611 Consider the following two mutually exclusive projects B

6.11 Consider the following two mutually exclusive projects B1 B2 Cas Flow $18,000 -2,000 -2,000 Salvage Value Cash Flow Salvage Value Il 0 6,000 4,000 3,000 2,000 2,000 $15,000 2,100 2,100 2,100 6,000 3,000 1,000 2,000 -2,000 -2,000 Salvage values represent the net proceeds (after tax) from disposal of the assets if they are sold at the end of each year. Both B1 and B2 will be available (or can be repeated) with the same costs and salvage values for an indefinite period (a) Assuming an infinite planning horizon, which project is a better choice at MARR-12%? (b) With a 10-year planning horizon, which project is a better choice at MARR-12%? (Note: In the 4th cycle for B2, the project terminates at the end of its first year, i.e. year 10)

Solution

a) Over Infinite planning horizon, B1 is sold after 5 years (with 2000 salvage value) and then again buying the same and repeating the process. It means we need to calculate the per year cost at MARR for B1

Now Net Negative value today for future cash outflow and salvage value is calculated as follows. To calculate the NPV of all future negative cash flows, enter the followin in the financial calculator

PMT = -2000; n=5; 1/y = 12%, FV = 2000; calculate PV = -$6074.7

Now total investment which we need to make for B1 is -6047.7-18000 = -$24,047.7. If this is the present value, equivalent per year cost is calculated as follows

PV = -24074.7; n=5, 1/y = 12%, FV = 0. calculate PMT = $6678.55

Now similarly, we need to do the same for B2

NPV of all future negative cash flows, enter the followin in the financial calculator

PMT = -2100; n=3; 1/y = 12%, FV = 1000; calculate PV = -$4332.07

Now total investment which we need to make for B1 is -4332.07-15000 = -$19,332.07. If this is the present value, equivalent per year cost is calculated as follows

PV = -19332.07; n=3, 1/y = 12%, FV = 0. calculate PMT = $5362.9

Clearly, if the machine is to be used infinitely, B2 is a better choice as its per year cost is less than B1

b) Now if project horizon is 10 years. The NPV of B1 will be 10 year negatively cash flow discounted to today\'s value. Enter the following in the financial calculator

PMT = 6678.55, n=10, FV = 0. 1/y = 12%, calculate PV = $37,735.3

For B2 it is slightly tricky, we can calculate the 9 year PV by similar way whcih is

PMT = 5362.9, n=9, FV = 0. 1/y = 12%, calculate PV = $28,574.87

Now at the end of 9th year, we will incur cost of $15,000 and in 10th year while he spends $2100 on machine, he gets $6000 as salvage value. So Present value of these 2 cash flows are

-15000/1.12^9 + 3900/1.12^10 = $4153.45

So total Present value = -28,574.87 - 4153.45 = -$32,728.32

Since again, B2 is having less cost than B1,

B2 is the better option in this case as well.