ABC is considering a project that has an up-front after tax cost at t = 0 of $1,

Question

ABC is considering a project that has an up-front after tax cost at t = 0 of $1,000,000. The project’s subsequent cash flows critically depend on whether its products become the industry standard. There is a 70 percent chance that the products will become the industry standard, in which case the project’s expected after- tax cash flows will be $900,000 at the end of each of the next three years (t = 1,2,3). There is a 30 percent chance that the products will not become the industry standard, in which case the after-tax expected cash flows from the project will be $200,000 at the end of each of the next three years (t = 1,2,3). NI will know for sure one year from today whether its products will have become the industry standard. It is considering whether to make the investment today or to wait a year until after it finds out if the products have become the industry standard. If it waits a year, the project’s up-front cost at t = 1 will remain at $1,000,000 (certain cash flow). If it chooses to wait, the estimated subsequent after-tax cash flows will remain at $900,000 per year if the product becomes the industry standard, and $200,000 per year if the product does not become the industry standard. There is no penalty for entering the market late. Assume that all risky cash flows are discounted at 8 percent and risk-free rate is 5 percent.

Please show work so I can learn.

1) What is the expected NPV of the project if NI proceeds today?

2) If NI chooses to wait a year before proceeding, what will be the project’s new NPV?

Explanation / Answer

1)

Calculate the expected NPV of the project if NI proceeds today:

At 70% probability:

Year

Cash flows

Discounting
factor @ 8%

Discounted
cash flows

0

$ (1,000,000)

1

$        (1,000,000)

1

$       900,000

0.92593

$              833,337

2

$       900,000

0.85734

$              771,606

3

$       900,000

0.79383

$              714,447

NPV

$           1,319,390

At 30% probability:

Year

Cash flows

Discounting
factor @ 5%

Discounted
cash flows

0

$ (1,000,000)

1

$        (1,000,000)

1

$       200,000

0.95238

$              190,476

2

$       200,000

0.90703

$              181,406

3

$       200,000

0.86384

$              172,768

NPV

$            (455,350)

Total = ($1,319,390 * 70%) + (-$455,350 * 30%)

= $923,573 - $136,605

=$786,968

Therefore, expected NPV of the project NI proceeds today is $786,968.

2)

Calculate NI chooses to wait a year before proceeding, what will be the project’s new NPV:

At 70% probability:

Year

Cash flows

Discounting
factor @ 8%

Discounted
cash flows

0

$ (1,000,000)

1

$        (1,000,000)

1

$       900,000

0.92593

$              833,337

2

$       900,000

0.85734

$              771,606

3

$       900,000

0.79383

$              714,447

4

$       900,000

0.73503

$              661,527

NPV

$           1,980,917

At 30% probability:

Year

Cash flows

Discounting
factor @ 5%

Discounted
cash flows

0

$ (1,000,000)

1

$        (1,000,000)

1

$       200,000

0.95238

$              190,476

2

$       200,000

0.90703

$              181,406

3

$       200,000

0.86384

$              172,768

4

$       200,000

0.8227

$              164,540

NPV

$            (290,810)

Total = ($1,980,917 *70%) + (-$290,810 *30%)

= $1,386,642 - $87,243

= $1,299,399

Year

Cash flows

Discounting
factor @ 8%

Discounted
cash flows

0

$ (1,000,000)

1

$        (1,000,000)

1

$       900,000

0.92593

$              833,337

2

$       900,000

0.85734

$              771,606

3

$       900,000

0.79383

$              714,447

NPV

$           1,319,390

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