What do coupon bonds pay investors at maturity?
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Their face value.
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What do coupon bonds pay investors at maturity?
Their face value.
What is the primary method for choosing among projects?
Compute the NPV of each project or alternative.
What should be selected when comparing projects?
The project with the highest NPV.
What is a perpetuity?
A security that provides a constant payment forever starting next year.
What is a major issue with ESG ratings?
They are not highly correlated.
What principle can be used to determine the price and yield of any default-free bond?
The Law of One Price.
What does the optimal level of investment depend on?
It does not depend on the individual preferences of shareholders.
What is the best alternative when faced with multiple options?
The one with the highest NPV.
What does the variable C represent in the context of perpetuities?
The constant payment received from the perpetuity.
What percentage of divergence in ESG ratings is attributed to scope?
38%.
What additional benefit do coupon bonds provide compared to zero-coupon bonds?
Regular coupon interest payments.
What is the formula for calculating the present value (PV) of an amount to be received in the future?
PV = q / (1 + r)^n
What happens to the value of a perpetuity as the interest rate (r) increases?
The present value of the perpetuity decreases.
What is the equivalent value of choosing to hire a manager and sell in one year?
$222,727 today.
What is the reason for 6% of the divergence in ESG ratings?
Different views on the relative importance of attributes.
What determines the rate at which we can exchange money today for money in the future?
The current interest rate.
What is the yield to maturity (YTM) of a coupon bond?
The interest rate that solves the present value of coupons as an annuity.
What is the relationship between APR and actual earnings or payments?
The APR quote is less than the actual amount one will pay or earn because it does not include the effect of compounding.
How is the value of a perpetuity at time t = 0 calculated?
By dividing the constant payment by (1 + r).
What percentage of divergence in ESG ratings is due to measurement?
56%.
What is a standard annuity?
An annuity with payments of C from time t = 1 to t = N.
What does the total return of a stock consist of?
The sum of the stock’s dividend yield and the capital gain rate.
How can a standard annuity be viewed?
As the difference between a perpetuity starting at t = 1 and a perpetuity starting at t = N + 1.
How can a three-year $1,000 bond that pays 10% annual coupon be replicated?
Using three zero-coupon bonds.
What does the graph illustrate regarding bond prices?
The effects of the passage of time on bond prices when the yield remains constant.
What does the separation of shareholder consumption decisions and firm production decisions imply?
They are independent of each other.
What is the price at which a three-year coupon bond must trade according to the Law of One Price?
$1,153.
What is the formula for the present value (PV) of an annuity at time t = 0?
It is calculated using the discount rate r per period.
What is the concept of the time value of money?
The idea that money available today is worth more than the same amount in the future due to its potential earning capacity.
What do we call the value of an investment expressed in terms of dollars today?
Present value (PV).
What is the principle of value additivity?
The total value of a portfolio is equal to the sum of the values of its individual assets.
What is the capital gain rate?
The capital gain the investor will earn on the stock divided by the current stock price.
What should we prioritize when choosing among projects?
Maximize NPV first.
What is a share repurchase?
When a firm uses excess cash to buy back its own stock.
How much does Ellen plan to save at the end of this year for her retirement?
$10,000.
What is compounding?
The process of earning interest on both the initial principal and the accumulated interest from previous periods.
What happens to the price of a coupon bond between coupon payments?
It rises.
What does the law of one price state?
In an efficient market, identical goods must sell for the same price when expressed in a common currency.
Who is referred to as a one-year investor?
An investor who holds the stock for one year.
What is a corporate bond?
A bond issued by a corporation, such as Apple or Roche.
What can we do after maximizing NPV to find preferred cash flow patterns?
Borrow or lend to shift cash flows through time.
Can we compute the yield to maturity for coupon bonds?
Yes, it can be computed.
What has replaced dividend payouts in recent years for some firms?
Share repurchases.
Why is compounding important in finance?
It allows investments to grow exponentially over time, significantly increasing the total return.
What happens if the price of a security does not equal the present value of its cash flows?
An arbitrage opportunity will appear.
What is the net value of the investment if the benefit is 105,000?
-$1,000.
