Question

A company is consicering a project that will require an investment today of $1,700,000. It will produce an after tax cash flow of $136,000 in year one, an amount that will grow at 4% per year forever. The required rate of return for this project is 11%

A, What is the net present value for this project? should the prpject be done
B, What will the next present value be if the after tax cash flow never grow (i.e. remain constant)? should the project be done at this case?
C, What is the minimum rate of growth in the after tax cash flows required to justify doing this project?

Please show calculation and formula.

Answer 1

Given Information

• Cash Outflow = $ 1700000
• Annual Cash Inflow at Year1 = $ 136000
• Growth Rate of Cashflows {g} = 4% ie. 0.04
• Required Rate of Return {Ko} = 11% ie. 0.11

?Ans part A]

Present Value of Perpetual Cash Inflows with Constant Growth = Cash Inflow at Year end 1 / (Ko - g)

Present Value of Perpetual Cash Inflows with Constant Growth = 136000 / (0.11 - 0.04)

Present Value of Perpetual Cash Inflows with Constant Growth = $1942857 approx

NPV = P.V of Cash Inflows (-) P.V of Cash Outflow

NPV = $ 1942857 (-) $ 1700000

NPV = $ 242857 approx

DECISION : ACCEPT THE PROJECT

Ans part B]

Present Value of Perpetual Cash Inflows with NO Growth = Cash Inflow at Year end 1 / Ko

Present Value of Perpetual Cash Inflows with NO Growth = 136000 / 0.11

Present Value of Perpetual Cash Inflows with NO Growth = $ 1236363.63 approx

NPV = $ 1236363.63 (-) $ 1700000

NPV = ( $ 463636.37) {Negative NPV}

DECISION : REJECT THE PROJECT SINCE NEGATIVE NPV

Ans Part C]

To Find Minimum Growth Rate Required to Accept the Project we will use following Equation :

Present Value of Cash Outflow = Present Value of Cash Inflows

$ 1700000 = $ 136000 / (0.11 - g)

0.11 - g = 0.08

g = 0.03 ie 3%

HOPE YOU ARE CLEAR WITH THE SOLUTUON. STILL IF ANY DOUBT PLEASE ASK IN COMMENT :)