Question

Spring Fish Fine Foods has $1,830,000 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 $600,000 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 $510,000 for the next six years. If the appropriate discount rate for the deli expansion is 9.4% 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 annual annuity.

a) If the appropriate discount rate for the deli expansion is 9.4%, what is the NPV of the deli expansion?

b) If the appropriate discount rate for the wine section is 9.0%, what is the NPV of the wine section?

c) What is the adjusted NPV equivalent annual annuity of the deli expansion?

d) What is the adjusted NPV equivalent annual annuity of the wine section?

Answer 1

First, we build the cash flow schedule as below:

Year	cash flow -Project 1	cash flow -Project 2
0	($1,830,000)	($1,830,000)
1	$600,000	$510,000
2	$600,000	$510,000
3	$600,000	$510,000
4	$600,000	$510,000
5	$600,000	$510,000
6		$510,000

(a) NPV of Project 1 is calculated using the NPV function in Excel with these inputs :

rate = 9.4%

values = array of cells with the cash flows

NPV = $438,546

(b)

NPV of Project 2 is calculated using the NPV function in Excel with these inputs :

rate = 9%

values = array of cells with the cash flows

NPV = $420,017

(c) adjusted NPV equivalent annual annuity = (r * NPV) / (1 - (1 + r)^-n)

where r = discount rate

n = project life

adjusted NPV equivalent annual annuity of the deli expansion = (0.094 * 438,546) / (1 - (1 + 0.094)^-5)

adjusted NPV equivalent annual annuity of the deli expansion = $113,919

(d)

adjusted NPV equivalent annual annuity = (r * NPV) / (1 - (1 + r)^-n)

where r = discount rate

n = project life

adjusted NPV equivalent annual annuity of the wine expansion = (0.09 * 420,017) / (1 - (1 + 0.09)^-6)

adjusted NPV equivalent annual annuity of the wine expansion = $93,630