Question

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 7 years, and produce annual cash flows of $ 15,000 per year. The alternative is the​ deluxe, award-winning​ Smoke-alator, which costs $ 80,000 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 $ 22,000 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.) ANSWER:

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

Rib​ & Wings-R-Us should purchase the Smoke-alator or standard smoker. ANSWER:

Answer 1

Equivalent Annual Annuity (EAA) of the standard smoker

Period	Annual Cash Flow ($)	Present Value factor at 10%	Present Value of Cash Flow ($)
1	15,000	0.909091	13,636
2	15,000	0.826446	12,397
3	15,000	0.751315	11,270
4	15,000	0.683013	10,245
5	15,000	0.620921	9,314
6	15,000	0.564474	8,467
7	15,000	0.513158	7,697
TOTAL		4.868419	73,026

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $73,026 - $50,000

= $23,026

Equivalent Annual Annuity (EAA) of the standard smoker

Equivalent Annual Annuity (EAA) of the standard smoker = Net Present Value / (PVIFA 10%, 7 Years)

= $23,026 / 4.868419

= $4,730

Equivalent Annual Annuity (EAA) of the Smoke-alator

Period	Annual Cash Flow ($)	Present Value factor at 10%	Present Value of Cash Flow ($)
1	22,000	0.909091	20,000
2	22,000	0.826446	18,182
3	22,000	0.751315	16,529
4	22,000	0.683013	15,026
5	22,000	0.620921	13,660
6	22,000	0.564474	12,418
7	22,000	0.513158	11,289
8	22,000	0.466507	10,263
9	22,000	0.424098	9,330
10	22,000	0.385543	8,482
11	22,000	0.350494	7,711
12	22,000	0.318631	7,010
13	22,000	0.289664	6,373
TOTAL		7.103356	1,56,274

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $156,274 - $80,000

= $76,274

Equivalent Annual Annuity (EAA) of the Smoke-alator

Equivalent Annual Annuity (EAA) of the Smoke-alator = Net Present Value / (PVIFA 10%, 13 Years)

= $76,274 / 7.103356

= $10,738

DECISION

Rib​ & Wings-R-Us should purchase the “SMOKE-ALATOR”, since the EAA of the Smoke-alator is higher than the EAA of the standard smoke.