Question

For a capital investment of $5M, a small mine returns an annual profit of $1.5M for a mine life of 5 years. If MARR is 12%, calculate a) Net present value, b) Internal rate of return, c) Discounted pay-back period.

Answer 1

(a)

NPV ($) = - 5,000,000 + 1,500,000 x P/A(12%, 5)

= - 5,000,000 + 1,500,000 x 3.6048

= - 5,000,000 + 5,407,200

= 407,200

(b)

IRR computed using Excel IRR function as follows.

Year	Cash Flow ($)
0	-50,00,000
1	15,00,000
2	15,00,000
3	15,00,000
4	15,00,000
5	15,00,000
IRR =	15.24%

(c)

Discounted payback period (DPBP) is the time by when cumulative discounted cash flows becomes zero.

Year	Cash Flow ($)	PV Factor @12%	Discounted Net Cash Flow ($)	Cumulative Discounted Net Cash Flow ($)
0	-50,00,000	1.0000	-50,00,000	-50,00,000
1	15,00,000	0.8929	13,39,286	-36,60,714
2	15,00,000	0.7972	11,95,791	-24,64,923
3	15,00,000	0.7118	10,67,670	-13,97,253
4	15,00,000	0.6355	9,53,277	-4,43,976
5	15,00,000	0.5674	8,51,140	4,07,164

Discounted payback period (DPBP) is the time by when cumulative discounted cash flows becomes zero.

DPBP lies between years 4 & 5.

DPBP = 4 + (Absolute value of cumulative discounted cash flow, year 4 / Discounted cash flow, year 5)

= 4 + (443,976 / 851,140)

= 4 + 0.52

= 4.52 years