Exam 2 Chap 4, 5, 8, 9 Flashcards
(16 cards)
What is a compounding process and what is a discounting process?
Compounding Process:
The compounding process refers to the method of calculating interest on both the initial principal and the accumulated interest from previous periods.
The discounting process is the reverse of compounding. It is used to determine the present value (PV) of a sum of money to be received or paid in the future, discounted at a specific interest rate.
What is the difference between simple interest and compound interest? How to find the
total interests earned in an investment?
Simple interest is calculated only on the initial principal amount for the entire duration of the investment or loan.
Compound interest is calculated on the initial principal as well as on the accumulated interest from previous periods.
Interest Earned:
For simple interest, the total interest is simply the amount calculated using the simple interest formula: SI=P×r×t
For compound interest, the total interest is the difference between the future value (FV) and the principal (P), calculated using the compound interest formula:
CI=FV−P =P(1+r/n)^nt−PCI
What is the definition of APR? How to find out the period rate using APR information?
APR is a measure of the cost of a loan or the interest rate charged for borrowing, expressed as a yearly interest rate. It includes not only the interest but also any additional fees or costs associated with the loan, which makes it a more comprehensive measure of the true cost of borrowing.
APR is used for loans, mortgages, credit cards, and other types of credit, allowing consumers to compare different credit options more easily.
Using APR you can find the period rate by dividing current APR by 12 (monthly) or 65 (daily).
Can you calculate the FV of perpetuity cash flows? Why?
Perpetuity refers to a series of cash flows that continue indefinitely into the future. The key characteristic of a perpetuity is that it has no end date.
The Future Value (FV) of a Perpetuity: The future value of a perpetuity cannot be calculated in the same way as a typical investment or loan because there is no “end date” to apply the compounding over. Since the cash flows continue forever, the concept of a future value doesn’t apply directly.
Instead, we can calculate the present value (PV) of a perpetuity, which is the value of the perpetual cash flows today.
The formula for the present value of a perpetuity is:
PV=C/r
What is defined benefit plan? What is defined contribution plan? What is 401(k)? How
does a defined contribution plan or 401(k) usually work?
Defined Benefit Plan (DB Plan):
A defined benefit plan is a type of retirement plan where the employer guarantees a specific retirement benefit amount for the employee, based on a formula typically involving factors like years of service and salary history.
The employer is responsible for ensuring that enough funds are available to pay the promised benefits.
Example: A pension plan that guarantees a retiree $3,000 per month for life after retirement.
Defined Contribution Plan (DC Plan):
In a defined contribution plan, the employer and/or employee contribute a fixed amount to the employee’s retirement account. The retirement benefit depends on the performance of the investments in the account, and there is no guaranteed payout.
Common types of defined contribution plans include 401(k) plans.
Example: An employee contributes 5% of their salary to their 401(k), and the employer matches it with a 3% contribution. The total amount available at retirement depends on the contributions and investment returns.
401(k):
A 401(k) plan is a type of defined contribution plan offered by employers to help employees save for retirement. Employees can contribute a portion of their salary to the plan, and in many cases, employers will match a percentage of those contributions.
Key features:
Contributions are tax-deferred, meaning you don’t pay taxes on the money you contribute until you withdraw it at retirement.
There are annual contribution limits set by the IRS.
Employees can choose how their contributions are invested from a range of options, such as stocks, bonds, and mutual funds.
How Defined Contribution Plans or 401(k) Work:
Employee Contributions: Employees decide how much money to contribute to the plan, typically through payroll deductions.
Employer Contributions: Employers may match employee contributions up to a certain percentage, but this varies by employer.
Investment Options: Employees usually choose how to invest their funds from a range of options provided by the plan, such as mutual funds, bonds, and stocks.
Tax Benefits: Contributions are often made pre-tax, meaning they reduce the employee’s taxable income for the year, and taxes are paid when the funds are withdrawn in retirement.
What are some of the important factors that have influenced a typical Gen X’s financial
condition in his or her retirement years? Please list at least two.
Housing Market:
Many in Gen X faced the burst of the housing bubble in the mid-2000s, which affected homeownership and their ability to build wealth. Some may have lost homes or saw property values decline.
Pension Decline:
Many Gen Xers are in the workforce during the decline of traditional pension plans. They have had to rely more on 401(k) plans and personal savings, making them more self-reliant in managing retirement funds.
