-07 95.7650 4.6240% 0.9910 0.9998 18-Oct-07 95.8200 0.9912 0.9998 4.5191% 4.3975% 19-Oct-07 95.9350 Table 3 Futures and Forward Rates Z(t, T) Z(t,t + dt) Date pfut, T) ft,T1, T2) 0.9763 0.9998 15-Jan-08 96.8400 3.4128% 0.9766 0.9998 16-Jan-08 96.8200 3.3952% 0.9768 0.9998 17-Jan-08 96.8750 3.4557% 0.9773 0.9998 18-Jan-08 96.9650 3.3795% 0.9780 0.9998 22-Jan-08 97.4000 3.0633% 0.9781 0.9998 23-Jan-08 97.4950 2.7888% 0.9783 0.9998 24-Jan-08 97.2850 2.8347% 0.9787 0.9998 25-Jan-08 97.3150 3.0457% 0.9789 0.9998 28-Jan-08 97.3750 2.8894% 0.9914 0.9998 22-Oct-07 95.9200 0.9922 0.9998 4.2910% 4.3708% 23-Oct-07 0.9931 0.9999 95.9200 96.0250 24-Oct-07 4.2684% 0.9934 0.9999 25-Oct-07 96.0250 4.1984% 0.9933 0.9999 26-Oct-07 95.9850 4.2208% 0.9937 0.9999 29-Oct-07 95.9500 4.2337% 0.9793 0.9998 29-Jan-08 97.3550 2.8914% 0.9938 0.9999 30-Oct-07 95.9300 4.3014% 0.9795 0.9998 30-Jan-08 97.4350 2.9048% 0.9939 0.9999 31-Oct-07 95.8000 4.2978% 0.9795 0.9998 97.4900 2.7524% 0.9941 0.9999 31-Jan-08 1-Feb-08 1-Nov-07 95.9200 4.4467% 0.9795 0.9998 97.4200 2.7229% 0.9999 0.9942 0.9944 2-Nov-07 96.0450 4.2823% 0.9998 4-Feb-08 97.3950 2.8175% 0.9999 0.9798 0.9801 95.9750 4.2683% 0.9998 5-Feb-08 97.4900 2.8289% 0.9944 0.9999 5-Nov-07 6-Nov-07 95.9550 4.3336% 0.9801 0.9998 6-Feb-08 97.5200 2.6975% 0.9946 0.9999 7-Nov-07 96.0050 4.2998% 0.9802 0.9998 7-Feb-08 97.5150 2.6797% 0.9947 0.9999 0.9999 8-Nov-07 96.1450 4.2525% 0.9805 0.9998 8-Feb-08 97.5400 2.7012% 0.9948 96.1800 4.1621% 0.9807 0.9998 11-Feb-08 2.6727% 0.9950 0.9999 97.5450 97.5400 96.1800 4.1147% 0.9812 0.9998 12-Feb-08 2.6667% 0.9951 0.9999 9-Nov-07 12-Nov-07 13-Nov-07 14-Nov-07 96.0500 4.1061% 0.9813 0.9998 13-Feb-08 97.5300 2.6624% 0.9952 0.9999 0.9999 96.0400 4.2176% 0.9813 0.9998 14-Feb-08 97.5150 2.6825% 0.9953 15-Nov-07 96.1950 4.1916% 0.9814 0.9998 97.5100 2.6946% 0.9954 0.9999 16-Nov-07 96.1950 4.1167% 0.9814 0.9998 15-Feb-08 19-Feb-08 20-Feb-08 97.4400 2.7201% 0.9957 0.9999 19-Nov-07 96.0850 4.1807% 0.9816 0.9998 97.4050 2.7613% 0.9958 0.9999 20-Nov-07 96.0800 4.1859% 0.9816 0.9998 21-Feb-08 97.4500 2.8112% 0.9958 0.9999 21-Nov-07 96.2000 4.1664% 0.9998 22-Feb-08 97.4000 2.7526% 0.9959 0.9999 0.9818 0.9820 23-Nov-07 96.2000 4.1445% 0.9998 25-Feb-08 97.3700 2.7999% 0.9961 0.9999 26-Nov-07 96.3450 4.2163% 0.9823 0.9998 26-Feb-08 97.3950 2.8041% 0.9962 0.9999 27-Nov-07 96.2200 4.1268% 0.9824 0.9998 27-Feb-08 2.7692% 0.9963 0.9999 97.4400 97.5000 28-Nov-07 96.1400 4.2386% 0.9824 0.9998 28-Feb-08 2.7251% 0.9964 0.9999 29-NOV-07 96.2350 4.2269% 0.9825 0.9998 