Finance Exam 2

Chapters 4 and 5, 8 and 9

What is the time value of money?

• The time value of money means that a dollar in your hand today is worth more than a dollar promised at some time in the future

• Money today is worth more because it can be invested and earn interest over time

What are the three parts of the time value of money

• Present Value

• Future Value

• Interest Rate

What is present value?

Money available earlier (today)

What is future value?

Money available later (in the future)

What is interest rate

Acts as an exchange rate between money today and money in the future

What is compounding?

Moving Forward (PV to FV)

• Accumulates interest over time to earn more interest

• Determines the future value of an investment

• Earns interest on the original principal AND interest accumulated in prior periods

What is discounting

Moving backwards (Future value to Present Value)

• Works backward from a future value to find the present value of a future amount

• Determines how much money must be invested today at a given interest rate to reach a future target

What is simple interest

• Interest earned only on the original principal amount

• The interest does not earn additional interest (it stays consistent each period)

What is compound interest

• Interest earned on both the initial principal and the interest accumulated from prior periods

• Interest can increase each period

• ‘Intrest on interest’

What is annual percentage rate (APR)

APR is the standard annual interest rate quoted as required by law. It measures interest on an annual basis without accounting for compound interest

What is perpetuity

Infinite series of equal payments that continue forever without stopping

How do you calculate the future value of a perpetuity

You cannot. It has an infinite duration, and payments continue forever. There is no end date, as calculating Future Value requires a specific ending time period (t)

• Since perpetuities never end, there is no financial period at which to calculate the total future value

• but you CAN calculate the present value of perpetuity

What is a defined benefit plan

Defined output

• Employer promises the employee and specific predetermined retirement benefit

• The final payout is calculated by using a formula based on salary and years of employment

• The employer bears the investment risk, and plan trustees decide how and where to invest the funds

What is a defined contribution plan

Defined input

• Employer and employee contribute money into an individual retirement account

• Contributions are defined, but the final payout is NOT guaranteed

• Employees generally choose when and where to invest

• Employee bears the investment risk

What is a 401(k)

• A common type of defined contribution plan

• Employees manage their own retirement accounts and investments

How does a 401(k) work?

1. Employee contributes money directly into their personal retirement accoujng

2. Employer sometimes matches employee’s contributions

3. Employee selects how to invest the money

4. Final retirement balance depends on investment performance over time

What challanges arise with a 401(k)

• Employees may lack sufficient investment knowledge

• Employees may save too little

• Employees may start saving too late

What factors influence Gen X’s retirement financial situation

Shift from guaranteed pensions

• Movement from defined benefit to defined contribution plans shifts investment risk to employees

Inadequate saving habits

• People save too little or begin saving too late

Market Volatility

• Economic downturns and financial crises can reduce retirement savings

Financial Knowledge Gaps

• Employees lack the skills to manage investments effectively.

Increased longevity:

• People live longer, meaning retirement savings must last longer

Social Security Strains

• Uncertainty about future benefits influences retirement decisions

How does social security work?

Uses a pay as you go funding structure

• a 12.4% payroll tax is collected on earned income up to an annual income cap

• Employer pays 6.2% and employee pays 6.2%

• Incoming money is used to pay current retirees rather than being saved in individual accounts

What problems are the U.S. social security system facing respectively

Pay as you go funding structure

• Current workers’ taxes fund current retirees

Outgo Exceeding Income

• Annual benefit payouts have grown larger than incoming tax revenue

• Social security trust fund reserves are declining

Demographic and Claiming Strains

• Growing retiree population

• Longer life expectancies

• Individuals can begin collecting early benefits at age 62

What challenges arise when solving the U.S. Social Security system problems?

• Raising payroll taxes

• Cutting benefit payments

• Increasing the full retirement age beyond 67

• Privatizing retirement accounts shifts investment risk to individuals

• Disagreements over whether retirement benefits should be guaranteed by the government or managed individually

What problems are the U.S. defined planned benefit plan (traditional pension) system facing respectively

Funding Shortfalls

• Future pension obligations exceed the assets currently available

Increased longevity

• Retirees live longer, increasing total pension obligations

Low interest rates

• Lower interest rates increase the Present Value of future pension obligations

Unsustainable employer risk

• Employers bear investment and longevity risks because payouts are guaranteed

What challenges arise when solving the U.S. defined benefit plan system problems?

Strain on corporate profits

• Companies must allocate more money toward pension funds instead of business growth

Interest rate dilemma

• Low interest rates can increase pension liabilities

Shifted Burden onto Workers

• Replacing pensions with 401(k)s transfers risks to employees who may not be prepared

Philosophical Disagreements

• Debate over whether employers should guarantee retirement benefits or individuals should manage their own retirement

What kind of problems are the U.S. defined contribution system facing respectively?