What kind of problem(s) is(are) the U.S. Social Security system facing respectively? What
is(are) the challenge(s) in solving the problem(s)?
Funding Shortfall: One of the biggest issues facing the U.S. Social Security system is a long-term funding shortfall. The system is primarily funded through payroll taxes (FICA), but with an aging population and fewer workers contributing relative to retirees, the system is expected to experience a deficit. By around 2034, the Social Security Trust Fund is projected to run out, leading to reduced payouts unless action is taken.
Aging Population: The U.S. population is aging due to the baby boomer generation reaching retirement age, which increases the number of people receiving benefits. Meanwhile, the birth rate has declined, meaning fewer people are entering the workforce to pay into the system.
Increased Life Expectancy: As people live longer, they draw Social Security benefits for a more extended period, putting additional strain on the system’s funding.
Challenges in Solving the Problems:
Political Gridlock: Social Security reforms often require bipartisan support, but political divisions in Congress make it difficult to pass necessary changes, such as raising the payroll tax rate or adjusting benefits.
Public Opposition: Many Americans are resistant to changes that would reduce their benefits, such as increasing the retirement age or cutting payments, due to concerns about their financial security in retirement.
Complexity of Reform: Addressing the system’s problems requires complex decisions, such as adjusting payroll taxes, modifying benefits, or introducing new sources of funding, all of which can have significant economic and social implications.
What kind of problem(s) is(are) the U.S. defined benefit plan (traditional pension)
system facing respectively? What is(are) the challenge(s) in solving the problem(s)?
Underfunding: Many defined benefit plans (traditional pensions) are underfunded, meaning the pension funds do not have enough assets to cover the promised benefits. This issue is particularly acute for private employers and some public sector pensions.
Pension Plan Liabilities: The future liabilities of pension plans can be difficult to predict, especially with fluctuating life expectancies and interest rates. This makes it challenging for employers to ensure they have enough funds to meet future obligations.
Decline in Employer Sponsorship: Fewer employers are offering defined benefit plans due to their high cost and risk. The shift toward defined contribution plans (like 401(k)s) has made traditional pensions less common, leaving workers with less guaranteed retirement income.
Pension Benefit Cuts: In some cases, pension plans have had to cut benefits or freeze plans due to financial difficulties, leading to uncertainty for retirees who depend on these pensions.
Challenges in Solving the Problems:
Funding Challenges: Solving underfunding requires large contributions from employers or the government, which may not be financially feasible, especially for businesses in industries with declining revenues.
Political and Economic Factors: Reforms to the pension system often face resistance from both employers and unions. Changes to pension plans, including cuts to benefits or adjustments to how they’re funded, can lead to political backlash.
Shifting Responsibility: The shift from defined benefit plans to defined contribution plans has transferred the risk of retirement savings to individuals, making it harder for workers to have guaranteed retirement income.
What kind of problem(s) is(are) the U.S. defined contribution plan system facing
respectively? What is(are) the challenge(s) in solving the problem(s)?
Problems with the U.S. Defined Contribution Plan System:
Inadequate Savings: Many workers do not contribute enough to their 401(k) plans or other defined contribution accounts, resulting in insufficient retirement savings. This is especially true for low-income workers who may not have enough disposable income to contribute.
Investment Risk: In defined contribution plans, the individual employee bears the investment risk. Poor investment choices or market downturns can significantly reduce the value of the retirement savings.
Lack of Financial Literacy: Many workers lack the financial literacy to make informed decisions about how to allocate their contributions and investments. Without proper guidance, employees may not take full advantage of employer matches or make poor investment choices.
Rising Fees: Many 401(k) and similar plans have high administrative fees, which can erode the growth of retirement savings over time. Additionally, the variety of investment options available can sometimes overwhelm employees, leading to poor decisions.
Inconsistent Participation: Not all workers participate in defined contribution plans, especially if the employer does not provide matching contributions. Without mandatory participation or automatic enrollment, some employees may miss out on the opportunity to build retirement savings.
Challenges in Solving the Problems:
Behavioral Factors: Convincing individuals to contribute more and make better investment decisions is a significant challenge, as many workers may not prioritize saving for retirement, especially when retirement seems far off.
Equity Concerns: Low-income workers and those without employer-sponsored plans are at a disadvantage, and simply expanding access to defined contribution plans may not be enough to solve the problem of retirement insecurity.
