Question

NPV unequal lives. Singing Fish Fine Foods has ​$2,030,000 for capital investments this year and is considering two potential projects for the funds. Project 1 is updating the​ store's deli section for additional food service. The estimated​ after-tax cash flow of this project is ​$620,000 per year for the next five years. Project 2 is updating the​ store's wine section. The estimated annual​ after-tax cash flow for this project is ​$480,000 for the next six years. If the appropriate discount rate for the deli expansion is 9.3​% and the appropriate discount rate for the wine section is 9.0​%, use the NPV to determine which project Singing Fish should choose for the store. Adjust the NPV for unequal lives with the equivalent annual annuity. Does the decision​ change?

Answer 1

Net Present Value - Store's Deli Section

Year	Annual Cash Flow ($)	Present Value factor at 9.30%	Present Value of Cash Flow ($)
1	6,20,000	0.91491	5,67,246.11
2	6,20,000	0.83707	5,18,980.89
3	6,20,000	0.76584	4,74,822.41
4	6,20,000	0.70068	4,34,421.23
5	6,20,000	0.64106	3,97,457.67
TOTAL		3.85956	23,92,928.30

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

= $23,92,928.30 - $20,30,000

= $3,62,928.30

Net Present Value - Store's Wine Section

Year	Annual Cash Flow ($)	Present Value factor at 9%	Present Value of Cash Flow ($)
1	4,80,000	0.91743	4,40,366.97
2	4,80,000	0.84168	4,04,006.40
3	4,80,000	0.77218	3,70,648.07
4	4,80,000	0.70843	3,40,044.10
5	4,80,000	0.64993	3,11,967.07
6	4,80,000	0.59627	2,86,208.32
TOTAL		4.48592	21,53,240.92

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

= $21,53,240.92 - $20,30,000

= $1,23,240.92

Decision based on Net Present Value Analysis

Singing Fish should choose the Store's Deli Section, since it has the highest Net Present Value of $3,62,928.30 as compared to the Net Present Value of Store's Wine Section.

Equivalent Annual Annuity (EAA) - Store's Deli Section

Equivalent Annual Annuity (EAA) = Net Present Value / (PVIFA 9.30%, 5 Years)

= $3,62,928.30 / 3.85956

= $94,033.55

Equivalent Annual Annuity (EAA) - Store's Wine Section

Equivalent Annual Annuity (EAA) = Net Present Value / (PVIFA 9%, 6 Years)

= $1,23,240.92 / 4.48592

= $27,472.84

Decision based on Equivalent Annual Annuity

Singing Fish should choose the Store's Deli Section, since it has the highest Equivalent Annual Annuity of $94,033.55 as compared to the Equivalent Annual Annuity of Store's Wine Section.

NOTE

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.