Question

YEAR	1	2	3	4	5	6	7	8
CASH FLOW	-4090	-559	9380	3743	416	3276	-4677	-3074

a) Determine the maximum number of positive IRR roots for the given cash flow according to Descartes Rule.
b) Determine the maximum number of positive IRR roots for the given cash flow according to Norstrom Criterion.                                                                                                                     

c) Find ERR of the given cash flow if ε=10% per year.

IN EXCEL PLZ!!

Answer 1

Formula	Year (n)	1	2	3	4	5	6	7	8
	Cash flow (CF)	-4090	-559	9380	3743	416	3276	-4677	-3074
CCFn = CCFn-1 + CFn	Cumulative cash flow (CCF)	-4090	-4649	4731	8474	8890	12166	7489	4415

a). As per Descartes rule, the total number of positive real number roots will be less than or equal to the number of times, the sign changes in the cash flow. As we can see from the cash flow, the sign changes once from - to + (CF2 to CF3) and then, changes again from + to - (CF6 to CF7). So, the sign change occurs twice. Hence, there can be two positive real roots for the given cash flow.

b). As per the Nostrom criterion, in a cumulative cash flow in which the first cash flow has a negative sign and the sign changes only once, there can only be one positive root. As can be seen from the cumulative cash flow, CF1 has a negative sign and the sign changes only once (CF2 to CF3), so the Nostrom criterion is satisfied. Hence, this cash flow will have only one positive root.

c). ERR is calculated as:

Future value of (sum of cash outflows discounted to n = 0 at E = 10%) compounded to n = 8 @ ERR = Future value of (sum of cash inflows compounded to n = 8 at E = 10%

Calculations:

ERR = 15.34%