Question

Singing Fish Fine Foods has

​$2,020,000

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

​$570,000

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

​$490,000

for the next six years. If the appropriate discount rate for the deli expansion is

9.6​%

and the appropriate discount rate for the wine section is

8.9​%,

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

NPV analysis

Deli
Discount rate	9.600%
Year	0	1	2	3	4	5
Cash flow stream	-2020000	570000	570000	570000	570000	570000
Discounting factor	1.000	1.096	1.201	1.317	1.443	1.581
Discounted cash flows project	-2020000.000	520072.993	474519.154	432955.432	395032.329	360430.957
NPV = Sum of discounted cash flows
NPV Deli =	163010.86
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Wine
Discount rate	8.900%
Year	0	1	2	3	4	5	6
Cash flow stream	-2020000	490000	490000	490000	490000	490000	490000
Discounting factor	1.000	1.089	1.186	1.291	1.406	1.532	1.668
Discounted cash flows project	-2020000.000	449954.086	413180.979	379413.204	348405.146	319931.264	293784.448
NPV = Sum of discounted cash flows
NPV Wine =	184669.13
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Choose wine section as it has higher NPV

EAA analysis

Deli
Discount rate	9.600%
Year	0	1	2	3	4	5
Cash flow stream	-2020000.000	570000.000	570000.000	570000.000	570000.000	570000.000
Discounting factor	1.000	1.096	1.201	1.317	1.443	1.581
Discounted cash flows project	-2020000.000	520072.993	474519.154	432955.432	395032.329	360430.957
NPV = Sum of discounted cash flows
NPV Deli =	163010.86
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
Equvalent annuity(EAA)=	33750.75
Required rate =	9.600%
Year	0	1	2	3	4	5
Cash flow stream	33750.75	33750.75	33750.75	33750.75	33750.75	33750.75
Discounting factor	1.000	1.096	1.201	1.317	1.443	1.581
Discounted cash flows project	33750.753	30794.483	28097.156	25636.091	23390.594	21341.783
Sum of discounted future cashflows =	163010.86
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Wine
Discount rate	8.900%
Year	0	1	2	3	4	5	6
Cash flow stream	-2020000.000	490000.000	490000.000	490000.000	490000.000	490000.000	490000.000
Discounting factor	1.000	1.089	1.186	1.291	1.406	1.532	1.668
Discounted cash flows project	-2020000.000	449954.086	413180.979	379413.204	348405.146	319931.264	293784.448
NPV = Sum of discounted cash flows
NPV Wine =	184669.13
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
Equvalent annuity(EAA)=	33580.33
Required rate =	8.900%
Year	0	1	2	3	4	5	6
Cash flow stream	33580.33	33580.33	33580.33	33580.33	33580.33	33580.33	33580.33
Discounting factor	1.000	1.089	1.186	1.291	1.406	1.532	1.668
Discounted cash flows project	33580.328	30835.930	28315.822	26001.673	23876.651	21925.300	20133.425
Sum of discounted future cashflows =	184669.13
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Choose Deli as it has higher EAA