Yield to Maturity (YTM)
1.a) Describe briefly what is the Yield to Maturity (YTM).
1b) Suppose an 8% coupon, 30-year bond is selling at $1,276.76. What average rate of return (calculated as bond equivalent yield) would be earned by an investor purchasing the bond at this price?
1c) Considering the facts pattern in b) above, describe and comments on the critical assumptions embedded in the 30-Year Bond yield to maturity figure?
2a) Frantz Jones seeks your assistance to help him calculate the price of a two-year annual coupon bond where the yield is 9%, 10% and 11% at year 1, 2 and 3 respectively. Assume the coupon rate is 6% and the face value is $1,000:
2b) State clearly the formula for determining the price of the bond in terms of its yield to maturity?
2c) Is the yield at year 2 greater or less than the yield to maturity at year 2? And if so, why?
3a) Explain how does a bond ladder strategy work if you want to limit your investment horizons to fixed-income securities with maturities of 15 years or less. Support your answers with concrete example of a portfolio.
3b) Explain the key differences or similarities, if any, between a bond ladder strategy and dollar cost-averaging. Support your answers with a concrete example of an investment portfolio.
4. For each of the investment vehicle below, provide a definition of what it is and illustrate key similarities and differences:
4a) Open-Ended Mutual Fund vs Exchange Traded Fund (ETF)
4b) Open-Ended Mutual Fund vs. Hedge Fund
5. Anna Bella is ecstatic. She had just been offered a position with a choice employer with a starting annual salary of $58K (gross) plus benefits. Among those, her employer is offering matching 401K plan contributions of up to 5% of her annual gross salary. She is still single but has been steady with her boyfriend for a couple of years and both have started to have serious discussions about living together and founding a family. First things first though, she wants to ensure she starts her professional career on solid foundations, particularly as it pertains to savings and investments. In this regard, she is soliciting your professional advice to help get started on her savings/investment plan as to what amount she should save regularly, what investment vehicle she should consider (e.g. stocks, bonds, mutual funds, index funds, certificate of deposits, options, etc.) and what should be in her investment horizon considering she just turned 22 and has plan to eventually earn a MBA or master degree in a relevant field within the next 10 years. She mentioned that she had to borrow to go to college and her outstanding student loan at graduation would be $20,000. She intends to repay this debt, which carries an interest rate of 5% per year within the next 5 years. Currently, she does not anticipate to retire until she is past 60. While well-educated and knowledgeable enough about world and financial affairs, she considers herself a neophyte in investments and is eager to learn. She wants to minimize her tax liabilities. Through further discussions, she mentions that she is rather risk-averse (like an average person) and she would portray herself as a value investor who wants to preserve her capital while pursuing long-term growth. She would be satisfied if her portfolio yields the market benchmark and understands that the market and securities prices fluctuate constantly. She wants to make sure though her savings/investments do well over a long period of time. For this, she is keenly interested in being informed on how she should model her savings/investments during the different phases of her life span (i.e. her 20’s; 30-50 years old; 50-60 years old, retirement years).
Recommend a savings or investment plan to help Ana Bella get started on the right footing. In your plan, specify your recommended percentage of savings/investment, the frequency and the investment vehicles (e.g. stocks, bonds, mutual funds, index funds, certificate of deposits, options, cryptocurrencies, etc.) which are relevant as well as suggested allocations during each phase of our life cycle. Also describe, relevant factors or considerations that Anna needs to consider in designing her savings/investment portfolio.
6. You are in your first year as financial analyst within a large corporation which is considering a new acquisition (TagCo) to support its long term growth. You have been given the following information on TagCo:
Current Free Cash Flow to the Firm (FCFF) =$745 millions
Outstanding shares= 309.39 million
Equity beta = 0.90, risk-free rate = 5.04%; equity risk premium = 5.5%
Cost of debt = 7.1%
Marginal tax rate = 34%
Capital structure: 20% debt, 80% equity
Long-term debt = $1.518 billion
Growth rate of FCFF =
8.8% annually in years 1-4;
7.4% in year 5, 6.0% in year 6, 4.6% in year 7;
3.2% in year 8 and thereafter.
