Question

Please calculate on paper, and explain how should I calculate PI?

6. You are a following projects. Investment and cashflow figures are in millions of dollars Project manager with a limited investment budget of $8 million. You may invest in the Investment Project Life, Discount Rate % 10 12 Annual Cashflow ears 4 4 1.5 12 Using Profitability index, which project should you choose?

Answer 1

Profitability index = Present value of cash inflows / Investment cost

Figures are in millions.

Present value (P. V.) of cash inflow = Annual cash flow * ((1 - (1/(1+i)^n)) / i)

i) Project A :

i (Discount rate) = 10% or 0.10

n (years) = 5

P. V. Of cash inflow = $1*((1 - (1/(1+0.10)^5))/0.10)

P. V. Of cash inflow = $1 * ((1 - 0.6209)/0.10)

P. V. Of cash inflow = $1 * 3.791

P. V. Of cash inflow = $3.791

Initital investment = $3

Profitability index = P. V. Of cash inflows / Initial investments

Profitability index = $3.791 / $3

Profitability index = 1.26

ii) Project B : Initial investments = $4,

Annual cash inflow = $1

i = 12% or 0.12, n = 8

Using the P. V. formula,

P. V of cash inflows =$1*((1 - (1/(1+0.12)^8))/0.12)

P. V. Of cash inflows = $1 * ((1 - 0.4039)/0.12)

P. V. Of cash inflows = $1 * 4.9675

P. V. Of cash inflows = $4.9675

Profitability index = P. V. Of cash inflows / Initial investments

Profitability index = $4.9675 / $4

Profitability index = 1.24

iii) Project C : Initial investments = $5

Annual cash inflows = $2

i = 8% or 0.08, n = 4

P. V. Of cash inflows=$2*((1 - (1/(1+0.08)^4))/0.08)

P. V. Of cash inflows = $2 * ((1 - 0.7650)/0.08)

P. V. Of cash inflows = $2 * 2.9375

P. V. Of cash inflows = $5.875

Profitability index = P. V. Of cash inflows / Initital investments

Profitability index = $5.875 / $5

Profitability index = 1.18

iv) Project D : Initial investments = $3

Annual cash inflows = $1.5

i = 8% or 0.08, n = 3

P. V. Of cash inflows = $1.5 * ((1 - (1/(1+0.08)^3))/0.08)

P. V. Of cash inflows = $1.5 * ((1 - 0.7938)/0.08)

P. V. Of cash inflows = $1.5 * 2.5775

P. V. Of cash inflows = $3.8663

Profitability index = P. V. Of cash inflows / Initial investments

Profitability index = $3.8663 / $3

Profitability index = 1.29

v) Project E : Initital investments = $3,

Annual cash inflows = $1,

i = 12% or 0.12, n = 6

P. V. Of cash inflows = $1 * ((1 - (1/(1+0.12)^6))/0.12)

P. V. Of cash inflows = $1 * ((1 - 0.5066)/0.12)

P. V. Of cash inflows = $1 * 4.11

P. V. Of cash inflows = $4.11

Profitability index = P. V. Of cash inflows / Initital investments

Profitability index = $4.11 / $3

Profitability index = 1.37

As per profitability index, if it's greater than 1 then it generates values to the project & if it's less than 1 then it destroys the value of the project.

So, greater value is to be choosen rather lower value of profitability index.

Project E, Project D are having greater profitability index of 1.37 & 1.29 respectively than others & hence this project to be choosen.

This 2 projects are having investments of $6 million ($3 million each) & budget is $8 million which is under the budget limit.

Another project is not be choosen, as this will increase the investment costs above budget of $8 million. Hence project E & D is to be selected.