97.6300 2.7005% 29-Feb-08 3-Mar-08 0.9966 0.9968 0.9999 0.9999 30-Nov-07 96.2500 4.2295% 0.9826 0.9998 97.6050 2.6394% 3-Dec-07 96.2200 4.1883% 0.9830 0.9998 4-Mar-08 97.5900 2.6463% 0.9969 0.9999 4-Dec-07 96.2150 4.2106% 0.9831 0.9998 5-Mar-08 97.5500 2.6499% 0.9970 0.9999 5-Dec-07 96.2150 4.2254% 0.9832 0.9998 6-Mar-08 97.5850 2.6599% 0.9971 0.9999 6-Dec-07 96.1250 4.2285% 0.9834 0.9998 7-Mar-08 97.7300 2.5730% 0.9972 0.9999 0.9999 7-Dec-07 95.9900 4.2979% 0.9835 0.9998 10-Mar-08 97.7350 2.5766% 0.9975 10-Dec-07 95.9750 4.4052% 0.9838 0.9998 11-Mar-08 2.5463% 0.9976 0.9999 97.6500 97.6950 11-Dec-07 95.9550 4.3895% 0.9839 0.9998 12-Mar-08 2.5598% 0.9977 0.9999 12-Dec-07 96.0600 4.3833% 0.9841 0.9998 13-Mar-08 2.4937% 0.9978 0.9999 97.7400 97.8850 13-Dec-07 95.9850 4.2507% 0.9845 0.9998 14-Mar-08 2.4650% 0.9979 0.9999 14-Dec-07 95.8900 4.3378% 0.9998 17-Mar-08 98.0200 2.2305% 0.9999 0.9846 0.9850 0.9983 0.9984 17-Dec-07 95.9500 4.3672% 0.9998 18-Mar-08 97.8000 2.2285% 0.9999 18-Dec-07 96.0350 4.3408% 0.9852 0.9998 97.8100 2.3206% 0.9984 0.9999 19-Mar-08 20-Mar-08 19-Dec-07 96.0950 4.2711% 0.9854 0.9998 97.7775 0.9985 0.9999 2.3322% 2.4102% 20-Dec-07 96.1200 4.2180% 0.9856 0.9998 25-Mar-08 97.6850 0.9988 0.9999 21-Dec-07 96.0750 4.2125% 0.9858 0.9998 26-Mar-08 97.6750 0.9988 2.4171% 2.4216% 0.9999 0.9999 24-Dec-07 96.0550 4.2241% 0.9862 0.9998 27-Mar-08 97.6775 0.9988 27-Dec-07 96.0550 4.2554% 0.9866 0.9998 28-Mar-08 97.6750 2.4344% 0.9989 0.9999 28-Dec-07 96.1350 4.2421% 0.9870 0.9998 31-Mar-08 97.6900 2.4204% 0.9991 0.9999 31-Dec-07 96.1850 4.1691% 0.9873 0.9998 97.6300 2.4133% 0.9991 2-Jan-08 96.3100 4.1392% 0.9876 0.9998 97.5700 2.4437% 0.9992 0.9999 0.9999 0.9999 3-Jan-08 96.3350 3.9869% 0.9879 0.9998 97.5575 2.4804% 0.9993 4-Jan-08 96.4450 4.0055% 0.9880 0.9998 97.6100 2.4852% 0.9993 0.9999 7-Jan-08 96.4700 3.8896% 0.9886 0.9998 97.5650 2.4620% 0.9995 0.9999 1-Apr-08 2-Apr-08 3-Apr-08 4-Apr-08 7-Apr-08 8-Apr-08 9-Apr-08 10-Apr-08 11-Apr-08 14-Apr-08 8-Jan-08 96.4800 3.8683% 0.9888 0.9998 97.5050 2.4566% 0.9996 0.9999 9-Jan-08 96.5800 3.8023% 0.9891 0.9998 97.5300 2.4582% 0.9996 0.9999 10-Jan-08 96.6500 3.7389% 0.9894 0.9998 97.5300 2.4474% 0.9997 0.9999 11-Jan-08 96.8300 3.6358% 0.9898 0.9998 97.5350 2.4474% 0.9998 0.9999 14-Jan-08 96.8800 3.4026% 0.9906 0.9998 97.5412 2.4588% 1.0000 0.9999 Consider the data in Table 3, where pfut(t,T) is the price of a 90-day Eurodollar futures contract expiring on April 14, 2008; f(t,T1, T2) is the time t forward rate for 90-day LIBOR at April 14, 2008; Z(t,T) is