• Define net present value (NPV) from both a mathematical and conceptual viewpoint.
• Discuss the pros and cons of using the NPV method to make capital management decisions.
• Why is the NPV method preferred over the payback method?
• The article lists several common mistakes associated with the NPV method, one of which involves the discount rate. With the knowledge that you have acquired from studying Chapter 5, discuss in detail the issues associated with selecting an appropriate discount rate to calculate the NPV for a long-term project. ARTICLES BELOW

***To receive full credit, students are required to thoroughly answer all questions using a "synthesis- style" approach. A synthesis involves blending summary statements (paraphrased from the article) with reflective insights gleaned from studying the article in conjunction with material from the relevant course module. Each article synthesis should be written at a managerial level. Professionalism is to be maintained throughout each article synthesis submission.

Harvard Business Review:

Budgets And Budgeting

A Refresher on Net Present Value

by Amy Gallo November 19, 2014

Most people know that money you have in hand now is more valuable than money you collect later on. That's because you can use it to make more money by running a business, or buying something now and selling it later for more, or simply putting it in the bank and earning interest. Future money is also less valuable because inflation erodes its buying power. This is called the time value of money. But how exactly do you compare the value of money now with the value of money in the future? That is where net present value comes in.

To learn more about how you can use net present value to translate an investment's value into today's dollars, I spoke with Joe Knight, co-author of Financial Intelligence: A Manager's Guide to Knowing What the Numbers Really Mean and co-founder and owner of www.business-literacy.com.

What is net present value?

"Net present value is the present value of the cash flows at the required rate of return of your project compared to your initial investment, " says Knight. In practical terms, it's a method of calculating your return on investment, or ROI, for a project or expenditure. By looking at all of the money you expect to make from the investment and translating those returns into today's dollars, you can decide whether the project is worthwhile.

What do companies typically use it for?

When a manager needs to compare projects and decide which ones to pursue, there are generally three options available: internal rate of return, payback method, and net present value. Knight says that net present value, often referred to as NPV, is the tool of choice for most financial analysts. There are two reasons for that. One, NPV considers the time value of money, translating future cash flows into today's dollars. Two, it provides a concrete number that managers can use to easily compare an initial outlay of cash against the present value of the return.

"It's far superior to the payback method, which is the most commonly used, " he says. The attraction of payback is that it is simple to calculate and simple to understand: when will you make back the money you put in? But it doesn't take into account that the buying power of money today is greater than the buying power of the same amount of money in the future.

That's what makes NPV a superior method, says Knight. And fortunately, with financial calculators and Excel spreadsheets, NPV is now nearly just as easy to calculate. Managers also use NPV to decide whether to make large purchases, such as equipment or software. It's also used in mergers and acquisitions (though it's called the discounted cash flow model in that scenario). In fact, it's the model that Warren Buffet uses to evaluate companies. Any time a company is using today's dollars for future returns, NPV is a solid choice.

How do you calculate it?

No one calculates NPV by hand, Knight says. There is an NPV function in Excel that makes it easy once you've entered your stream of costs and benefits. (Plug "NPV" into the Help function and you'll get a quick tutorial or you can purchase the HBR Guide to Building Your Business Case + Tools, which includes an easyto-use pre-filled spreadsheet for NPV and the other ROI methods). Many financial calculators also include an NPV function. "A geek like me, I have it on my iPhone. I like to know it's in my pocket, " says Knight. Even if you're not a math nerd like Knight, it's helpful to understand the math behind it. "Even seasoned analysts may not remember or understand the math but it's quite straightforward, " he says. The calculation looks like this:

This is the sum of the present value of cash flows (positive and negative) for each year associated with the investment, discounted so that it's expressed in today's dollars. To do it by hand, you first figure out the present value of each year's projected returns by taking the projected cash flow for each year and dividing it by (1 + discount rate). That looks like this:

If the project has returns for five years, you calculate this figure for each of those five years. Then add them together. That will be the present value of all your projected returns. You then subtract your initial investment from that number to get the NPV. If the NPV is negative, the project is not a good one. It will ultimately drain cash from the business. However, if it's positive, the project should be accepted. The larger the positive number, the greater the benefit to the company. Now, you might be wondering about the discount rate. The discount rate will be company-specific as it's related to how the company gets its funds. It's the rate of return that the investors expect or the cost of borrowing money. If shareholders expect a 12% return, that is the discount rate the company will use to calculate NPV. If the firm pays 4% interest on its debt, then it may use that figure as the discount rate. Typically the CFO's office sets the rate. FURTHER READING The Value of Keeping the Right Customers Article by Amy Gallo A refresher on customer churn rate.

What are some common mistakes that people make?

There are two things that managers need to be aware of when using NPV. The first is that it can be hard to explain to others. As Knight writes in his book, Financial Intelligence, "the discounted value of future cash flows not a phrase that trips easily off the nonfinancial tongue" . Still, he says, it's worth the extra effort to explain and present NPV because of its superiority as a method. He writes, "any investment that passes the net present value test will increase shareholder value, and any investment that fails would (if carried out anyway), actually hurt the company and its shareholders. "

The second thing managers need to keep in mind is that the calculation is based on several assumptions and estimates, which means there's lots of room for error. You can mitigate the risks by double-checking your estimates and doing sensitivity analysis after you've done your initial calculation. There are three places where you can make misestimates that will drastically affect the end results of your calculation. First, is the initial investment. Do you know what the project or expenditure is going to cost? If you're buying a piece of equipment that has a clear price tag, there's no risk. But if you're upgrading your IT system and are making estimates about employee time and resources, the timeline of the project, and how much you're going to pay outside vendors, the numbers can have great variance. Second, there are risks related to the discount rate. You are using today's rate and applying it to future returns so there's a chance that say, in Year Three of the project, the interest rates will spike and the cost of your funds will go up. This would mean your returns for that year will be less valuable than you initially thought. Third, and this is where Knight says people often make mistakes in estimating, you need to be relatively certain about the projected returns of your project. "Those projections tend to be optimistic because people want to do the project or they want to buy the equipment, " he says.