Required:
From the information provided to you above, estimate the following:
6a) TagCo Weighted Average Cost of Capital (WACC);
6b) Total value of the firm;
6c) Total value of equity;
6d) Value per share.
Show all your calculations to derive the above estimates.
7a) As an investor, how do you pay attention to interest rates and yield spreads?
7b) Explain the key factors that cause interest rates to move:
8a) Considering your investment horizon, how would you execute a strategy to ‘ride the yield curve’ by buying bonds. Specifically how relevant would be the purchased bonds maturities in executing your strategy
8b) Assume a flat yield curve of 6%. A three-year $1,000 bond is issued at par paying an annual coupon of 6%. What is a bond’s expected return if you anticipate that the yield curve one year from today will be flat at 7%. Show the relevant details of your results.
9a) Portfolio A and Portfolio B had the same holding period return last year. Most of the returns from Portfolio A came from dividends, while most of the returns from Portfolio B came from capital gains. Which portfolio was likely owned by a single working person making a high salary, and which one was likely owned by a retired couple? Why?
9b) Mom and Pop had a portfolio of long-term bonds that they purchased many years ago. The bonds pay 12% interest annually, and the face value is $100,000. If Mom and Pop are in the 25% tax bracket, what is their annual after-tax HPR on this investment? (Assume it trades at par.)
9c) Your portfolio has a beta equal to 1.3. It returned 12% last year. The market returned 10%; the risk-free rate is 2%. Calculate Treynor’s measure for your portfolio and the market. Did you earn a better return than the market given the risk you took?
1. a) Yield to maturity is the rate that is used to discount the future cash flows associated with the bond. Typically it is the return earned by the bondholder for purchasing and holding the bonds till their maturity. This rate equates the present value of the cash flows related to bond with their current market price. YTM is also referred as internal rate of return or the market interest rate (Stack Exchange, 2018).
Part b
| Formula | $1,276.76 = $80 ×Annuity factor(r, 30) + $1,000 ×PV factor(r, 30) |
| FV | 1000 |
| Price | 1276.76 |
| Maturity | 30 |
| Coupon | 8% |
| PMT | $80.00 |
| Bond Equivalent Yield | 6% (rounded off) |
c. The critical assumptions embedded in the 30-Year Bond yield to maturity figure are as follows:
- The holder of the bond will keep the bond till the maturity of such bonds.
- The coupon (interest on bonds) must be invested at the same rate as that of YTM (Stack Exchange, 2018).
2. a)
| Years | Cash Flows ($) | DCF | PV ($) |
| 1 | 60 | 0.917 | 55.046 |
| 2 | 60 | 0.982 | 58.934 |
| 2 | 1000 | 0.982 | 982.240 |
| Price of bond | 1096.220 |
b)
| Bond Price= | ( (Coupon/YTM)* ( 1-(1/(1+YTM/2)2M) ) + (FV/(1+YTM/2)^2M) |
c) Yield at year 2 is lesser than yield to maturity at year 2 because the yield to maturity includes the year 1 interest payment made on the bond. However, year 2 yield only covers only interest and principle payment.
3. a) Bond Laddering is a strategy which involves maturity weighting under which funds of the investors are divided among different bonds that have longer maturities. This strategy is used to reduce or minimise the risk of interest rate fluctuation and re-investment risk (Investinginbonds.com., 2018).
For example:
John has invested funds in equal amounts to different bonds which will mature at the regular intervals.
| Bond A | Bond B | Bond C | Bond D | Bond E |
| Maturity: 2 Years | Maturity: 4 Year | Maturity: 6 Year | Maturity: 8 Year | Maturity: 10 Year |
| Amount= $20000 | Amount= $20000 | Amount= $20000 | Amount= $20000 | Amount= $20000 |
| Interest Rate= 1.55% | Interest Rate= 2.05% | Interest Rate= 2.80% | Interest Rate= 3.22% | Interest Rate= 3.30% |
The average maturity of the portfolio consisting of above bonds is 15 years. Now, when the bond A will mature after 2 years, John will have two options:
Either to reinvest his principle in a fresh 10 year bond or to take the money out and invest somewhere else. The other bonds will be 2 years closer to their respective maturity now.