Market Volatility: The reliance on individual investments in defined contribution plans makes workers vulnerable to market volatility. Policy changes that guarantee a certain level of security or offer better investment choices could help, but they could also reduce the benefits of investing in the stock market for those who do well.
Fee Transparency and Regulation: There is a need for better regulation and transparency in terms of fees associated with defined contribution plans. Ensuring that workers understand and can avoid high fees is crucial to improving their retirement outcomes.
Have a sense of numbers:
(a) What is the reasonable range of the rate offered by a typical savings account?
(b) What is the reasonable range of the average yearly return that can generate from stock
Market?
(c) What is the reasonable range of the size of a retirement account that can support an
average standard of living in retirement?
a) The interest rate offered by a typical savings account varies depending on the bank and the current economic environment, but the reasonable range typically falls between 0.01% and 4% annually.
Traditional savings accounts at most banks tend to offer rates on the lower end of the range (0.01% to 0.5%).
Online banks or high-yield savings accounts may offer rates from 1% to 4% or more, depending on the current market conditions and competition.
b) The historical average annual return for the U.S. stock market (specifically the S&P 500 index) is about 7% to 10% after adjusting for inflation.
During periods of growth, the return can be higher, but during downturns (such as recessions or market crashes), the returns can be negative.
This range reflects the long-term nature of stock market investments, where volatility can occur in the short term, but over time, returns tend to grow at a solid rate.
c) The size of a retirement account required to support an average standard of living depends on several factors, including lifestyle, location, and spending habits. However, a general rule of thumb is that you should aim to have between 10 to 20 times your annual expenses saved by retirement.
For example, if you expect to need $50,000 per year in retirement, you would want a retirement account of around $500,000 to $1,000,000 to cover those needs.
Many financial planners suggest that people should aim to accumulate a retirement savings that will allow them to withdraw 4% annually without depleting the principal. So, if you need $50,000 a year, you would aim for a total retirement savings of about $1,250,000 (i.e., $50,000 / 0.04).
Please use your own language to describe some financial situations that reflect (a) PV of
annuity; (b) FV of annuity; and (c) perpetuity scenarios.
(a) Present Value of Annuity (PV of Annuity):
Scenario: Think about a situation where someone is offered a retirement pension, where they will receive $2,000 per month for the next 20 years. To evaluate how much that future cash flow is worth in today’s terms (present value), you would discount each of those future payments to the present using an assumed interest rate.
For example, if you want to know how much you would need to invest today in a savings account (or another investment) that would provide you with $2,000 per month for the next 20 years, you would use the present value of annuity formula. The calculation would give you the total amount of money that, if invested today, would produce those monthly payments over the course of 20 years.
In simple terms: If you want to know what the pension is worth today, the present value of the annuity would help you calculate that.
(b) Future Value of Annuity (FV of Annuity):
Scenario: Imagine you’re saving for retirement, and you decide to invest $500 every month into an investment account for the next 30 years. You’re hoping to see your savings grow over time at a 7% annual return.
The future value of annuity is used to calculate how much money your regular contributions will accumulate by the end of the investment period. In this case, by investing $500 monthly for 30 years, the future value of your annuity would give you the total amount you would have at the end of the 30 years, taking into account the compounding interest.
In simple terms: The future value of the annuity shows how much your consistent investments will be worth in the future.
(c) Perpetuity Scenario:
Scenario: Imagine you inherit a trust fund that will pay you $5,000 annually for the rest of your life. The trust is structured to make those payments indefinitely, no matter how long you live. This is an example of a perpetuity — an ongoing stream of equal payments forever.
The present value of a perpetuity can be calculated by dividing the annual payment ($5,000) by the discount rate. For instance, if the discount rate (or interest rate) is 5%, the present value of this perpetuity would be $5,000 / 0.05 = $100,000. This means that in today’s terms, the perpetuity is worth $100,000.
In simple terms: A perpetuity is a financial situation where you get fixed payments indefinitely, and its value is calculated based on the consistent cash flows you’ll receive forever.
Please indicate which line in the graph below reflects the pattern of principle payments
and which line reflects the pattern of interest payments in mortgage payment scenario.
Please also briefly explain why it is the case
The green line represents interest payments because it starts high and gradually decreases over time.
The purple line represents principal payments because it starts low and gradually increases over time.
