a = Task: Let time be counted in years. Consider an investor who leases a machine for 3 years. At time t = 1 the investor has to pay the lease L in advance for the whole period. At t = 1 he also has a cost M1 to modify the machine for his purposes. At t = 3 there is a further cost M2 to remove all the modifications. The income I generated from operating the machine is received at t = 2. There is no income in the first and last year due to the modification of the machine. = (i) For both of the following investments write down the equation of value in terms of the interest rate i per annum: cash flows of investment M1 L M2 time 1 2 3 4 investment A 51,000 9,000 69,000 6,000 investment B 51,000 9,000 69,000 12,000 (ii) What information (if any) about the roots is provided by the criterion with cumulative amounts above? In each case find all the roots of the equations of value. Answer: (i) Let amounts be counted in '000s. The equations of value are [Select ] -(51 +9) 1^2 + 69 i - 6 = 0, -(51 +9) (1 + i)^2 + 69 (1 + i) - 6 = 0, -(51 +9) (1 + i^2) + 69 (1 + i) - 6 = 0, and + and [ Select ] -(51 +9) i^2 + 69 i - 12 = 0, -(51 + 9) (1 + i)^2 + 69 (1 + i) - 12 = 0, -(51 + 9) (1 + i^2) + 69 (1 + i) - 12 = 0, + (ii) The criterion [ Select ] a = Task: Let time be counted in years. Consider an investor who leases a machine for 3 years. At time t = 1 the investor has to pay the lease L in advance for the whole period. At t = 1 he also has a cost M1 to modify the machine for his purposes. At t = 3 there is a further cost M2 to remove all the modifications. The income I generated from operating the machine is received at t = 2. There is no income in the first and last year due to the modification of the machine. = (i) For both of the following investments write down the equation of value in terms of the interest rate i per annum: cash flows of investment M1 L M2 time 1 2 3 4 investment A 51,000 9,000 69,000 6,000 investment B 51,000 9,000 69,000 12,000 (ii) What information (if any) about the roots is provided by the criterion with cumulative amounts above? In each case find all the roots of the equations of value. Answer: (i) Let amounts be counted in '000s. The equations of value are [Select ] -(51 +9) 1^2 + 69 i - 6 = 0, -(51 +9) (1 + i)^2 + 69 (1 + i) - 6 = 0, -(51 +9) (1 + i^2) + 69 (1 + i) - 6 = 0, and + and [ Select ] -(51 +9) i^2 + 69 i - 12 = 0, -(51 + 9) (1 + i)^2 + 69 (1 + i) - 12 = 0, -(51 + 9) (1 + i^2) + 69 (1 + i) - 12 = 0, + (ii) The criterion [ Select ]
