Suppose that on October 16, 2007 a firm loses a lawsuit and has to pay $100 million within 9 months. Currently it has no money to pay, so it decides to sell a piece of equipment. Although the equipment could go for up to $150 million, the firm is desperate and is willing to take much less so as to make the lawsuit payment. A buyer comes up, who offers to buy the equipment at a significant discount and will pay for it in six months. The firm's CFO thinks that the deal might work if they enter into a futures contract or a forward contract. (a) Using only the information available on October 16, 2007 in Table 6.11, what is the least that the firm should accept, if it decides to enter into a futures contract? (b) Using only the information available on October 16, 2007 what is the least that the firm should accept, if it decides to enter into 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?

Table 6.11 Futures and Forward Rates Date 16-Oct-07 95.3900 17-Oct-07 95.5150 18-Oct-07 95.5700 19-Oct-07 95.6850 22-Oct-07 95.6700 23-Oct-07 95.6700 24-Oct-07 95.7750 25-Oct-07 95.7750 26-Oct-07 95.7350 29-Oct-07 95.7000 30-Oct-07 95.6800 31-Oct-07 95.5500 1-Nov-07 95.6700 2-Nov-07 95.7950 5-Nov-07 95.7250 6-Nov-07 95.7050 7-Nov-07 95.7550 8-Nov-07 95.8950 9-Nov-07 95.9300 12-Nov-07 95.9300 13-Nov-07 95.8000 14-Nov-07 95.7900 15-Nov-07 95.9450 16-Nov-07 95.9450 19-Nov-07 95.8350 20-Nov-07 95.8300 21-Nov-07 95.9500 23-Nov-07 95.9500 26-Nov-07 96.0950 27-Nov-07 95.9700 28-Nov-07 95.8900 29-Nov-07 95.9850 30-Nov-07 96.0000 3-Dec-07 95.9700 4-Dec-07 95.9650 5-Dec-07 95.9650 6-Dec-07 95.8750 7-Dec-07 95.7400 10-Dec-07 95.7250 11-Dec-07 95.7050 12-Dec-07 95.8100 13-Dec-07 95.7350 14-Dec-07 95.6400 17-Dec-07 95.7000 18-Dec-07 95.7850 19-Dec-07 95.8450 20-Dec-07 95.8700 21-Dec-07 95.8250 24-Dec-07 95.8050 27-Dec-07 95.8050 28-Dec-07 95.8850 31-Dec-07 95.9350 2-Jan-08 96.0600 3-Jan-08 96.0850 4-Jan-08 96.1950 7-Jan-08 96.2200 8-Jan-08 96.2300 9-Jan-08 96.3300 10-Jan-08 96.4000 11-Jan-08 96.5800 14-Jan-08 96.6300 Source: Bloomberg. pfut (t, T) f(t, T, T) Z(t, T) Z(t, t + dt) 4.9377% 0.9751 4.8740% 0.9998 0.9998 0.9753 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 4.7691% 0.9756 4.6475% 0.9761 4.5410% 0.9768 4.6208% 0.9769 0.9772 4.5184% 4.4484% 0.9776 4.4708% 0.9777 4.4837% 0.9781 4.5514% 0.9784 4.5478% 0.9784 4.6967% 0.9784 4.5323% 0.9787 4.5183% 0.9790 4.5836% 0.9790 0.9792 4.5498% 4.5025% 0.9794 4.4121% 0.9797 4.3647% 0.9801 4.3561% 0.9803 4.4676% 0.9803 4.4416% 4.3667% 0.9804 4.4307% 0.9806 4.4359% 0.9807 4.4164% 0.9808 4.3945% 0.9810 4.4663% 0.9803 0.9813 4.3768% 0.9815 4.4886% 0.9815 4.4769% 0.9816 4.4795% 0.9817 4.4383% 0.9821 4.4606% 0.9822 4.4754% 0.9823 