Question

Hack Wellington Co. is considering a three-year project that will require an initial investment of $35,000. It has estimated that the annual cash flows for the project under good conditions will be $70,000 and $11,000 under bad conditions. The firm believes that there is a 60% chance of good conditions and a 40% chance of bad conditions.

If the firm is using a weighted average cost of capital of 11.0000%, what will be the expected net present value (NPV) of the project?

$47,033

$58,791

$78,388

$66,630

Hack Wellington Co. wants to take a potential growth option into account when calculating the project’s expected NPV. If conditions are good, the firm will be able to invest $3,000 in year 2 to generate an additional cash flow of $23,000 in year 3. If conditions are bad, the firm will not make any further investments in the project.

Using the information from the preceding problem, determine what the expected NPV of this project will be when taking the growth option into account.

$82,667

$100,071

$87,018

$104,422

What is the value of Hack Wellington Co.’s growth option?

$9,493

$7,336

$9,062

$8,630

Answer 1

Option 1

Cash flow for year 1, C1 = $70,000

Cash flow for year 2, C2 = $70,000

Cash flow for year 3, C3 = $70,000

Initial investment , I = -35000

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

= [ (70,000/1.11) + (70,000/(1.11)²) + (70,000/(1.11)³) ] - 35000

= [ 63063.06306 + 56813.57033 + 51183.39669 ] - 35000

= 136,060.030081

Option 2

Cash flow for year 1, C1 = $11000

Cash flow for year 2, C2 = $11000

Cash flow for year 3, C3 = $11000

Initial investment , I = -35000

NPV of option2 = [ (C1/(1.11)¹) + (C2/(1.11)²) + (C3/(1.11)³) ]- I

= [ (11000/1.11) + (11000/(1.11)²) + (11000/(1.11)³) ] - 35000

= [ 9909.90991 + 8927.846766 + 8043.105194 ] - 35000

= -8119.138130

expected net present value (NPV) of the project = (0.60*NPV of option 1) + (0.40* NPV of option 2) = (0.60*136,060.030081)+(0.40*-8119.138130)

= 78,388.36 or 78,388( after rounding off to 2 decimal places)

2)

when conditions are good

Cash flow for year 1, C1 = $70,000

Cash flow for year 2, C2 = $70,000 - 3000 = 67000

Cash flow for year 3, C3 = $70,000 + 23000 = 93000

Initial investment , I = -35000

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

= [ (70,000/1.11) + (67000/(1.11)²) + (93000/(1.11)³) ] - 35000

= [ 63063.06306 + 54378.70303 + 68000.79846 ] -35000

= 150,442.564551

Expected NPV with growth = (0.6* NPV of option 1)+(0.4*NPV of option2) = (0.6*150,442.564551)+(0.4*-8119.138130) = 87017.88 or 87018 ( after rounding off)

3)

Value of option = Expected NPV with growth - Expected NPV = 87017.88 - 78388.36 = 8629.52 or 8630 ( after rounding off )