Fin 3414 Miles Cam

Definition of NPV

the total PV of all future cash flows minus the initial outlay. It tells you exactly how much wealth (in today's dollars) a project adds to the firm. A positive NPV means the project return more than it costs, after accounting for the time value of money.

Rule for NPV

Accept if NPV > 0

Reject if NPV < 0

When ranking competing projects choose the highest NPV

Why do we use NPV?

Accepting positive NPV projects benefits shareholders

- Uses cash flows

- Uses all cash flows of the project

- Discounts the cash flows properly

- Assumes all cash flows are reinvested at discount rate

Ranking Criteria for NPV

Ranking Criteria for NPV

Payback Period

Years it takes before the cumulative forecasted cash flow equals the initial outlay

Rule for Payback Period

Accepts projects that "payback" in the desired time frame.

Flaws of Payback Period

Ignores later year cash flows and the present value of future cash flows

Discounted Payback Period

Calculate the PV of each cash flow - then calculate payback period

Discounted Payback Period Flaw

By the time you have discounted the cash flows, you might as well calculate the NPV!

Average Accounting Return

Average Income divided by average book value over project life. Also called book rate of return

Internal Rate of Return

IRR is the rate of return that makes the PV of the cash flows equal to the initial outlay or the NPV = 0

Internal Rate of Return Rule

Accept when IRR > Required Return

Reject when IRR < Required Return

choose highest IRR but watch out for scale/timing problems

Ranking Criteria for IRR

Choose the IRR that is the highest

IRR Reinvestment assumption

All future cash flows assumed invested at the IRR

IRR Advantages and why it is still used

easy to understand and communicate

IRR Disadvantages

-Does not distinguish between investing and borrowing.

-IRR may not exist or there may be multiple IRRs.

-Problems with mutually exclusive investments.

-Scale and timing.

When and how do we use incremental IRR?

You use this method when you are looking at mutually exclusive projects and can only choose one and you do this by subtracting the smaller cash flow from the bigger cash flow, finding the IRR of those incremental cash flows and comparing the incremental cash flow to your discount rate.

incremental IRR Rules

Incremental IRR > Discount Rate (Take the larger project)

Incremental IRR < Discount Rate (Take the smaller project)

When does IRR give same answer as NPV?

- When there are normal cash flows, money goes out first, then only comes in (no sign changes)

-When a project is independent, you're not choosing between projects just deciding yes or no on one

Sensitivity Analysis

Investigation of what happens to NPV when only ONE variable is changed while everything else is held constant. Measures how sensitive the project is to a single input (price, units, variable cost, fixed cost). Use when asked for ΔNPV/ΔQ or ΔOCF/Δv. Formula: recalculate OCF/NPV with the new value, then find the difference.

Scenario Analysis

Examines NPV under completely different sets of assumptions by changing MULTIPLE variables simultaneously. Typically produces a Best Case, Base Case, and Worst Case outcome to show the full range of possible results. Use when given different unit, price, and cost assumptions together to compare scenarios.

Break-even analysis

Determines the minimum level of sales needed for a project to break even.,

whenever your professor frames a question around protecting NPV or ensuring the project is worth doing, that's always financial break-even — because it's the only method that directly ties unit sales to your return requirement.

Option to Expand

When to use: Demand turns out higher than expected

Has value if demand turns out to be higher than expected.

Example: A company builds a small pilot plant instead of a full factory. If the product succeeds, it has the option to expand production. That right to expand has value even if you don't end up using it.

Option to Abandon

When to use: Demand turns out lower than expected

Has value if demand turns out to be lower than expected.

Example: If a project is failing, management can sell the assets and cut losses rather than continuing. The ability to abandon (rather than being locked in) adds value to the project today.

Option to Delay

When to use: Underlying variables are changing with a favorable trend

Has value if the underlying variables are changing with a favorable trend.

Example: A mine owner waits for commodity prices to rise before investing. The option to delay (rather than invest today) is valuable when conditions are improving.

Cash Break Even

At what sales level does OCF = 0

Financial Break Even

How many units to ensure NPV > 0 (most common exam ask)

Decision Tree

Multiple stages of investment with go/no-go decisions

How can there be multiple IRR's?

