Solution 14.6
 
 

a) Calculate the payback period, the net present value and the internal rate of return for the project

Approach: In this question one must firstly calculate the relevant cash flows for the project. In this case sales and variable costs are relevant to the decision however of the fixed costs depreciation should be excluded as it is only a restatement of the initial cost of the asset and is a non-cash item. Thus only €30,000 of the fixed costs are relevant to the decision.

Payback period

Year

Cash flow

Cumulative cash flow

0

-(500,000)

(500,000)

1

94,000

(406,000)

2

106,400

(299,600)

3

162,200

(137,400)

4

137,400

 

5

150,200

 

 

 

 

The payback period is exactly 4 years. Thus the payback is projected to occur 80% through the life of the project. Relatively speaking this is a long payback period.

Net present Value

Year

Cash flow

Disc  10%

P.V.

0

-500,000

1

-500000

1

94,000

0.909

85446

2

106,400

0.826

87886.4

3

162,200

0.751

121812.2

4

137,400

0.683

93844.2

5

150,200

0.621

93274.2

 

 

NPV

-17737

The net present value is a negative value of €17,737. Thus the sum of the present value of the cash outflows exceeds the sum of the present value of the cash inflows. That implies that the project is offering returns below the cost of capital for the business. The Internal rate of return can calculate the actual return on the project taking into account the time value of money

 

Internal rate of return

This involves through trial and error finding and discount factor that will give a positive NPV. At 10% the NPV is negative. Thus reducing the cost of capital should help ensure a positive NPV. Let us try discounting the cash flows at 5%.

Year

Cash flow

Disc  10%

P.V.

 

Disc  5%

P.V.

0

-500,000

1

-500000

 

1

-500000

1

94,000

0.909

85446

 

0.952

89488

2

106,400

0.826

87886.4

 

0.907

96504.8

3

162,200

0.751

121812.2

 

0.864

140140.8

4

137,400

0.683

93844.2

 

0.823

113080.2

5

150,200

0.621

93274.2

 

0.784

117756.8

 

 

NPV

-17737

 

 

56970.6

 

 

 

 

 

 

 

 

Through the use of the interpolation formula one can calculate the IRR as follows

 

 

 

 

 

56971

             x

10 - 5

 

IRR

       5  +

 17737 + 56971

 

 

 

 

 

 

 

 

 

       5 +

3.81

 

 

 

 

 

8.81

 

 

The IRR of this project is 8.81% and is below the cost of capital of 10%.

 

b) State, with reasons, whether you feel the project is financially viable

The project is not financially viable according to the projected figure given and thus the project should be rejected on the basis that

  • The payback period is projected to happen very late in the life of the project.
  • The net present value of the project is decisively negative at the company’s cost of capital.
  • The IRR is less that the company’s cost of capital.