Question

​(Equivalent annual annuity​)

Rib​ & Wings-R-Us is considering the purchase of a new smoker oven for cooking​ barbecue, ribs, and wings. It is looking at two different ovens. The first is a relatively standard smoker and would cost $50,000​, last for 8 ​years, and produce annual cash flows of

$16,000 per year. The alternative is the​ deluxe, award-winning​ Smoke-alator, which costs $78,000 ​and, because of its patented humidity​ control, produces the​ "moistest, tastiest barbecue in the​ world." The​ Smoke-alator would last for 11 years and produce cash flows of $23,000 per year. Assuming a required rate of return of 10 percent on both​ projects, compute their equivalent annual annuities ​(EAAs​).

The EAA of the standard smoker is ​$______​(Round to the nearest​ dollar.)

The EAA of the​ Smoke-alator is ​$______ ​(Round to the nearest​ dollar.)

Rib​ & Wings-R-Us should purchase the ▼ Smoke-alator or standard smoker . ​(Select from the​ drop-down menu.)

Answer 1

Calculation of EAA of two smokers
Year	Standard Smoker	Smoke alator
Cash flows	Discount Factor @10%	Discounted Cashflows	Cash flows	Discount Factor @10%	Discounted Cashflows
A	B	C = 1/(1+10%)^A	D = B*C	E	F = 1/(1+10%)^A	G = E*F
0	-50000	1	-50000	-78000	1	-78000
1	16000	0.909090909	14545.45455	23000	0.909090909	20909.09091
2	16000	0.826446281	13223.1405	23000	0.826446281	19008.26446
3	16000	0.751314801	12021.03681	23000	0.751314801	17280.24042
4	16000	0.683013455	10928.21529	23000	0.683013455	15709.30947
5	16000	0.620921323	9934.741169	23000	0.620921323	14281.19043
6	16000	0.56447393	9031.582881	23000	0.56447393	12982.90039
7	16000	0.513158118	8210.529892	23000	0.513158118	11802.63672
8	16000	0.46650738	7464.118083	23000	0.46650738	10729.66974
9		0.424097618	0	23000	0.424097618	9754.245223
10		0.385543289	0	23000	0.385543289	8867.495657
11		0.350493899	0	23000	0.350493899	8061.359688
NPV			35358.81917			71386.40312
EAA of standard smoker =	[r * NPV] / [1 - (1+r)^-n]
	=	[10% * $35,358.81917] / [1 - (1+10%)^-8]
	=	$3,535.881917 / 0.53349262
	=        $6,627.799121
	=        $6,628
EAA of Smoke Alator       =	[r * NPV] / [1 - (1+r)^-n]
	=	[10% * $71,386.40312] / [1 - (1+10%)^-11]
	=	$7,138.640312 / 0.649506101
	=        $10,990.87492
	=        $10,991
EAA of Standard Smoker is $6,628
EAA of Smoke Alator is $10,991
Rib & Wings- R-Us should purchase the Smoke Alator since EAA of Smoke Alator is higher EAA of Standard Smoker