Question

Year Cash Flow

0 −$8,500

1 2,200

2 3,200

3 3,200

a. What is the profitability index for the cash flows if the relevant discount rate is 10 percent?

b. What is the profitability index for the cash flows if the relevant discount rate is 14 percent?

c. What is the profitability index for the cash flows if the relevant discount rate is 23 percent?

Answer 1

a.	Profitability Index	=	Present value of cash inflows	/	Year 0 cost of project
		=	$ 7,048.84	/	$ 8,500.00
		=	0.83
Working;
Year	Cash flow	Discount factor	Present value
a	b	c=1.10^-a	d=b*c
1	$       2,200	0.909091	$ 2,000.00
2	3200	0.826446	$ 2,644.63
3	3200	0.751315	$ 2,404.21
Total			$ 7,048.84
b.	Profitability Index	=	Present value of cash inflows	/	Year 0 cost of project
		=	$ 6,552.03	/	$ 8,500.00
		=	0.77
Working;
Year	Cash flow	Discount factor	Present value
a	b	c=1.14^-a	d=b*c
1	$       2,200	0.877193	$ 1,929.82
2	3200	0.769468	$ 2,462.30
3	3200	0.674972	$ 2,159.91
Total			$ 6,552.03
c.	Profitability Index	=	Present value of cash inflows	/	Year 0 cost of project
		=	$ 5,623.39	/	$ 8,500.00
		=	0.66
Working;
Year	Cash flow	Discount factor	Present value
a	b	c=1.23^-a	d=b*c
1	$       2,200	0.813008	$ 1,788.62
2	3200	0.660982	$ 2,115.14
3	3200	0.537384	$ 1,719.63
Total			$ 5,623.39