Question

a) Kitwe city council under the leadership of his worship the Mayor Christopher Pikiti
Kang’ombe is considering an investment project in a new machinery. It is
anticipated that this investment project will enhance the council’s cash flow. The
annual incremental profits/ (losses) relating to the investment are estimated as
follows.
Year         K
1          (22,000,000)
2            6,000,000
3           68,000,000
4           94,000,000
5           16,000,000
The investment at the start of the project would be 350,000.The investment sum,
assuming nil disposal value after five years, would be written off using the straight
line method. The depreciation has been included in the profit estimates above, which
should be assumed to arise at each year end.
Assume the cost of capital is 10%
Year 0   Year1   Year2    Year3    Year4    Year5
D.f 1.00 0.909   0.826    0.751     0.683      0.621
Required
Calculate the following:
i. Net present value (NPV) of the investment.
ii. Payback period of the investment.
iii. Internal rate of return (IRR).
iv. Accounting rate of return (ARR).
v. Discounted payback period.

Answer 1

i. NPV of the investment: K 110,079,300

	0	1	2	3	4	5
Initial investment	(350,000)
Incremental profit ( loss)		(22,000,000)	6,000,000	68,000,000	94,000,000	16,000,000
Add: Annual depreciation		70,000	70,000	70,000	70,000	70,000
Operating cash flows		(21,930,000)	6,070,000	68,070,000	94,070,000	16,070,000
Total cash flows	(350,000)	(21,930,000)	6,070,000	68,070,000	94,070,000	16,070,000
DF	1.000	0.909	0.826	0.751	0.683	0.621
Present values	(350,000)	(19,934,370)	5,013,820	51,120,570	64,249,810	9,979,470
NPV	110,079,300

ii. Payback period:

	1	2	3	4	5
Operating cash flows	(21,930,000)	6,070,000	68,070,000	94,070,000	16,070,000
Cumulative cash flows	(21,930,000)	(15,860,000)	52,210,000

Payback period = 2 years + 350,000 / 68,070,000 = 2.01 years.

iii. IRR:

Spreadsheet calculation of IRR: 135 %

	A	B	C	D	E	F	G
1	Year	0	1	2	3	4	5
2	Cash Flows	(350,000)	(21,930,000)	6,070,000	68,070,000	94,070,000	16,070,000
		= IRR( B2:G2)	135%