Every time cash flows switch from positive to negative (or back), it creates a potential new IRR. Multiple IRRs mean you can't identify one true return for the project — so you can't make a reliable accept/reject decision.

Underpricing

The IPO price is set too low relative to the stock's true value. On the first of trading, the price jumps - the average first - day return is approximately 18%, and can exceed 100%. This happens because underwriters have an incentive to set at a low price to make brokerage customers happy and to make the issue easy to sell.

Money left on the table

the indirect cost of underpricing. It represents the value the issuing firm gave away by pricing shares too cheap

Money left on Table Equation

= (First Day Closing Price - Offer Price) x Number of Shares

Spread

the direct cost paid to the underwriter. The underwriter typically charges a 7% spread - meaning the difference between what the investor pay (offer price) and what the issuing firm actually receives. The underwriter keeps that 7% as compensation.

Negotiated Deal

the issuing firm works directly with one underwriter to set terms. Most common for equity issues.

Competitive Deal

Multiple underwriters bid. Only feasible for large issuers by major firms. Still rare for equity, it costs investment bankers too much to learn about the company to make an intelligent bid.

Firm Commitment (Most Common)

The underwriter buys all the shares from the issuer and resells them. The underwriter takes on the risk of being stuck with unsold shares. Price is not set until investor interest is assessed and oral commitments are obtained.

Best Efforts

The underwriter only tries to sell the shares but makes no guarantee that the shares will be sold. Used for very small, risky deals where the investment banker insists on this arrangement.

Book Building (Roadshow)

During the roadshow, the investment banker asks institutional investors to indicate how many shares they plan to buy and records this in a "book." The banker hopes for an oversubscribed issue. Based on this demand, the investment banker sets the final offer price on the evening before the IPO.

Dutch Auction

An alternative to book building for setting the IPO price. Instead of the banker collecting indications of interest privately, all investors submit bids specifying how many shares they want and at what price. The final offer price is set at the which all shares can be sold.

Green Shoe Provision

An overallotment option that allows the underwriter to sell more shares than originally planned (typically 15% more) if the issue is oversubscribed. It gives the underwriter flexibility to stabilize the stock price after the IPO by buying shares in the open market if the price falls.

Special Purpose Acquisition Company

Also called a "blank check company." A shell company listed on an exchange whose sole purpose is to acquire a private company. Founders sometimes have a target in mind, but investors are essentially betting on the founders ability to find a good deal. SPACs offer a faster IPO process for the target company compared to a traditional IPO.

Rights Offering (Rights Issue)

When a company raises new equity, current shareholders get the first right to buy new shares (before the public). This protects their ownership percentage and prevents dilution. Shareholder can either exercise the right (buy new shares) or sell the right to someone else. Either way, the shareholders total wealth does not change.

Carve Out

The Parent company sells a minority stake in a subsidiary to the public through an IPO. The parent retains control but raises cash from the partial sale.

Spin off

the parent company distributes shares of subsidiary to existing shareholders. No cash is raised, existing shareholders just end up owing share in two separate companies instead of one.

IRR Disadvantages: Mutually Exclusive Projects — Scale & Timing:

IRR ignores the size (scale) of the project. A 50% return on $1 is less valuable than a 20% return on $1,000,000. Also, timing of cash flows matters — projects with early vs. late cash flows can rank differently under IRR vs. NPV depending on the discount rate.

IRR Disadvantages: Multiple IRRs

If cash flows change signs more than once (e.g., outflow → inflows → outflow again), there can be multiple IRRs or no IRR at all, even with a positive NPV. You can't use IRR reliably here.

IRR Disadvantages Investing vs. Financing:

If the cash flow pattern is reversed (borrow-like: inflow first, outflows later), the IRR rule flips — you'd want IRR < r to be good, not IRR > r.

Initial CF

Year 0 contains the upfront costs to get the project started Year 0 CF = -Equipment cost - Initial NWC Investment

Depreciation

not a cash flow but a tax shield, it reduces taxable income, which reduces taxes paid ( a real cash savings) You want depreciation sooner because of time value of money

MACRS

Modified Accelerated Cost Recovery System , you depreciate faster than striaght line getting bigger tax shiels early

Profitability Index Rule

PI > 1 Accept

PI < 1 Reject

Profitability Index Decision

Choose project with greater PI

Profitability index disadvantags

scaling problems