Question

Spandust Industries Inc. is looking at investing in a production facility that will require an initial investment of $500,000. The facility will have a three-year useful life, and it will not have any salvage value at the end of the project’s life. If demand is strong, the facility will be able to generate annual cash flows of $255,000, but if demand turns out to be weak, the facility will generate annual cash flows of only $120,000. Spandust Industries Inc. thinks that there is a 50% chance that demand will be strong and a 50% chance that demand will be weak.

If the company uses a project cost of capital of 12%, what will be the expected net present value (NPV) of this project?

-$49,657

-$27,311

-$24,828

-$34,760

Spandust Industries Inc. could spend $510,000 to build the facility. Spending the additional $10,000 on the facility will allow the company to switch the products they produce in the facility after the first year of operations if demand turns out to be weak in year 1. If the company switches product lines because of low demand, it will be able to generate cash flows of $250,000 in years 2 and 3 of the project.

What is the expected NPV of this project if Spandust Industries Inc. decides to invest the additional $10,000 to give themselves a flexibility option?

$79,276

$35,234

$88,084

$38,427

What will be the value of Spandust Industries Inc.’s flexibility option?

$79,276

$38,427

$35,234

$88,084

Answer 1

Option 1

Cash flow for year 1, C1 = $255,000

Cash flow for year 2, C2 = $255,000

Cash flow for year 3, C3 = $255,000

Initial investment , I = -500,000

cost of capital = 12% = 0.12

NPV of option 1 = [ (C1/(1.12)¹) + (C2/(1.12)²) + (C3/(1.12)³) ]- I

= [ (255,000/1.12) + (255,000/(1.12)²) + (255,000/(1.12)³) ] - 500,000

= [ 227678.5714 + 203284.4388 + 181503.9632 ] - 500,000

= 112,466.973397

Option 2

Cash flow for year 1, C1 = $120,000

Cash flow for year 2, C2 = $120,000

Cash flow for year 3, C3 = $120,000

Initial investment , I = -500,000

NPV of option2 = [ (C1/(1.12)¹) + (C2/(1.12)²) + (C3/(1.12)³) ]- I

= [ (120,000/1.12) + (120,000/(1.12)²) + (120,000/(1.12)³) ] - 500,000

= [ 107142.8571 + 95663.26531 + 85413.62974 ] - 500,000

= -211,780.247813

expected net present value (NPV) of the project = (0.50*NPV of option 1) + (0.50* NPV of option 2) = (0.50*112,466.973397)+(0.50*-211,780.247813)

= -49656.64 or -49657( after rounding off to 2 decimal places)

2)

when demand is low in year 1

Cash flow for year 1, C1 = $120,000

Cash flow for year 2, C2 = $250,000

Cash flow for year 3, C3 = $250,000

Initial investment , I = -510,000

NPV 1 = [ (C1/(1.11)¹) + (C2/(1.11)²) + (C3/(1.11)³) ]- I

= [ (250,000/1.11) + (250,000/(1.11)²) + (250,000/(1.11)³) ] - 510,000

= [ 107142.8571 + 199298.4694 + 177945.062 ] -510,000

= -25613.61

NPV when demand is good

Cash flow for year 1, C1 = $255,000

Cash flow for year 2, C2 = $255,000

Cash flow for year 3, C3 = $255,000

Initial investment , I = -510,000

cost of capital = 12% = 0.12

NPV = [ (C1/(1.12)¹) + (C2/(1.12)²) + (C3/(1.12)³) ]- I

= [ (255,000/1.12) + (255,000/(1.12)²) + (255,000/(1.12)³) ] - 510,000

= [ 227678.5714 + 203284.4388 + 181503.9632 ] - 510,000

= 102,466.973397

Expected NPV with option = (0.5* NPV 1)+(0.5*NPV 2) = (0.5*-25613.61)+(0.5*102,466.973397) = 38,426.68 or 38,427 ( after rounding off)

3)

value of Spandust Industries Inc.’s flexibility option = Expected NPV with option - Expected NPV = 38,426.68 - (-49,656.64) = 38,426.68 + 49,656.64 = $88,084