Question

​(NPV with varying required rates of return​) Gubanich Sportswear is considering building a new factory to produce aluminum baseball bats. This project would require an initial cash outlay of ​$6,000,000 and would generate annual free cash inflows of ​$1,000,000 per year for 6 years. Calculate the​ project's NPV ​given:
a. A required rate of return of 9 percent

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b. A required rate of return of 11 percent

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c. A required rate of return of 14 percent

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d. A required rate of return of 17 percent

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Answer 1

a.	NPV	$ -15,14,081.41
Working;
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.09)^-6)/0.09		i	9%
	=	4.48591859		n	6
Present value of cash inflows	=	Annual cash inflows	x	Present value of annuity of 1	=	$       10,00,000	x	4.485919	=	$   44,85,918.59
Less Initial cash outlay										$   60,00,000.00
NPV										$ -15,14,081.41
b.	NPV	$ -17,69,462.15
Working;
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.11)^-6)/0.11		i	11%
	=	4.230537854		n	6
Present value of cash inflows	=	Annual cash inflows	x	Present value of annuity of 1	=	$       10,00,000	x	4.230538	=	$   42,30,537.85
Less Initial cash outlay										$   60,00,000.00
NPV										$ -17,69,462.15
c.	NPV	$ -21,11,332.48
Working;
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.14)^-6)/0.14		i	14%
	=	3.888667517		n	6
Present value of cash inflows	=	Annual cash inflows	x	Present value of annuity of 1	=	$       10,00,000	x	3.888668	=	$   38,88,667.52
Less Initial cash outlay										$   60,00,000.00
NPV										$ -21,11,332.48
d.	NPV	$ -24,10,815.25
Working;
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.17)^-6)/0.17		i	17%
	=	3.589184754		n	6
Present value of cash inflows	=	Annual cash inflows	x	Present value of annuity of 1	=	$       10,00,000	x	3.589185	=	$   35,89,184.75
Less Initial cash outlay										$   60,00,000.00
NPV										$ -24,10,815.25