What occurs to the price of a coupon bond on the coupon date?
It tumbles, reflecting the amount of the coupon payment.
What happens to your purchasing power if the price of a car increases by less than 2%?
Your purchasing power increases, as you can buy more than the car with your investment.
How does value additivity relate to investment decisions?
It allows investors to assess the value of combined investments based on individual asset values.
How is the stock's dividend yield calculated?
By dividing the expected annual dividend of the stock by its current price.
How does the price of a zero-coupon bond behave over time?
It rises smoothly.
What does 'q' represent in the present value formula?
'q' represents the amount to be received in the future.
What do we call the value of an investment expressed in terms of dollars in the future?
Future value.
What does 'n' represent in the present value formula?
'n' represents the number of years until the amount is received.
What is an example of a risk-free interest rate?
The rate paid by the Swiss Confederation on its debt.
How does the interest earned change with the number of compounding periods?
The interest earned increases with the number of compounding periods.
What significant action did Switzerland take in 2022 regarding green financing?
Issued its first green bond.
If the current annual interest rate is 5%, how much will $1 grow in one year?
$1.05.
What is the present value of a benefit of $104,000 in one year at a 5% interest rate?
$99,048.
What is the yield to maturity on a bond with a face value of 100, coupon rate of 10%, and price of 110?
The yield to maturity is lower than the coupon rate due to the bond being sold at a premium.
What is the net present value (NPV) of a project?
The difference between the project’s present value and the cost of implementing the project.
Why is linking CEO compensation to ESG performance challenging?
CEOs might meet rating targets but fail to improve the firm's overall ESG performance.
What does a firm implicitly choose when it sets the coupon rate on a bond?
The funds raised with the bond.
What formula is used to compute the yield to maturity for a one-year corporate bond?
The yield solves YTM = FV / P - 1.
How much do you have after 2 periods if you invest $1 at an interest rate r?
You have 1 + 2r + r².
What are positive net present value investments?
Investments where a cash flow series can be produced more cheaply within the firm than by investing in financial assets.
What example illustrates that not all issuers of green bonds are environmentally friendly?
Saudi Arabia's Public Investment Fund selling green bonds.
What is the relationship between the current price, face value, and yield to maturity for a zero-coupon bond?
The YTM can be calculated using the current price, face value, and the number of periods to maturity.
How much cash does the firm currently have?
How does investing affect equity in the example provided?
Equity increases from 200 to 210, an increase of 10.
What is the spot rate for a 1-year term?
0.91%.
What is the spot rate for a 5-year term?
2.01%.
How does an increase in interest rates affect the NPV of an investment?
It typically reduces the NPV.
How do SLBs adjust during their lifetime?
The coupon is adjusted depending on whether the company meets predetermined and externally verified sustainability objectives.
What is the cost of an investment of $100,000 in one year at an interest rate of 5%?
$105,000.
What type of bonds are used to determine the price of other default-free bonds?
Default-free zero-coupon bonds.
What condition must be met for the growth rate g in a growing annuity?
The growth rate g must be less than the discount rate r.
What is the formula used to find the yield of a coupon bond?
The yield is calculated using the present value of future cash flows from the bond.
What is sustainable financing?
Financing that takes into account environmental, social, and governance (ESG) factors.
What is a zero-coupon bond?
A bond that does not make coupon payments and only pays the face value at maturity.
What model should be used when a firm repurchases shares?
The total payout model.
What is the formula for the price of a security according to the no arbitrage principle?
Price Security = PV(All the cash flows paid by the security).
What should a firm do if it has enough money regarding projects?
It should accept all projects that have a positive net present value (NPV).
What is the Nominal Interest Rate (rn)?
The rates quoted by financial institutions and used for discounting cash flows.
What role do ESG ratings play in sustainable financing?
They assess a company's performance on environmental, social, and governance criteria, influencing investment decisions.
What is the present value (PV) of a $1000 cash flow owed by the U.S. government to be paid in 5 years?
The PV can be calculated using the appropriate discount rate from the provided rates.
What is a normal market?
A market without arbitrage opportunities.
What is the present value of $100 in two years at an annual interest rate of 5%?
