Question

1. (show step by step calculation and formula, no excel or fina calculator) Based on the below cash flows, HappyBear Ltd. uses the NPV decision rule. At a required return of 12 percent, should the firm accept this project? What if the required return is 30 percent?

Year	Cash Flow
0	-$32,000
1	16,000
2	20,000
3	17,000

Answer 1

NPV at 12%

Year	Cash flow	× discount factor @12%	Present value
0	$(32,000.00)	1.000000	$(32,000.00)
1	$ 16,000.00	0.892857	$ 14,285.71
2	$ 20,000.00	0.797194	$ 15,943.88
3	$ 17,000.00	0.711780	$ 12,100.26
	NPV		$ 10,329.86

Firm should accept project at 12% as NPV is positive.

Decision at 30%:

Year	Cash flow	× discount factor @30%	Present value
0	$(32,000.00)	1.000000	$(32,000.00)
1	$ 16,000.00	0.769231	$ 12,307.69
2	$ 20,000.00	0.591716	$ 11,834.32
3	$ 17,000.00	0.455166	$    7,737.82
	NPV		$      (120.16)

Firm should not accept as NPV is negative.

Formula based solution:

NPV @12%= present value of cash inflows – present value of cash outflows

= $16,000/(1+12%)^1 + $20,000/(1+12%)^2 + $17,000/(1+12%)^3 - $32,000 = $10,329.86

NPV @30%= present value of cash inflows – present value of cash outflows

= $16,000/(1+30%)^1 + $20,000/(1+30%)^2 + $17,000/(1+30%)^3 - $32,000 = -$120.16