the LIBOR discount from t to April 14, 2008; and Z(t, t + dt) is the overnight LIBOR discount (where dt =1 day). Date 16-Oct-07 pfut (t.1) f(t, Ti,T2) 95.6400 4.6877% Zt, T1) Z(t,t + dt) 0.9908 0.9998 17-Oct-07 95.7650 4.6240% 0.9910 0.9998 18-Oct-07 95.8200 0.9912 0.9998 4.5191% 4.3975% 19-Oct-07 95.9350 Table 3 Futures and Forward Rates Z(t, T) Z(t,t + dt) Date pfut, T) ft,T1, T2) 0.9763 0.9998 15-Jan-08 96.8400 3.4128% 0.9766 0.9998 16-Jan-08 96.8200 3.3952% 0.9768 0.9998 17-Jan-08 96.8750 3.4557% 0.9773 0.9998 18-Jan-08 96.9650 3.3795% 0.9780 0.9998 22-Jan-08 97.4000 3.0633% 0.9781 0.9998 23-Jan-08 97.4950 2.7888% 0.9783 0.9998 24-Jan-08 97.2850 2.8347% 0.9787 0.9998 25-Jan-08 97.3150 3.0457% 0.9789 0.9998 28-Jan-08 97.3750 2.8894% 0.9914 0.9998 22-Oct-07 95.9200 0.9922 0.9998 4.2910% 4.3708% 23-Oct-07 0.9931 0.9999 95.9200 96.0250 24-Oct-07 4.2684% 0.9934 0.9999 25-Oct-07 96.0250 4.1984% 0.9933 0.9999 26-Oct-07 95.9850 4.2208% 0.9937 0.9999 29-Oct-07 95.9500 4.2337% 0.9793 0.9998 29-Jan-08 97.3550 2.8914% 0.9938 0.9999 30-Oct-07 95.9300 4.3014% 0.9795 0.9998 30-Jan-08 97.4350 2.9048% 0.9939 0.9999 31-Oct-07 95.8000 4.2978% 0.9795 0.9998 97.4900 2.7524% 0.9941 0.9999 31-Jan-08 1-Feb-08 1-Nov-07 95.9200 4.4467% 0.9795 0.9998 97.4200 2.7229% 0.9999 0.9942 0.9944 2-Nov-07 96.0450 4.2823% 0.9998 4-Feb-08 97.3950 2.8175% 0.9999 0.9798 0.9801 95.9750 4.2683% 0.9998 5-Feb-08 97.4900 2.8289% 0.9944 0.9999 5-Nov-07 6-Nov-07 95.9550 4.3336% 0.9801 0.9998 6-Feb-08 97.5200 2.6975% 0.9946 0.9999 7-Nov-07 96.0050 4.2998% 0.9802 0.9998 7-Feb-08 97.5150 2.6797% 0.9947 0.9999 0.9999 8-Nov-07 96.1450 4.2525% 0.9805 0.9998 8-Feb-08 97.5400 2.7012% 0.9948 96.1800 4.1621% 0.9807 0.9998 11-Feb-08 2.6727% 0.9950 0.9999 97.5450 97.5400 96.1800 4.1147% 0.9812 0.9998 12-Feb-08 2.6667% 0.9951 0.9999 9-Nov-07 12-Nov-07 13-Nov-07 14-Nov-07 96.0500 4.1061% 0.9813 0.9998 13-Feb-08 97.5300 2.6624% 0.9952 0.9999 0.9999 96.0400 4.2176% 0.9813 0.9998 14-Feb-08 97.5150 2.6825% 0.9953 15-Nov-07 96.1950 4.1916% 0.9814 0.9998 97.5100 2.6946% 0.9954 0.9999 16-Nov-07 96.1950 4.1167% 0.9814 0.9998 15-Feb-08 19-Feb-08 20-Feb-08 97.4400 2.7201% 0.9957 0.9999 19-Nov-07 96.0850 4.1807% 0.9816 0.9998 97.4050 2.7613% 0.9958 0.9999 20-Nov-07 96.0800 4.1859% 0.9816 0.9998 21-Feb-08 97.4500 2.8112% 0.9958 0.9999 21-Nov-07 96.2000 4.1664% 0.9998 22-Feb-08 97.4000 2.7526% 0.9959 0.9999 0.9818 0.9820 23-Nov-07 96.2000 4.1445% 0.9998 25-Feb-08 97.3700 2.7999% 0.9961 0.9999 26-Nov-07 96.3450 4.2163% 0.9823 0.9998 26-Feb-08 97.3950 2.8041% 0.9962 