Question

Year Cash Flow 0 −$9,100 1 2,200 2 3,600 3 4,800 a. What is the profitability index for the cash flows if the relevant discount rate is 9 percent? b. What is the profitability index for the cash flows if the relevant discount rate is 16 percent? c. What is the profitability index for the cash flows if the relevant discount rate is 23 percent?

Answer 1

a.	Profitability Index		0.96
Working:
	Year	Cash Inflow	Discount factor	Present Value of cash inflow
	a	b	c=1.09^-a	d=b*c
	1	$         2,200	0.917431193	$         2,018.35
	2	$         3,600	0.841679993	$         3,030.05
	3	$         4,800	0.77218348	$         3,706.48
	Total			$         8,754.88
	Profitability Index	=	Present Value of cash inflow	/	Initial cost
		=	$            8,754.88	/	$ 9,100.00
		=	0.96
b.	Profitability Index		0.84
Working:
	Year	Cash Inflow	Discount factor	Present Value of cash inflow
	a	b	c=1.16^-a	d=b*c
	1	$         2,200	0.862068966	$         1,896.55
	2	$         3,600	0.743162901	$         2,675.39
	3	$         4,800	0.640657674	$         3,075.16
	Total			$         7,647.10
	Profitability Index	=	Present Value of cash inflow	/	Initial cost
		=	$            7,647.10	/	$ 9,100.00
		=	0.84
c.	Profitability Index		0.74
Working:
	Year	Cash Inflow	Discount factor	Present Value of cash inflow
	a	b	c=1.23^-a	d=b*c
	1	$         2,200	0.81300813	$         1,788.62
	2	$         3,600	0.66098222	$         2,379.54
	3	$         4,800	0.537383918	$         2,579.44
	Total			$         6,747.60
	Profitability Index	=	Present Value of cash inflow	/	Initial cost
		=	$            6,747.60	/	$ 9,100.00
		=	0.74