$90.70.
What percentage of earnings does Titan plan to pay out?
50%.
What is the effect of an increase in interest rates on NPV?
It typically reduces the NPV of an investment.
What are bonds and loans used for by firms?
To raise money from debt investors.
What is the discounted cash flow (DCF) formula used for?
To calculate the present value of a stream of cash flows.
What is the term structure of interest rates?
The relationship between the term of an investment and the interest rates offered by banks.
What is the future value of a $1 investment after one year at an APR of 10% compounded semi-annually?
$1.1025.
How does money grow over time at 10% interest after 7 years?
Your money nearly doubles.
What role does third-party certification play in green bonds?
It is key to ensuring the credibility of the green bond's environmental commitment.
Why are green bonds linked to spending on green projects rather than environmental outcomes?
Because it's easier to monitor monetary transactions than timely environmental outcomes.
Who typically issues bonds?
Corporations or governments to raise money from investors.
What is the formula for the value at time t=0 of a growing perpetuity?
The value is calculated using the formula C / (r - g), where C is the first payment, r is the discount rate, and g is the growth rate.
What is the risk-free interest rate?
The interest rate at which money can be borrowed or lent without risk.
Why is the insight about NPV fundamental to our economic system?
It explains the reason for the existence of large companies.
What formula applies when interest rates vary with the horizon?
A specific discounting formula for time-varying interest rates.
What is credit risk?
The risk of default, meaning the bond is not repaid in full.
How much cash is needed today in the example provided?
$60,000.
How do compounding and discounting relate to time?
They extend to multiple periods.
What does the law of one price imply about asset C?
Asset C is equivalent to a portfolio of assets A and B, so PC = PA + PB.
What is the coupon rate of the Lonza Swiss Finanz AG bonds due 2023?
1.000%.
What is the difference between EAR and APR?
EAR accounts for compounding, while APR indicates the amount of simple interest earned in one year, ignoring compounding.
How are other interest rates on the yield curve set?
They are set in the market and adjusted until the supply of lending matches the demand for borrowing at each loan term.
What characterizes projects that create value?
Their present values exceed their costs.
How is APR calculated with k compounding periods?
It reflects the actual interest earned each compounding period.
What is the yield to maturity (YTM) in the context of zero-coupon bonds?
The rate of return that an investor earns if they hold the bond until maturity.
What happens when you reinvest interest earned at the same rate?
You earn interest on interest, increasing the total return.
What percentage of Titan's earnings is used for share repurchases?
20%.
What is a concern associated with growing green opportunities?
Greenwashing, where firms overstate or mislead about their environmental performance.
How can debt structuring help mitigate concerns about greenwashing?
By providing a framework for accountability and transparency in sustainability claims.
What happens to your investment after 20 years at 10% interest?
It increases almost 7-fold.
What is the implication of low interest rates on the Swiss pension system?
It is detrimental when rates are low.
What happens to the NPV if the interest rate rises to 2.5%?
The NPV becomes negative.
What can shareholders instruct managers to do?
Undertake positive net present value projects.
How do you compute the net value of an investment?
By subtracting costs from benefits.
What does the old lady at BMW's shareholder meeting want?
She wants money now and suggests investing in small cars for quick profit.
At what annual increase rate does Ellen expect her savings to grow each year?
5%.
What is the future value formula for an investment?
FV = q(1 + r)^n.
What is a coupon bond?
A bond that pays periodic interest payments (coupons) to the bondholder.
How does the length of time affect the power of compounding?
The longer the time period, the greater the effect of compounding on the investment's growth.
What happens to your purchasing power if the price of a car increases by more than 2%?
Your purchasing power decreases, as you can no longer buy the car with your investment.
Which financial institutions are heavily involved in issuing green bonds?
Banks.
What role does the interest rate play in compounding?
A higher interest rate increases the amount of interest earned, enhancing the compounding effect.
If you have $50,000 and invest it in government bonds with a nominal interest rate of 2%, what is the opportunity cost of not buying a car?
The potential return from the investment in government bonds.
What principle do present values (PVs) obey?
The principle of value additivity.