Amy Gallo is a contributing editor at Harvard Business Review, co-host of the Women at Work podcast, and the author of the HBR Guide to Dealing with Conflict. She writes and speaks about workplace dynamics. Watch her TEDx talk on conflict and follow her on Twitter.

2nd Article

Harvard Business Review

Financial Analysis

What Net Present Value Can't Tell You

by Maxwell Wessel

November 20, 2014

Let me pose a question: What's more valuable?

1. Investing 10 million dollars in a program that will return 20 million dollars in 3 years with 100% certainty...or

2. Investing 1 million dollars in a program that will return 3 million dollars in 3 years with 50% certainty?

Basic theory says the first option is more valuable. I can expect to accrue 10 million in profit on an initial investment of 10 million. In the second scenario, if I can find 10 similar investments, I can expect to receive 5 million in profit since I am losing the principle on half of my investments. Even absent the runaway administrative costs that are pervasive in so many corporate organizations, it's easy to see that 10 million is greater than 5 million, so as a corporate finance executive, that's where I'll place my bet.

Easy, right?

Unfortunately, it's potentially too easy. In the above example, the only information I've provided is information about the potential outcomes for the investor in the first three years of an investment's performance. The truth is that most programs don't simply up and disappear after three years. And the longer they can impact your organization, the more difficult it is for people to project their exact financials with any sort of certainty. If I told you that the million-dollar investment was the experiment that led to the Kindle at Amazon, or the iPod at Apple, you'd likely think twice about suggesting that Option A was the more valuable even though it might look that way in a simple spreadsheet. Instead of comparing the above projects with a simple 3-year net present value calculation (all too common in corporate America), more executives need to think of project investments as complex options. A small, uncertain, investment can give us the option on extreme upside, while often a larger, more certain, investment might give us no option value at all. And instead of the simple financial tools we're handed in college courses in corporate finance, when we're valuing projects based on the option value they confer - we need to be very careful to match the valuation methodology to the opportunity. Complex options require a more complex way of thinking about the investment in front of us.

Many of us intuitively understand complex options. Consider young students deciding to track towards surgery in the United States. It's a long, hard road, costing hundreds of thousands of dollars and taking as long as 15 years. But when students evaluate the opportunity, they consider what they could achieve when they finish nd what they need to do to leave the option to surgery the highest-paying specialty open. With their time, money, and psyche, they invest, knowing the only way to miss out entirely is by not investing in their options at all. Venture capitalists pursue investments in much the same fashion. In an interview with New York Magazine, Marc Andreesen recently suggested that the most important question a venture capitalist can ask is, "What if it works?" The best VCs don't invest in the company today, or the projected cash flows they'll receive in 5 years. They look at a young entrepreneur and ask, "If we set out down this path, how large can this business become? How transformational will its technology and information be if it's successful? How many industries will this impact?" Just like the surgeon that sets out to go to college and study biology as a first step towards something bigger, the best Venture Capitalists ensure that both they and their entrepreneurs are leaving their options open to capture the biggest gains at every step of the way. Inside large corporations we make investment decisions differently. Instead of buying options on some sort of transformational opportunity, most executives invest only in the next logical step. We typically see folks concentrate on measures like ROI, IRR, and, in the best case, projected cash flows. Each a measure that holds its investor captive to the construct of an excel spreadsheet. While these types of tools can be extremely valuable for incremental change, they do very little to help us peer out into the future and make large strategic bets. They help us optimize which turbine to purchase or which geographic area to approach next. But when it comes to transforming the organization, combating disruption, or the creating new growth businesses, these measures fall flat. Their horizons are too short.

Large companies everywhere would be benefited by asking themselves three questions:

What if it works? To understand the value of an option, investors need to be able to think through the possible outcomes. No outcome is more important in the case of innovation than the success of the project. If it works, what can you accomplish? Only once you have a sense for how much upside exists in the option and how likely it is to occur, can you actually start comparing it to the other investment opportunities in front of you.

What's required to leave the option open to upside?

The second question is about minimizing downside. Many companies falter here. They might see the option for upside, but then overcommit. Instead of investing to get to the next step to learn whether or not it's worthwhile to invest in the stage afterwards executives often commit to everything all at once. They make public announcements to much fanfare that results in either wasted capital or embarrassing backstepping if the option doesn't pay off.

Do we have what it takes to follow this through?

In the public markets, we can sell options without executing them. Inside our organizations, an option is only valuable if we can follow it through. IBM Research, Bell Labs, and Xerox Parc each provided their parent with options on breakthrough technologies. Now even worse than simply fumbling the opportunity provided (as was the case with much of what was invented in those venerated halls), is investing in an option without a plan or capability to follow it through. That's simply wasted cash.

So when you set out to transform the way you invest in long term growth opportunities, make sure to ask yourself, if this is a wild success, "do we have what it takes to keep investing in its growth?" Will culture permit it? Will your investment process accomodate? Will your public market investors understand? Investment decisions are always complicated. But over simplifying them only leads to trouble. Instead of forcing everything you do onto a single page DCF in Excel, ask yourself "What if it works?" the next time something truly inspirational comes across your desk. Then make sure you leave open the option for upside.

Maxwell Wessel is the general manager of SAP.iO, a lecturer at Stanford's Graduate School of Business, and an investor with Nextgen Venture Partners. Connect with him on twitter @maxwellelliot