Question

NPV unequal lives.

Grady Enterprises is looking at two project opportunities for a parcel of land the company currently owns. The first project is a​restaurant, and the second project is a sports facility. The projected cash flow of the restaurant is an initial cost of $1,560,000 with cash flows over the next six years of ​$200,000 ​(year one), ​$300,000 ​(year two), $310,000 ​(years three through​five), and ​$1,710,000 ​(year six), at which point Grady plans to sell the restaurant. The sports facility has the following cash​flows: an initial cost of ​$2,310,000 with cash flows over the next four years of ​$450,000 ​(years one through​ three) and $3,390,000​ (year four), at which point Grady plans to sell the facility. If the appropriate discount rate for the restaurant is 10.5% and the appropriate discount rate for the sports facility is 12.0%, use the NPV to determine which project Grady should choose for the parcel of land. Adjust the NPV for unequal lives with the equivalent annual annuity. Does the decision​ change?

1. If the appropriate discount rate for the restaurant is 10.5%, what is the NPV of the restaurant​project?

2. If the appropriate discount rate for the sports facility is 12.0%, what is the NPV of the sports​facility?

3. Based on the​ NPV, Grady should pick the ______

4. What is the adjusted NPV equivalent annual annuity of the restaurant​ project?

5. What is the adjusted NPV equivalent annual annuity of the sports​ facility?

6. Based on the adjusted​ NPV, Grady should pick the ______

7. Does the decision​ change?

Answer 1

Solution

On the basis of information provided, following cash flow chart can be drawn,

Year	Restaurant Project	Sports Facility Project
0	-1560000	-2310000
1	200000	450000
2	300000	450000
3	310000	450000
4	310000	3390000
5	310000	-
6	1710000	-

Now under given scenario, Net Present Values will be calculated as follows,

Year	Restaurant Project	Sports Facility Project
Cash Flow	PVIF @ 10.50%	Discounted Cash Flow	Cash Flow	PVIF @ 12%	Discounted Cash Flow
0	-1560000	1.000	-1560000	-2310000	1.000	-2310000
1	200000	0.905	181000	450000	0.893	401850
2	300000	0.819	245700	450000	0.797	358650
3	310000	0.741	229710	450000	0.712	320400
4	310000	0.671	208010	3390000	0.636	2156040
5	310000	0.607	188170
6	1710000	0.549	938790
NET PRESENT VALUE			431380			926940

Therefore, on the basis of NPV, Sports Facility Option should be chosen as it is yielding higher NPV.

Now, under equivalent annual annuity method, adjusted NPV will be as follows,

Project	Net Present Value	Rate	Terms	PVAF	Adjusted NPV under Equivalent Annual Annuity
Restaurant	431380	10.50%	6	4.292	100508
Sports Facility	926940	12%	4	3.037	305216

Therefore, under equivalent annual annuity method, Sports Facility Option should be chosen again as the adjusted NPV is still higher.

Answer:
1. NPV of Restaurant Facility = 431380
2. NPV of Sports Facillity = 926940
3. Based on NPV, Grady should pick Sports Facility project
4. Adjusted NPV of Restaurant Facility = 100508
5. Adjusted NPV of Sports Facility = 305216
6. Based on adjusted NPV, Grady should pick Sports Facility project
7. There is no change in decision