Question

An investment in an item of equipment would cost GH¢150,000. It is estimated that sales in the first
year would be GH¢120,000 rising by 10% a year for the next four years. Variable costs would be
50% of sales. Annual fixed costs would be GH¢40,000 in the first three years, rising to GH¢60,000
in years 4 and 5. Fixed costs of 60% would be avoidable if the project did not go ahead. The scrap
value of the equipment at the end of year 5 would be GH¢10,000. The project would also require
an investment in working capital of GH¢30,000 at the start of year 1 rising to GH¢40,000 at the
start of year 2 and to GH¢50,000 at the start of year 4. The company’s cost of capital is 9%.
Required: Calculate the NPV of the project and suggest whether it should be undertaken.

Answer 1

Given Information,

Cost of equipmet = GHC 150,000

Sales = GHC 120,000 rising by 10% per year for four years

Variable costs are 50% of sales.

Fixed costs would be GHC 40,000 for first three years and GHC 60,000 for year 4 and 5.

Sxrap vlue of equipment = GHC 10,000

Working capital requirement for year 1 = GHC 30,000

Working capital requirement for year 2 = GHC 40,000

Working capital requirement for year 4 = GHC 50,000

Cost of capital = 9%

Computation of NPV of the project

Initial Investment = GHC 150,000

Computation of cashflows in each year    (Amount in GHC)

Particulars	Year 1	Year 2	Year 3	Year 4	Year 5
Sales	120,000	132,000	145,200	159,720	175,692
Variable cost	60,000	66,000	72,600	79,860	87,846
Contribution	60,000	66,000	72,600	79,860	87,846
Fixed costs	40,000	40,000	40,000	60,000	60,000
Fixed costs avoidable(if project doesn't go ahead)60% of fixed costs	24,000	24,000	24,000	36,000	36,000
profit	36,000	42,000	48,600	43,860	51,846
Working capital	30,000	10,000	0	10,000	0
Profit	6000	32,000	48,600	33,860	51,846
Scrap	0	0	0	0	10,000
Working capital					50,000
Cashflows	6000	32,000	48,600	33,860	1,11,846
PvF(9%,ny)	0.917	0.842	0.772	0.708	0.650
Present value of cashflows	5,502	26,944	37,519.2	23,972.88	72,700

Net Present Value = Present value of cash inflows - Present value of cash outflows

5,502 + 26,944 + 37,519.2 + 23,972.88 + 72,700 - 150,000 = 16,638.08

Since NPV is positive, Project can be accepted.

Note

Since tax rate is not given in the quetion, we ignore depriciation for calculating cashflows.

Only avoidable fixed costs are reduced from contribution because unavoidable costs would be sunk cost and is irrelavant to decision making.