Bond laddering strategy is a buy-hold strategy that can be used as support for the potential impact of rising interest rates (Carlson, 2018).
b) Dollar cost averaging involves purchasing of more shares when the market is down and less shares when the market is up. While bond ladder involves investment in multiple securities at a single time, in almost equal amount (Leach, 2018). Bond ladder is for high interest yielding securities.
4. a) Open-Ended Mutual Fund v/s Exchange Traded Fund (ETF)
- The prime similarity among Open ended Mutual Funds and Exchange Traded Fund is that they both portray professionally managed baskets or the collections of various bonds or securities.
- Further, both of these funds provide a wide variety for the investment options.
| Basis | Exchange traded funds | Open Ended Mutual Funds |
| Expense Ratio | The expense ratio of ETFs lies in between the range of 0.1% to 1.25% | The expense ratio of Open ended mutual funds lies in between the range of 0.1% to 10% |
| Pricing | These funds are priced throughout the day at the market price on the trading day which may not be similar to the Net asset value. | These are priced once per day and that too at the end of the trading day. These are priced at NAV |
| Tax efficiency | Low Cost, Tax efficient and involves transparency. | These are less tax efficient (Anspach, 2018). |
b. Open-Ended Mutual Fund vs. Hedge Fund
- Both the funds work as an investment pool and involve investment in various securities such as stocks bonds and commodities.
- Further, both the funds are managed by the professional experts.
| Basis | Hedge funds | Open Ended Mutual Funds |
| Investors | In hedge funds, funds of limited investors are permitted to be pooled for the purchase of assets. | In Mutual funds, the funds of number of investors are managed by the fund manager to purchase bunch of securities from the market. |
| Aim | These funds aim at offering maximum possible returns to the investors. | These funds aim at provision of return in excess of risk free return rate that is offered in market. |
| Investors | Established individuals with high risk bearing capacity. | Retail investors who invests their limited income to multiply their money. |
5. An investment plan must be diversified so as to manage the risk of overall investment. Diversification involves making investment in different types of investment vehicles in the amounts that must be decided according to the risk and reward generating capacity of each investment vehicle. Stocks give the investors income in two forms: dividend and capital gain. When the investors are not looking for a source of steady income they can opt for equity investment which will not only provide them return in the form of dividend but also it will provide them the stake in the company’s holding in the form of voting rights (Finra, 2018). However, when the investors expect steady returns they must invest in bonds as they generally provide fixed income. Mutual funds are again a better option for the potential investors as these funds allow them to put their savings in the pool of investments on the basis of benefits and limitations of each security. Since in the current case, Anna will require a loan to be repaid and for this purpose it will require funds it must invest prudently.
For example Anna has 100 lacks dollars to be invested. Then it must invest 40% in equity, 30% in debt or bond and in mutual funds. This will allow her to diversify the investment.
6.
| Current Free Cash Flow to the Firm (FCFF) | 745 | ||
| Outstanding shares | 309.39 | ||
| Equity beta | 0.9 | ||
| risk-free rate | 5.04% | ||
| Equity risk premium | 5.50% | ||
| Cost of debt = | 7.10% | ||
| Marginal tax rate | 34% | ||
| Capital structure: | |||
| Debt | 20% | ||
| Equity | 80% | ||
| Long-term debt= | |||
| Growth rate of FCFF | |||
| 1-4th Years | 8.80% | ||
| Year 5 | 7.40% | ||
| Year 6 | 6.00% | ||
| Year 7 | 4.60% | ||
| Year 8 | 3.20% | ||
| Ke | RF + Beta (Risk Premium) | ||
| 9.99% | |||
| Kd | Before tax Kd (1-tax rate) | ||
| 4.69% | |||
| WACC | Proportions | Rates | Weighted Rates |
| Debt | 20% | 4.69% | 0.94% |
| Equity | 80% | 9.99% | 7.99% |
| WACC | 8.93% | ||
| Value of firm | |||
| 1 | 810.56 | 0.918 | 744.12 |
| 2 | 881.88928 | 0.843 | 743.23 |