What is the internal rate of return (IRR) for a zero-coupon bond?
The rate of return earned if the bond is bought at its current price and held to maturity.
What is the effect of time on bond prices?
As a bond approaches its maturity date, its price tends to converge to its face value.
What is the total amount Ellen will have saved by age 65 if she follows her plan?
This requires calculation based on her savings plan and interest rate.
What aspect does the dominant strategy in impact investing primarily focus on?
It focuses on 'E' rather than the broader ESG criteria.
What issue arises from ESG ratings according to the text?
Desilution and confusion when people realize the labels do not measure what they want them to measure.
If the APR is 10% compounded twice a year, what is the effective interest earned each period?
5% every 6 months.
What do empirical studies show about green bonds?
They have a real impact and are not merely a tool of greenwashing.
What is the total value of Titan's equity calculated from payouts?
$17.2 billion.
How is Titan's share price calculated?
By dividing the total equity value by the number of outstanding shares.
What is the annual cash flow generated by the project?
$2.5 million per year for four years.
What is the face value of a bond?
The notional amount used to compute the interest payments.
What is the yield of the bond priced at 1,000 and a coupon payment of $100?
4.44%.
What is the nominal interest rate (rn)?
The rates quoted by financial institutions and used for discounting cash flows.
Why is green financing important?
It matters for many sectors of the economy.
What do ESG ratings measure?
A firm's ESG performance.
What is arbitrage?
The practice of buying and selling equivalent goods in different markets to take advantage of a price difference.
Which companies provide ESG ratings?
MSCI, Sustainalytics, InRate, among others.
What is the only cash payment received by investors of zero-coupon bonds?
The face value of the bond on the maturity date.
How can coupon bonds trade in the market?
They may trade at a discount, at par, or at a premium.
At what age does Ellen plan to retire?
65 years old.
Why is the law of one price important in finance?
It ensures that markets are efficient and helps prevent arbitrage opportunities.
What happens to the price of a coupon bond when market interest rates increase?
The price of the coupon bond decreases.
What is the benefit of the investment opportunity in one year?
$104,000.
What is the impact of inflation on purchasing power?
Inflation can decrease purchasing power if prices increase faster than nominal interest rates.
What does the law of one price state?
If equivalent investment opportunities trade simultaneously in different markets, they must trade for the same price in both markets.
What does MSCI state about its ESG ratings?
They are not designed to measure a company’s impact on climate change.
What does the equation rr = rn - i / (1 + i) represent?
It shows the relationship between real interest rate, nominal interest rate, and inflation.
What happens to the firm's value when it invests in a project with a positive NPV?
The value of the firm and the value of equity increase.
If a firm has a project with a cost of 50 and an NPV of 10, what is the present value of benefits?
How is the amount of each coupon payment determined?
By the coupon rate of the bond set by the issuer.
What environmental improvements are associated with green bonds?
They improve environmental performance, including environmental ratings and CO2 emissions.
What did investors primarily care about until recently?
Cash flows.
What does EAR stand for in relation to APR?
Effective Annual Rate.
What is the yield to maturity on a bond with a face value of 100, coupon rate of 10%, and price of 90?
The yield to maturity is higher than the coupon rate due to the bond being sold at a discount.
What is a primary challenge of ESG ratings divergence?
It makes it difficult to evaluate the ESG performance of companies, funds, and portfolios.
How is the value at time t=0 of a growing annuity calculated?
It is calculated using the formula C * [(1 - (1 + g)^n / (1 + r)^n) / (r - g)], where C is the first payment, r is the discount rate, g is the growth rate, and n is the number of periods.
What is a characteristic of zero-coupon bonds?
They always trade at a discount.
What is the expected annual return on Ellen's savings?
10%.
What is the face value of the Coop-Gruppe bonds issued on April 7, 2020?
CHF 320,000,000.
What is the market's response to firms' ESG performance when there is ratings divergence?
Markets are less likely to price firms’ ESG performance ex post.
What is the cost of the investment opportunity mentioned?
$100,000 today.
What is the effect of accepting a positive NPV project on stock price?
It will immediately increase the stock price, even if payoffs are far in the future.