0.9999 27-Nov-07 96.2200 4.1268% 0.9824 0.9998 27-Feb-08 2.7692% 0.9963 0.9999 97.4400 97.5000 28-Nov-07 96.1400 4.2386% 0.9824 0.9998 28-Feb-08 2.7251% 0.9964 0.9999 29-NOV-07 96.2350 4.2269% 0.9825 0.9998 97.6300 2.7005% 29-Feb-08 3-Mar-08 0.9966 0.9968 0.9999 0.9999 30-Nov-07 96.2500 4.2295% 0.9826 0.9998 97.6050 2.6394% 3-Dec-07 96.2200 4.1883% 0.9830 0.9998 4-Mar-08 97.5900 2.6463% 0.9969 0.9999 4-Dec-07 96.2150 4.2106% 0.9831 0.9998 5-Mar-08 97.5500 2.6499% 0.9970 0.9999 5-Dec-07 96.2150 4.2254% 0.9832 0.9998 6-Mar-08 97.5850 2.6599% 0.9971 0.9999 6-Dec-07 96.1250 4.2285% 0.9834 0.9998 7-Mar-08 97.7300 2.5730% 0.9972 0.9999 0.9999 7-Dec-07 95.9900 4.2979% 0.9835 0.9998 10-Mar-08 97.7350 2.5766% 0.9975 10-Dec-07 95.9750 4.4052% 0.9838 0.9998 11-Mar-08 2.5463% 0.9976 0.9999 97.6500 97.6950 11-Dec-07 95.9550 4.3895% 0.9839 0.9998 12-Mar-08 2.5598% 0.9977 0.9999 12-Dec-07 96.0600 4.3833% 0.9841 0.9998 13-Mar-08 2.4937% 0.9978 0.9999 97.7400 97.8850 13-Dec-07 95.9850 4.2507% 0.9845 0.9998 14-Mar-08 2.4650% 0.9979 0.9999 14-Dec-07 95.8900 4.3378% 0.9998 17-Mar-08 98.0200 2.2305% 0.9999 0.9846 0.9850 0.9983 0.9984 17-Dec-07 95.9500 4.3672% 0.9998 18-Mar-08 97.8000 2.2285% 0.9999 18-Dec-07 96.0350 4.3408% 0.9852 0.9998 97.8100 2.3206% 0.9984 0.9999 19-Mar-08 20-Mar-08 19-Dec-07 96.0950 4.2711% 0.9854 0.9998 97.7775 0.9985 0.9999 2.3322% 2.4102% 20-Dec-07 96.1200 4.2180% 0.9856 0.9998 25-Mar-08 97.6850 0.9988 0.9999 21-Dec-07 96.0750 4.2125% 0.9858 0.9998 26-Mar-08 97.6750 0.9988 2.4171% 2.4216% 0.9999 0.9999 24-Dec-07 96.0550 4.2241% 0.9862 0.9998 27-Mar-08 97.6775 0.9988 27-Dec-07 96.0550 4.2554% 0.9866 0.9998 28-Mar-08 97.6750 2.4344% 0.9989 0.9999 28-Dec-07 96.1350 4.2421% 0.9870 0.9998 31-Mar-08 97.6900 2.4204% 0.9991 0.9999 31-Dec-07 96.1850 4.1691% 0.9873 0.9998 97.6300 2.4133% 0.9991 2-Jan-08 96.3100 4.1392% 0.9876 0.9998 97.5700 2.4437% 0.9992 0.9999 0.9999 0.9999 3-Jan-08 96.3350 3.9869% 0.9879 0.9998 97.5575 2.4804% 0.9993 4-Jan-08 96.4450 4.0055% 0.9880 0.9998 97.6100 2.4852% 0.9993 0.9999 7-Jan-08 96.4700 3.8896% 0.9886 0.9998 97.5650 2.4620% 0.9995 0.9999 1-Apr-08 2-Apr-08 3-Apr-08 4-Apr-08 7-Apr-08 8-Apr-08 9-Apr-08 10-Apr-08 11-Apr-08 14-Apr-08 8-Jan-08 96.4800 3.8683% 0.9888 0.9998 97.5050 2.4566% 0.9996 0.9999 9-Jan-08 96.5800 3.8023% 0.9891 0.9998 97.5300 2.4582% 0.9996 0.9999 10-Jan-08 96.6500 3.7389% 0.9894 0.9998 97.5300 2.4474% 0.9997 0.9999 11-Jan-08 96.8300 3.6358% 0.9898 0.9998 97.5350 2.4474% 0.9998 0.9999 14-Jan-08 96.8800 3.4026% 0.9906 0.9998 97.5412 2.4588% 1.0000 0.9999