Question

SIMPLE EXAMPLE: A company must decide whether to invest $100 Million in developing and implementing a new enterprise system in the face of considerable technological and market (demand for product and market share) uncertainty. The firm's cost of capital is 10%.

1. Evaluate Using NPV Analysis

There can be a good and bad result for this investment.

Good Result: A good result has a probability of .5 of occurring. Here the planned cost reductions have been realized and better integration of the supply chain is possible. These benefits are leveraged by strong market demand for the firm's product. There have also been feedback benefits, the enterprise system has significantly improved perceived quality and service from the customer's point of view. Annual benefits under this scenario equal $15 million in after tax cash flow per year forever.

Bad Result: The system proves to be more difficult to implement and improvements in management of the supply chain are less. In addition, the growth in market demand for the product is lower. Annual benefits under this scenario are $2 million in after tax cash flow per year.

Using traditional "all or nothing" NPV analysis, we get the following

Year 0 (now) cash flows: $-100 million for ERP purchase and implementation

Year 1, 2, 3…etc. cash flows (after tax):

(a)    good result: $+15 million/year (prob. = .5)

(b)   bad result: $+2 million/year (prob. = .5)

Expected annual cash flows for year 1 and forward:

$15 mil * .5 + $2 mil * .5 = $7.5 mil + $1 mil = $8.5 mil

The value of these expected after tax cash flows (a perpetuity) = $8.5/COC = $8.5/.10 = $85 mil

Then the NPV of this investment = $-100 mil + $85 mil = $-15 mil

The decision is: DO NOT UNDERTAKE THE INVESTMENT

2. Real Options Approach (all cash flows are after tax)

The real options alternative allows for flexibility and the delay of the investment for 1 year. In this case, if we do a pilot project we will be better able to evaluate ERP implementation complexities, achievable supply chain benefits, and the market share our products will achieve. However, the cost of the project will rise to $110 Million ($10 Million this year and $100 Million next year) with the one-year delay and additionally management decides to purchase and implement the financial module in year 1 at a cost of $10 Million (real option).

The results are slightly different:

Year 0 (now) cash flows: $10 million for the pilot project, the financial module

After year 1, if the conditions indicate a good result, the firm will invest the $100 million for the ERP with expected benefits (cash flows) of $15 million annually beginning in year 2. Benefits in year one from the financial module are $1 million.

If a bad result is indicated, the firm makes no further investments beyond the financial module, which yield annual benefits of $.5 million in year 1 and each year there after.

Here the firm has flexibility and has exercised its option to make no further investments based on better information/knowledge of expected future benefits.

Let's evaluate the NPV of this project using the described real option.

Present value of cash outflows: $-10 mil - $100 mil/(1+COC) * .5 = -$55.45 mil

Present value of expected cash inflows:

Good result (expected value): {$1 mil/(1+COC) + [($15 mil/COC)/(1+COC)] }* .5 = $68.64 mil

Bad Result (expected value): {$.5 mil/(1+COC) + [($.5 mil/ COC)/(1+COC)] }* .5 = $2.50 mil

Total NPV of expected cash inflows = $68.64 mil + $2.50 mil = $71.14 mil

NPV of the project = -$55.45 mil + $71.14 mil = $15.69 mil

The right decision here is DO THE PILOT PROJECT

Real Options Homework This is an individual assignment.

Please refer to Practice Problem I (not the "more difficult" one) in the Session 7 Conference. The assignment is to evaluate both parts, the traditional NPV calculation as well as the Real Options approach. The probability of a successful pilot project is now .75 (instead of .5) and the probability of an unsuccessful pilot is .25 (instead of .5). What is the expected NPV in each case now? What do you recommend? Why? If you don't know the probability of success for the pilot, is there a value that is critical to your recommendation? Is there a probability of success above or below which you will recommend undertaking the pilot and below or above which you will recommend a go/ no go decision on the underlying project without undertaking a pilot test?

Answer 1

Conventional NPV Analysis

Good Result : $100 million invested in Year 0, and $15 million receives as benefit in perpetuitry

NPV = Present Value of all inflow - Present Value of Outflow

  = 15 / 0.10 - 100 * PVIF (10%,0)

= 150 - 100 * 1

= 150 - 100 = $50 million

Note: Present value of perpetutity is (1 / discounting rate ) and Present value Interest Factor (PVIF) is 1 at 0 year at any rate.

Bad Result : $100 million invested in Year 0, and $2 million receives as benefit in perpetuitry

NPV = Present Value of all inflow - Present Value of Outflow

  = 2 / 0.10 - 100 * PVIF (10%,0)

= 20 - 100 * 1

= 20 - 100 = - $80 million

Note: Present value of perpetutity is (1 / discounting rate ) and Present value Interest Factor (PVIF) is 1 at 0 year at any rate.

Probability	0.75	0.25
NPV	$50	- $80
Expected NPV		$17.50

Real Option Approach

Good Result :

Year	Cash Outflow	Cash Inflow
0	- $10 million	-
1	- $100 million	$1 million

and $15 million annual benefit in perpetutiy (starting from year 2)

NPV = Present Value of all inflow - Present Value of Outflow

= $1 * PVIF (10%,1) + ( $15/ 0.10 ) * PVIF(10%,1) - [ $10 * PVIF (10%,0) +  $100 * PVIF (10%,1) ]

= ( 1 * 0.9091 + 150 * 0.9091 ) - ( 10 * 1 + 100 * 0.9091 )

= ( 0.9091 + 136.37 ) - ( 10 + 90.91 )

= 137.27 - 100.91

= $36.36

Note: PVIF can be derived from PVIF table of PVIF formula = 1/(1+r)ⁿ . from beginning of year 2 perpetuity started so we take PVIF at year 1.

Bad Result : $10 million invested in Year 0, and $0.5 million receives as benefit in perpetuitry

NPV = Present Value of all inflow - Present Value of Outflow

  = 0.5 / 0.10 - 10 * PVIF (10%,0)

= 5 - 10 * 1

= 5 - 10 = - $5 million

Probability	0.75	0.25
NPV	$36.36	- $5
Expected NPV		$26.02

NPV under Real Option Approach is $26.02 million and NPV under Conventional NPV Analysis is $17.50 million. So in Real option NPV of $8.52 million higher than Conventional NPV.

This Project can be accepted in any case as expected NPVs are positive in both cases.

In the Real Option Approach has high value of $8.52 million because it increases the value of project by reducing the uncertanity.

I recommend the company should spend $10 million in year 0 to evaluate project implementation as well as market conditions before make any decision regarding additional investment in Year 1.

If assume forecasted benefits accurate, the critical value for determine expected NPV would be probability of Success.

If probability is unknown, we will do breakeven or sensitivity analysis.

For derive probability I use here "Goal Seek" function of Excel.

Step 1 :

Step 2 :

In set Cell we choose cell where formula is applicable.

To vale : In this we put value which we want to derive.

By changing cell : select cell which change the answer is affected, here probability cell.

So we get below table

Probability	0.54	0.46
NPV	$36.36	- $5
Expected NPV		$17.50

This NPV is under conventional NPV analysis, for getting break even probability. If probability of success is more than 0.54, Real Option Approach has positive Value.