Investment Risk Shifted to Employees

• Final retirement payout is not guaranteed

• Depends on investment gains and losses

Market volatility:

• Economic downturns can significantly reduce retirement account balances

Saving too Little or Starting too Late

• Employees may not contribute enough money

• Starting late leaves less time for investments to grow

What challenges arise when solving the U.S. defined contribution plan system problems

• Lack of financial knowledge and investment skills

• Behavioral inertia: Employees delay increasing contributions because of immediate financial pressures

• Employers are generally reluctant to return to Defined Benefit plans because of the financial and longevity risks

What is the reasonable range of the rate offered by a typical savings account

Traditional savings account APY:

• 0.4%-0.5%

High yield savings account APY:

• 4% to 5%

What is the reasonable range of the average yearly return that can generate from the stock market

Stock market nominal annual return

• About 10%

Stock market real annual return:

• 6.5-7%

What is the reasonable range of the size of a retirement account that can support an average standard of living in retirement

Retirement savings target:

• 10-12x final annual salary

Alternative retirement savings target:

• 25x annual retirement spending gap

What is the PV of annuity

Value today

• An annuity is a finite series of equal payments occurring at regular intervals

• PV determines what all of those future payments are worth as one lump sum today

Real world example of PV of annuity

• Auto lonas

• Mortgages

• Pension fund liabilities

What is FV of an annuity

Value in the future

• Calculates the total amount accumulated at a specific future date through regular, equal deposits

What is a real world example of FV of annuity

Retirement savings accumulation

What is perpetuity

Continues forever

• Indefinite series of equal cash payments

• No ending date

• You can calculate PV, but not a finite FV

Real world example of perpetuity

• Preferred stock dividends

• Endowment funds and perpetual grants

What is capital budgeting

Process of evaluating investment projects to determine whether they should be accepted or rejected

What are the three major decision-making methods

• Payback period

• NPV

• IRR

What is the payback period

Calculates how long it takes to recover the intiial investment cost using estimated future cash flows

How does the payback period work

• Start with the initial investment cost

• Subtract estimated future cash flows from the initial cost

• Continue until the initial investment is fully recovered

• The amount of time needed to recover the investment is the payback period

What is the payback period decision rule

• Accept if the payback period is less than a present limit

• Reject if the payback period exceeds the present limit

What is net present value (NPV)

Measures the difference between the fair present value of expected future cash flows (discounted at the required rate of return) and the initial investment cost

How does NPV work

• Estimate the project’s future cash flows

• Discount those cash flows using the required rate of return

• Subtract the initial investment cost

• Determine whether the project adds or decreases value

What is the NPV decision rule

Positive NPV

• Accept

Negative NPV:

• reject

NPV=0

• Neither of these add nor destroy value

What is the internal rate of return (IRR)

• the discount rate that makes a project’s NPV equal to 0

• it represents the actual percentage rate of return generated by the invesment

How does IRR work

• Determine the discount rate that makes NPV equal zero

• Compare the IRR to the required rate of return

• Decide whether the investment generates a sufficient return

What is the IRR decision rule

• Accept if the IRR is greater than the required rate of return

• Reject if IRR is less than the required rate of return

What are the advantages of a payback period

Easy to understand

• Provides a simple, intuittive metric

• Straightforward to calculate and communicate

Adjusts for Uncertainty:

• Emphasizes earlier cash flows

• Helps mitigate risk by reducing reliance on uncertain cash flows further in the future

Biased towards liquidity

• Prioritizes projects that return cash quickly

• Particularly useful for capital-contrained firms

• Helps firms maintain operations or fund future investments

What are the disadvantages of the payback period

Ignores the time value of money

• Treats cash received in later years as equal to cash received today

• Does not account for the fact that money today is worth more than the same amount in the future

Requires an arbitrary cutoff point:

• The maximum acceptable payback period is chosen arbitratily

• Is not derived from an economic or market benchmark

Ignores Cash Flows beyond the cutoff date

• Once the initial investment is recovered, additional cash flows are ignored

• EVen if the project generates significant returns afterward, they are not considered

Biased against long-term projects:

• Penalizes investments with longer payback timelines

Why is NPV a subjective number

NPV is subjective because it relies on estimates and forecasts about the future rather than fixed historical facts

• Estimated future cash flows

  • Future sales, operational costs, and timing

• Required rate of return

  • Benchmark returns and risk adjustments

What is intrinsic value

• The estimated fair value of a company or investment based on the present value of its expected future cash flows

• The process is similar to capital budgeting because both involve estimating future cash flows and determining what those cash flows are worth today

What are the steps of cash flow valuation

1. Create projected financial statements to estimate the company’s future operations

2. Determine operating and net cash flows

3. Account for cash flows that occur at the end of the project’s life

4. Discount all expected future cash flows back to today’s dollars using the required rate of return (discount rate)

Why is the net working capital invested in a project generally recouped at the end

Net working capital is generally recovered because the short-term resources used to support a project’s operations are converted back into cash when the project ends

• The initial investment in NWC is a cash outflow because money is tied up in the project

• At the end of the project, that investment becomes a cash inflow because the resources are converted back into cash

What are the stages of NWC?

Upfront investment- Cash outflow (beginning of the project)

• The company purchases initial inventory

• Cash is set aside for operations

• Credit is extended to customers

• This creates an initial investment in NWC

Capital remains tied up (during the project)

• Working capital supports everyday business operations

• Inventory, cash, and accounts receivable are needed to keep the project running

• The investment remains tied up throughout the project’s life

Recovery- cash inflow (end of the original project)

• Remaining inventory is sold

• Outstanding customer bills (accounts receivable) are collected

• Short-term obligations (accounts payable) are settled

• The business no longer needs the working caputal for future operations, so it is released