What happens when a bond trades at a discount?
An investor earns a return from both receiving the coupons and from the face value that exceeds the price paid for the bond.
What is the cost of the project mentioned?
What is the maturity date for the Straumann Holding AG bonds?
March 27, 2023.
How is the present value of multiple cash flows calculated?
PV = c1/(1+r) + c2/(1+r)^2 + ... + cN/(1+r)^N.
What is the relationship between the coupon rate and bond price?
If the coupon rate is higher than the market rate, the bond price will be above par; if lower, it will be below par.
What is a sustainability-linked loan?
A loan where the interest rate is tied to the borrower's sustainability performance.
What happens if the bond price is not $952.38?
The opportunity for arbitrage will force the price of the security to rise until it equals $952.38.
What is the future value after 75 years at 10% interest?
1,271,895.72.
How do green bonds affect financial performance?
They increase financial performance metrics such as CAR and ROA.
What do green bonds signal to investors?
A credible commitment toward the environment.
What is a bond?
A financial security in which the issuer promises to make interest and principal payments to the holder.
What are the primary characteristics of bonds?
Maturity date, face value, and coupon.
What does the little girl's trust want from BMW?
It wants money in the long term and suggests building solar-powered cars.
What does 'r' represent in the present value formula?
'r' represents the interest rate.
What is the role of central banks in determining interest rates?
They influence very short-term interest rates through the rate at which banks can borrow overnight.
Why do investors pay less for bonds with credit risk?
Because the expected cash flow is lower due to the probability of non-payment.
What does the total payout model value?
All of the firm’s equity rather than a single share.
What is Single Materiality in ESG ratings?
It measures how well a company manages ESG risks to its own bottom line.
How does credit risk affect bond yields?
The yield of bonds with credit risk will be higher than that of otherwise identical default-free bonds.
What simplifications can be applied to the total payout model?
The same simplifications obtained by assuming constant growth.
What is impact investing?
Investing with the intention to generate positive social and environmental impact alongside a financial return.
What does it mean when results are equivalent but expressed as values at different points in time?
The decision to reject the investment remains the same.
How is the growth of purchasing power calculated?
Growth of purchasing power = Growth of money - Growth of prices.
How much of Titan's earnings is allocated for dividends?
30%.
How does an increase in interest rates affect the demand for loans?
It typically reduces the demand for loans.
What is the total amount of the Lonza Finance Intl NV bonds issued on April 8, 2020?
EUR 500,000,000.
What is the yield curve?
A graphical representation of the term structure of interest rates.
What does an inverted yield curve indicate?
It is often interpreted as a negative forecast for economic growth.
If the firm finances the investment by issuing equity, what is the total equity after investment?
What is the initial investment required for the project mentioned?
$9.5 million.
What is the maturity date of a bond?
The final repayment date.
What does the effective annual rate (EAR) indicate?
The total amount of interest that will be earned at the end of one year.
How does ESG ratings divergence affect companies' incentives?
It decreases their incentives to improve ESG performance due to mixed signals from rating agencies.
What does the gray line represent for each coupon bond in the graph?
The trend of the bond price just after each coupon is paid.
How do bond prices relate to interest rates?
Bond prices inversely move with interest rates; when rates rise, bond prices fall and vice versa.
Why is calculating present value important?
It helps in saving for the future by understanding the value of future cash flows today.
What is the future value of $100 today in two years at an annual interest rate of 5%?
$110.25.
What is Titan Industries' expected earnings at the end of this year?
$860 million.
What have asset/wealth managers created in relation to green bonds?
Green Bond Funds.
How are stocks and bonds rated in ESG assessments?
Based on their ability to manage risks compared to peers in their industry.
What is the relationship between yield to maturity and coupon rate for a bond trading at a discount?
The yield to maturity will exceed the coupon rate.
What is the NPV of the project?
What is the price of a bond promising a risk-free payment of $1000 in one year at a 5% interest rate?
$952.38.
What role do green bonds or loans play for firms?
They indicate a firm's commitment to sustainability.
What is the expected growth rate of Titan's earnings per year?
7.5%.
What is the total value of productive assets?
