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 $ 52,000 last for 9 ?years, and produce annual cash flows of $ 18,000 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 13 years and produce cash flows of $ 24,000 per year. Assuming a required rate of return of 11 percent on both? projects, compute their equivalent annual annuities (EAAs?).

Answer 1

Discount rate	11.0000%
Cash flows	Year	Discounted CF= cash flows/(1+rate)^year	Cumulative cash flow
(52,000.00)	0	(52,000.00)	(52,000.00)
18,000.000	1	16,216.22	(35,783.78)
18,000.000	2	14,609.20	(21,174.58)
18,000.000	3	13,161.44	(8,013.14)
18,000.000	4	11,857.16	3,844.02
18,000.000	5	10,682.12	14,526.15
18,000.000	6	9,623.54	24,149.68
18,000.000	7	8,669.85	32,819.53
18,000.000	8	7,810.68	40,630.21
18,000.000	9	7,036.65	47,666.86

PV = 47,666.86, FV = 0, N = 9, rate = 11%

Use PMT function in Excel

EAA = 8,608.71

Discount rate	11.0000%
Cash flows	Year	Discounted CF= cash flows/(1+rate)^year	Cumulative cash flow
(78,000.00)	0	(78,000.00)	(78,000.00)
24,000.000	1	21,621.62	(56,378.38)
24,000.000	2	19,478.94	(36,899.44)
24,000.000	3	17,548.59	(19,350.85)
24,000.000	4	15,809.54	(3,541.30)
24,000.000	5	14,242.83	10,701.53
24,000.000	6	12,831.38	23,532.91
24,000.000	7	11,559.80	35,092.71
24,000.000	8	10,414.24	45,506.95
24,000.000	9	9,382.19	54,889.14
24,000.000	10	8,452.43	63,341.57
24,000.000	11	7,614.80	70,956.37
24,000.000	12	6,860.18	77,816.55
24,000.000	13	6,180.34	83,996.89

PV = 83,996.89, FV = 0, N = 13 , rate =11%

use PMT funciton in Excel

EAA = 12,444.22

so the second one is better