4.4785% 4.5479% 0.9825 0.9826 4.6552% 0.9829 4.6395% 0.9831 4.6333% 0.9833 4.5007% 0.9836 4.5878% 0.9838 4.6172% 0.9842 4.5908% 0.9844 4.5211% 0.9846 4.4680% 0.9849 4.4625% 0.9851 4.4741% 0.9855 4.5054% 0.9859 0.9863 4.4921% 4.4191% 0.9866 4.3892% 0.9869 4.2369% 0.9872 4.2555% 0.9874 4.1396% 0.9879 4.1183% 0.9882 4.0523% 0.9884 3.9889% 0.9887 3.8858% 0.9891 3.6526% 0.9900 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 Date 28-Jan-08 97.1250 29-Jan-08 97.1050 30-Jan-08 97.1850 31-Jan-08 97.2400 1-Feb-08 97.1700 4-Feb-08 97.1450 5-Feb-08 97.2400 6-Feb-08 97.2700 7-Feb-08 97.2650 8-Feb-08 97.2900 11-Feb-08 97.2950 12-Feb-08 97.2900 13-Feb-08 97.2800 14-Feb-08 97.2650 15-Feb-08 97.2600 19-Feb-08 97.1900 20-Feb-08 97.1550 21-Feb-08 97.2000 22-Feb-08 97.1500 25-Feb-08 97.1200 26-Feb-08 97.1450 27-Feb-08 97.1900 28-Feb-08 97.2500 29-Feb-08 97.3800 3-Mar-08 97.3550 4-Mar-08 97.3400 5-Mar-08 97.3000 6-Mar-08 97.3350 7-Mar-08 97.4800 10-Mar-08 97.4850 11-Mar-08 97.4000 12-Mar-08 97.4450 13-Mar-08 97.4900 14-Mar-08 97.6350 17-Mar-08 97.7700 18-Mar-08 97.5500 19-Mar-08 97.5600 20-Mar-08 97.5275 25-Mar-08 97.4350 26-Mar-08 97.4250 27-Mar-08 97.4275 28-Mar-08 97.4250 31-Mar-08 97.4400 1-Apr-08 97.3800 2-Apr-08 97.3200 3-Apr-08 97.3075 4-Apr-08 97.3600 7-Apr-08 97.3150 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 9-Apr-08 97.2800 0.9998 10-Apr-08 97.2800 0.9998 11-Apr-08 97.2850 0.9998 14-Apr-08 97.2912 8-Apr-08 97.2550 0.9998 0.9998 0.9998 pfut(t, T) f(t, T, T) Z(t, T) Z(t, t + dt) 0.9998 0.9998 0.9998 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 15-Jan-08 96.5900 96.5700 16-Jan-08 17-Jan-08 96.6250 18-Jan-08 96.7150 22-Jan-08 97.1500 23-Jan-08 24-Jan-08 97,2450 97.0350 25-Jan-08 97.0650 3.6628% 3.6452% 3.7057% 3.6295% 3.3133% 0.9902 0.9904 0.9906 0.9908 0.9916 3.0388% 0.9926 3.0847% 0.9928 3.2957% 0.9928 3.1394% 0.9932 3.1414% 0.9933 0.9934 3.1548% 3.0024% 0.9936 2.9729% 0.9938 0.9939 0.9940 0.9941 3.0675% 3.0789% 2.9475% 2.9297% 0.9942 2.9512% 0.9943 2.9227% 0.9946 2.9167% 0.9947 2.9124% 0.9948 2.9325% 0.9949 2.9446% 0.9950 2.9701% 0.9953 3.0113% 3.0612% 0.9954 0.9955 3.0026% 0.9956 3.0499% 0.9958 3.0541% 0.9959 3.0192% 0.9960 2.9751% 0.9961 2.9505% 0.9963 0.9965 2.8894% 2.8963% 0.9966 2.8999% 0.9967 2.9099% 0.9968 2.8230% 2.8266% 0.9969 0.9972 2.7963% 0.9974 2.8098% 2.7437% 0.9975 0.9976 2.7150% 0.9977 2.4805% 0.9981 2.4785% 0.9982 2.5706% 0.9982 2.5822% 2.6602% 0.9983 0.9986 2.6671% 0.9987 2.6716% 0.9987 2.6844% 0.9988 2.6704% 2.6633% 0.9990 0.9990 2.6937% 0.9991 2.7304% 0.9992 2.7352% 0.9993 2.7120% 0.9995 2.7066% 0.9995 0.9996 2.7082% 2.6974% 0.9997 2.6974% 0.9997 2.7088% 1.0000 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999