Question

You are thinking about setting up a fish farm in your pond. You can rig it up to farm Tilapia or Pollock, but not both. You have the following information on the two possibilities:

Type of
Fish Farm Initial
Cost Annual
Cash Flow
Tilapia $1,000 $200
Pollock $1,800 $350
Each option will yield the annual cash flows for 10 years and then will be finished with no additional cost or revenue. If the required return is 8%, what is the PI of the incremental project that you would use to decide between these two types of fish farms?
a.) 0.6468
b.) 0.3420
c.) 0.2581

Answer 1

`\huge\color{blue}\boxed{ANSWER:}`

To calculate the Present Value (PV) of each project, we need to discount the annual cash flows at the required return rate of 8%. Then, we can calculate the Net Present Value (NPV) for each option:

For Tilapia:

`PV = (200/1.08) + (200/1.08^2) + ... + (200/1.08^10) = 1473.40 \: </p><p>Initial \: Cost = 1000`

NPV of Tilapia = PV - Initial Cost = 1473.40 - 1000 = 473.40

For Pollock:

`PV = (350/1.08) + (350/1.08^2) + ... + (350/1.08^10) = 2581.61 \: </p><p>Initial \: Cost = 1800`

NPV of Pollock = PV - Initial Cost = 2581.61 - 1800 = 781.61

To calculate the Profitability Index (PI), we divide the NPV of each project by the initial cost:

`PI \: of \: Tilapia = NPV of \: Tilapia / Initial Cost = 473.40 / 1000 = 0.4734 \\ </p><p>PI \: of \: Pollock = NPV of \: Pollock / Initial Cost = 781.61 / 1800 = 0.4342`

Since we are interested in the increment (difference) between the two projects, we calculate:

`Incremental \: PI = \: PI \: of \: Pollock - PI \: of \: Tilapia = 0.4342 - 0.4734 = - \: 0.0392`

The Profitability Index of the incremental project is approximately -0.0392. None of the given choices match this value precisely, but the closest option is:

`\large\color{green}\boxed{C. \: 0.2581}`