Question

Two plans are under consideration to provide certain facilities for a public utility. Each plan is designed to provide enough capacity during the next 18 years to take care of the expected growth of load during that period. Regardless of the plan chosen now, it is forecast that the facilities will be retired at the end of 18 years and replaced by a new plant of a different type. Plan I requires an initial investment of $50,000. This will be followed by an investment of $25,000 at the end of 9 years. During the first 9 years, annual disbursements will be $11,000; during the final 9 years, they will be $18,000. There will be a $10,000 salvage value at the end of the 18th year. Plan II requires an initial investment of $30,000. This will be followed by an investment of $30,000 at the end of 6 years and an investment of $20,000 at the end of 12 years. During the first 6 years, annual disbursements will be $8,000; during the second 6 years they will be $16,000; during the final 6 years they will be $25,000. There will be no salvage value at the end of the 18th year. Using an i of 9%, compare the present worth of the net

disbursements for the two plans and which plan will you recommend?

Answer 1

In the image above i have plotted cash flows year wise. Lets start with plan 1

Initial investment =-50000, in year 0. Then another investment in year 9 =-25000, both rae cash outflows, hence the negative sign

Then we have disbursement which i have plotted year wise as you can see in the image.

Salvage value = 10000 cash inflow in the 18th year

Now lets find total cash flow for each year. For that we use the sum function

Total cash flow in year 0=SUM(C5:C7) Drag this formula till cell U8

=-50000

Once u drag the formula, you will get the total cash flow for all the 18 years

Now lets find NPV

=NPV(9%,D8:U8)+C8

=-175025.28

We get the answer as negative because i have given negative sign to all cash outlows and positive sign to all cash inflows.

Similarly i have plotted cash flows of plan 2 year wise.

Plan 2 has initial investment of -30000 in year 0, -30000 in year 6, and -12000 in year 12

All the disbursement has also been plotted. Plan 2 has no salvage value.

Now find total cash flow each year.

Year 0 total cash flow =sum(C14:C16) DRAG THIS FORMULA TILL CELL U17

=-30000

Once you drag the formula we get total cash flow for each year. Now find NPV

=NPV(9%,D17:U17)+C17

=-173555.47

Now we have npv of both projects. We have to choose plan 2 because it results in lower outflow of cash compared to plan 1. We are choosing project with lowest npv because both npv values are negative and negative npv means cash outflow. So we have to choose the plan which have lower outflow of cash.