Question

You are a senior manager at Poeing Aircraft and have been authorized to spend up to $400,000 for projects. The three projects you are considering have the following characteristics:
Project A: Initial investment of $280,000. Cash flow of $190,000 at year 1 and $170,000 at year 2. This is a plant expansion project, where the required rate of return is 10%.
Project B: Initial investment of $390,000. Cash flow of $270,000 at year 1 and $240,000 at year 2. This is a new product development project, where the required rate of return is 20%.
Project C: Initial investment of $230,000. Cash flow of $160,000 at year 1 and $190,000 at year 2. This is a market expansion project, where the required rate of return is 15%.
Assume the corporate discount rate is 10%. Please offer your recommendations, backed by your analysis:

A B C
Payback
IRR
PI
NPV

Please give me a full equation answer not the excel answers so I can study. One by one solutions. Thank you.

Answer 1

A)

Payback: Year 1 : $190,000 Balance : $280,000 - $190,000 = $90,000

Payback = 1 + ( 90,000 / 170,000 ) = 1.53 years   {Answer}

IRR : $280,000 = $190,000 / (1+r) + $170,000 / (1+r)²

Solving the above equation, IRR = 18.91 %  {Answer}

PI :  PV of Future Cash Flows = 190,000 / 1.1 + 170,000 / 1.1² = $310,703

Profibility Index , PI =  PV of Future Cash Flows / Initial Investment = $310,703 / $280,000 = 1.10965 {Answer}

NPV :

NPV = PV of Future Cash Flows - Initial Investment = 310,703 - 280,000 = $30,703 {Answer}

As, all the ratios & values indicate project is profitable, we should go ahead with Project A

B:

Payback: Year 1 : $270,000 Balance : $390,000 - $270,000 = $120,000

Payback = 1 + ( 120,000 / 240,000 ) =  1.5 years   {Answer}

IRR  : $390,000 = $270,000 / (1+r) + $240,000 / (1+r)²

Solving the above equation, IRR =  20.36 %  {Answer}

PI :  PV of Future Cash Flows = 270,000 / 1.1 + 240,000 / 1.1² = $440,244

Profibility Index ,  PI =  PV of Future Cash Flows / Initial Investment = $440,244 / $390,000 =   1.12883 {Answer}

NPV :

NPV = PV of Future Cash Flows - Initial Investment = 440,244 - 390,000 = $50,244 {Answer}

As, all the ratios & values indicate project is profitable, we should go ahead with Project B

C:

Payback: Year 1 : $160,000 Balance : $230,000 - $160,000 = $70,000

Payback = 1 + ( 70,000 / 190,000 ) =  1.37 years   {Answer}

IRR  : $230,000 = $160,000 / (1+r) + $190,000 / (1+r)²

Solving the above equation, IRR =  32.1 %  {Answer}

PI :  PV of Future Cash Flows = 160,000 / 1.1 + 190,000 / 1.1² = $299,663

Profibility Index ,  PI =  PV of Future Cash Flows / Initial Investment = $299,663 / $230,000 =  1.30288 {Answer}

NPV :

NPV = PV of Future Cash Flows - Initial Investment = 299,663 - 230,000 = $69,663 {Answer}

As, all the ratios & values indicate project is profitable, we should go ahead with Project C

ANS : Also, as the PI is maximum for Project C, if we had to choose one among the 3 Projects, we should choose Project C.