Question

Fantastic Flooring (FF) is a carpet wholesale company. FF is considering building a new inventory warehouse for $800,000. The warehouse would allow FF to increase their pre-tax cash flows by $98,000 each year. The company would plan to use the warehouse for 20 years before selling it for $200,000. The company uses straight-line depreciation. FF’s tax rate is 30%, and the required rate of return is 8%.

What is the Excess Present Value Index of the proposed investment (rounded to 3rd decimal places)?

Select one or more:

a. 0.354

b. 0.759

c. 1.006

d. 1.643

e. 1.000

Answer 1

Solution

Fantastic Flooring (FF) has furnished the given information

Initial Outflow = $ 800000

Life of the asset = 20 years

Salvage value at the end of 20 years = $ 200000

Depreciation per year under Straight Line Method = (Initial Outflow - Salvage value) / Life of the asset

= $ [ (800000 - 200000) / 20]

= $ (600000 / 20)

= $ 30000

Pre-tax Cash flow = $ 98000

Rate of Tax = 30%, or 0.30 per $

Net Cash flow after tax = [ ( Pre-tax Cash flow - Depreciation ) X (1 - Tax%) ] + Depreciation

= $ [ ( 98000 - 30000 ) X ( 1 - 0.30) ] + 30000

= $ ( 68000 X 0.70 ) + 30000

= $ ( 47600 + 30000 )

= $ 77600

So the required information are as follows,

Initial Outflow = $ 800000

Annual Cash Flow after Tax = $ 77600

Salvage value = $ 200000

Required rate of return (r) = 8% or 0.08 per $

Period (n) = 20 years

Present value of interest factor of 8% for 20 years = 1 / (1+r) ^ n

= 1 / (1 + 0.08) ^ 20

= 0.2145 (Approx)

Present value of interest factor of annuity of 8% for 20 years = [ 1 - (1+r) ^ (-n) ] / r

= [ 1 - (1 + 0.08) ^ (-20) ] / 0.08

= 9.8181 (Approx)

(Note: Instead of this formula, PV table can be also used, if found more convenient)

Discounted cash flow after tax = Annual Cash flow X Present value of interest factor of annuity

= $ (77600 X 9.8181)

= $ 761885 (Approx)

Present value of salvage value = Salvage value X PV factor at the terminal year

= $ (200000 X 0.2145)

= $ 42900

Net Present Value = (Discounted cash flow + Present value of salvage value) - Initial Outflow

= $ [ ( 761885 + 42900 ) - 800000 ]

= $ ( 804785 - 800000 )

= $ 4785

Present Value index = ( NPV + Initial Investment) / Initial Investment

= ( 4785 + 800000 ) / 800000

= 804785 / 800000

= 1.006 (Approx)

Answer: Therefore the answer is (c) 1.006 using the given parameters