What does APR stand for in the context of bond coupon rates?
Annual Percentage Rate.
What is Titan's share price?
$79.26 per share.
What is the NPV of the project at an interest rate of 1%?
0.245 (approximately 0).
What is the yield to maturity on a bond with a face value of 100, coupon rate of 10%, and price of 100?
The yield to maturity equals the coupon rate of 10% since the bond is sold at par.
What happens to a dollar invested at an APR of r with continuous compounding?
It grows to e^(r) as k approaches infinity.
How is the future value of an investment calculated using EAR?
By raising the interest rate factor (1 + r) to the appropriate power.
What happens when central banks increase interest rates?
They aim to curb inflation by slowing down the economy (demand).
What is the net value when comparing the present value of benefits and costs?
-$952.
What is the Real Interest Rate (rr)?
The rate of growth of your purchasing power, after adjusting for inflation.
How can a shareholder with a liquidity need today benefit from a long-term project?
By selling her share in the market.
What is the dominant strategy in impact investing?
Invest in firms perceived to be 'green' and divest from those perceived to be 'brown'.
What are some common structures of sustainable financing?
Green bonds, sustainability-linked loans, and social impact bonds.
What is the coupon rate for the Sonova Holding AG bonds due 2022?
0.550%.
What is the present value of benefits from the project?
What is the future value after 20 years at 10% interest?
6,727.50.
What is Titan's equity cost of capital?
10%.
How many shares are there before the investment?
How much will a $1,000 bond with a 10% coupon rate pay every six months?
$50.
What is the value of risky assets after the investment?
What are sustainability-linked bonds (SLBs)?
Bonds whose financial characteristics can vary based on whether the issuer achieves predefined sustainability/ESG objectives.
What does the bond certificate describe?
The terms of the bond, including amounts and dates of all payments.
What are promised interest payments on a bond called?
Coupon.
What is the present value of $1 to be received in one year at a 10% interest rate?
$0.91 (approximately).
What should be done if the net value of an investment is negative?
Reject the investment.
What are green bonds?
Debt securities issued to raise funds for projects with positive environmental impacts.
What is a key implication of the law of one price for arbitrage?
If two identical assets are priced differently, arbitrageurs will buy the cheaper one and sell the more expensive one until prices converge.
What defines an arbitrage opportunity?
It occurs when it is possible to make a profit without taking any risk or making any investment.
What is the formula for continuous compounding?
lim (k→∞) (1 + r/k)^k = e^r.
Why do zero-coupon bonds trade at a discount?
Because they are priced lower than the face value when interest rates are positive.
What is the concept of earning interest on interest?
It refers to the interest earned on previously earned interest, increasing the total amount over time.
How many years will Ellen save for retirement if she starts at age 35?
30 years.
What is the present value (PV) of a $1000 cash flow owed by Gap Inc. to be paid in 5 years?
The PV can be calculated using the appropriate discount rate from the provided table.
Does issuing a green bond guarantee that the issuer is environmentally friendly?
No, it does not directly imply that the issuing company/entity is green.
What is the relationship between bond price and yield to maturity?
Given the bond price, we can compute the yield to maturity.
What is the formula for future value after 7 years at 10% interest?
1,948.72.
What questions arise regarding the effectiveness of the impact investing strategy?
Does this strategy make sense? Can it work? How does it compare to imposing a carbon tax?
What is the coupon rate of the Nestlé Finance Intl Ltd bonds due 2030?
1.500%.
What is the primary goal of firms in relation to their shareholders?
To create value by investing in 'good' projects.
What does the time value of money imply?
1 in one year.
What should firms identify to assess their decisions?
The costs and benefits of their decisions.
Why do investors need rules when investing in different firms?
To invest optimally across various firms.
What is the formula to calculate the future value of $1 today at an interest rate of r?
Future Value = $1 × (1 + r).
What factors differentiate projects according to the text?
What do corporations need to choose among projects?
Rules that allow fair comparison based on risk, level, and timing of cash flows.
Why is 1 in the future?
Because it can be invested and start earning interest immediately.
If the interest rate is 10%, what will $1 grow to in one year?
$1.10.
