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 $ 49,000 , last for 9 years, and produce annual cash flows of $ 14,000 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 $20,000 per year. Assuming a required rate of return of 8 percent on both projects, compute their equivalent annual annuities (EAAs ).

The EAA of the standard smoker is $?.

The EAA of the Smoke-alator is $?

Answer 1

Equivalent Annual Annuity ("EAA") = [r*NPV]/[1-(1+r)^-n]

Where, r = rate per period, NPV = Net Present Value, n = number of period

Now, we will evaluate two available options :

1 ) Calculation of EAA for Standard Smoker

Cost of Standard Smoker = $49000

Annual Cash Inflow = $ 14000

Life = 9 Years

On the basis of the above information, we will calculate the NPV of Standard Smoker as follows :

NPV = PV of future cash inflows - initial cost

NPV = $14000*PVAF(8%,9Years) - $49000

NPV = $14000*6.2469 - $49000

NPV = $87456.60 - $ 49000

NPV = $38456.60

Now, we will calculate EAA of Standard Smoker = [r*NPV]/[1-(1+r)^-n]

EAA = [8%*$38456.60 ]/[1-(1+.08)^(-9)]

EAA = $3076.53/(1-.50)

EAA of Standard Smoker = $ 6153.06

2 ) Calculation of EAA for Smoke-alator

Cost of Standard Smoker = $80000

Annual Cash Inflow = $ 20000

Life =13 Years

On the basis of the above information, we will calculate NPV of Smoke-Alator as follows :

NPV = PV of future cash inflows - initial cost

NPV = $20000*PVAF(8%,13Years) - $80000

NPV = $20000*7.9038 - $80000

NPV = $158076 - $ 80000

NPV = $78076

Now, we will calculate EAA of Smoke -Alator = [r*NPV]/[1-(1+r)^-n]

EAA = [8%*$78076]/[1-(1+.08)^(-13)]

EAA = $6246.08/(1-.3677)

EAA = $6246.09/.6323

EAA Smoke-Alator = $ 9878.35