How do Payback Period, NPV, and IRR capital budgeting decision rules work?
Capital budgeting decision rules help businesses evaluate investment projects. The three common methods are:
1. Payback Period (PP)
Measures how long it takes for a project to recover its initial investment from cash inflows.
Formula:
Payback Period=Initial Investment/Annual Cash Inflows
Decision Rule:
Accept the project if the payback period is less than or equal to a predetermined cutoff.
Reject if it exceeds the cutoff.
- Net Present Value (NPV)
Measures the total value created by a project, considering the time value of money.
Formula:
NPV = ∑Ct/(1+r)t−C0
where:
Ct = cash inflows at time ttt
r = discount rate (cost of capital)
C0= initial investment
Decision Rule:
Accept if NPV > 0 (the project creates value).
Reject if NPV < 0.
- Internal Rate of Return (IRR)
The discount rate that makes NPV = 0. It represents the project’s expected return.
Formula: Solve for rrr in:
0 = ∑Ct/(1+IRR)^t − C0
Decision Rule:
Accept if IRR > required return (cost of capital).
Reject if IRR < required return.
What are the advantages and disadvantages of payback period rule?
Advantages
✅ Simple & Easy to Use – Quick to calculate and understand.
✅ Useful for Liquidity Concerns – Helps businesses with cash flow constraints prioritize fast payback.
✅ Lower Risk Exposure – Shorter payback means less risk of loss due to uncertainty in future cash flows.
Disadvantages
❌ Ignores Time Value of Money – Doesn’t discount future cash flows.
❌ Ignores Cash Flows After Payback – Projects may generate significant value after the payback period but are not considered.
❌ No Clear Decision Rule for Profitability – A project with a shorter payback is not necessarily more profitable.
❌ Bias Against Long-Term Projects – May reject profitable projects with longer payback periods, like infrastructure investments.
Overall:
The Payback Period rule is useful for quick liquidity assessments but is not reliable for evaluating project profitability. NPV and IRR provide better decision-making criteria when considering value creation and risk.
Please use your own language to describe the basic steps in valuing a company’s
fair/intrinsic value (a market value that investors think is fair).
Valuing a company’s fair (intrinsic) value means estimating what it’s truly worth based on its financial performance, assets, and future potential. Investors use this to decide if a stock is overvalued or undervalued. Here’s how it’s generally done:
Step 1: Understand the Business & Industry
Before crunching numbers, investors analyze the company’s business model, competitive position, and industry trends. Factors like market demand, competition, and growth potential play a big role in valuation.
Step 2: Choose a Valuation Method
There are several ways to estimate value, but the three most common methods are:
Discounted Cash Flow (DCF) Method: Estimates the present value of future cash flows the company will generate.
Comparable Company Analysis (CCA): Compares the company to similar businesses using valuation multiples (like P/E ratio or EV/EBITDA).
Asset-Based Valuation: Looks at the company’s total assets and liabilities to determine its net worth.
Step 3: Project Future Cash Flows
For methods like DCF, investors estimate how much money the company will generate in the coming years. This includes revenue, expenses, profit margins, and reinvestment needs.
Step 4: Discount Future Cash Flows to Present Value
Since money today is worth more than money in the future, future cash flows are “discounted” using a rate (usually the company’s cost of capital). The sum of these discounted values gives an estimate of the company’s intrinsic value.
Step 5: Compare with Market Price
Once the intrinsic value is calculated, investors compare it with the company’s current stock price.
If intrinsic value > market price → The stock is undervalued (good buy).
If intrinsic value < market price → The stock is overvalued (risky buy).
Please use your own language to explain why the net working capital invested in a
project is generally recouped at the end of the project
Net Working Capital (NWC) refers to the money tied up in a project for things like inventory, accounts receivable (money owed to the company), and accounts payable (money the company owes).
During a project, businesses need to set aside cash to cover these working capital needs. However, once the project ends, this investment is usually recovered. Here’s why:
Inventory is Sold Off → Any leftover raw materials or products are sold, converting them back into cash.
Receivables Are Collected → Customers who owe money for goods/services provided during the project eventually pay up.
Payables Are Settled → Any outstanding payments the company owes are paid off, closing the cycle.
At the end of the project, the company no longer needs to keep extra funds tied up in working capital, so that cash is freed up and returned to the business.