| 3 | 959.4955366 | 0.774 | 742.35 |
| 4 | 1043.931144 | 0.710 | 741.47 |
| 5 | 1121.182049 | 0.652 | 731.06 |
| 6 | 1188.452971 | 0.599 | 711.40 |
| 7 | 1243.121808 | 0.550 | 683.13 |
| 8 | 1282.901706 | 0.504 | 647.20 |
| PV of Cash Flows | 5743.97 | ||
| Continuing Value | 1282.90 | ||
| 5.73% | |||
| CV | 22392.33586 | ||
| PV of CV | 11296.52549 | ||
| Part c | Value of firm | 17040.50 | |
| Part d | Value of Equity | ||
| Value of firm | 17040.50 | ||
| Less: Value of Debt | 1518 | ||
| Value of Equity | 15522.50 |
| Value per share | |
| Value of Equity/ Number of shares | 15522.50/309.39 |
| Value per share | $ 50.17 |
7. a) An investor pays attention to interest rates and yield spreads because:
The yield of any bond is mainly comprised of two things: Interest rate and the Credit spread. Interest rate serves as the base rate for each type of bond which is denominated in a particular currency and it compensates for the baseline economic risks of the investors (Finra, 2018). The credit spread or yield spread reflects the difference between rates quoted for two investments with different qualities and maturities. This spread represents idiosyncratic risks which is associated with the specific issuer of the bond or security (Fidelity, 2018).
b) The key factors that cause interest rates to move:
- Supply or demand: The demand and supply of money in an economy leads to change in movement in interest rates. Increase in demand or decrease in supply of money leads to the interest rates of an economy go up and vice versa.
- Inflation: When the rates of goods and services in an economy rise, the interest rates also increases and vice versa.
- International borrowings: With the increased scope of globalisation it has become quite common that the companies can borrow required funds from the foreign markets and when foreign investors competes the local finance providing institutions, the interest rates moves.
- Federal fund rates: These are the rates that are being charged by one bank from another for their short term borrowing and lending transactions. When federal banks charges higher rates, the interest rates for the normal citizens of the country increase.
8. a) Riding the yield curve means purchasing the long term bonds or securities and selling them before their maturity. The basic purpose behind their execution is to reap certain interest rate benefits from the market. Suppose we are riding a yield curve and the yields rises considerably we will have to bear a capital loss on such a riding position. If such instrument was purchased which matched our investment horizon, it would certainly result in positive return (Bieri & Chincarini, 2005).
b)
| Year | CFS | PVF | PV of CFS |
| 1 | 60 | 0.934579 | 56.07477 |
| 2 | 60 | 0.889996 | 53.39979 |
| 3 | 60 | 0.816298 | 48.97787 |
| 3 | 1000 | 0.816298 | 816.2979 |
| 974.7503 |
9. a) Portfolio A offers most of the income to the investors in the form of dividend and it seems to be held by the retired couple as they would be looking for an investment that is less risky in terms of return fluctuations and they could have a steady source of income. The portfolio that provides dividend as the income generally involves less risk because of constant income. On the other hand, portfolio B provides returns to the investors in the form of capital gains. This is likely to be held by someone who is not in the need of current income and is willing to bear high risk as the prices of the shares keeps on fluctuating and there is a risk of fluctuation of such price on a negative side and also there are possibilities of price increment where one can make higher returns.
b)
| Face Value | 100000 |
| Bond Interest Rate | 12% |
| Income | 12000 |
| Tax Rate | 25% |
| Tax | 3000 |
| Net Tax Income | 9000 |
| Annual HPR | 9.00% |
c)
| Beta | 1.3 |
| Market Return | 10% |
| Risk Free Rate | 2% |
| Portfolio Return | 12% |
| Treynor’s Measure | Portfolio Return – Risk Free Rate |
| for portfolio | Portfolio beta |
| 7.69% | |
| Treynor’s Measure | Market Return – Risk Free Rate |
| for portfolio | Portfolio beta |
| 6.15% |
References:
Stack Exchange. 2018. Yield-to-Maturity and its assumption. Retrieved from: https://quant.stackexchange.com/questions/33028/yield-to-maturity-and-its-assumption
Investinginbonds.com. 2018. Bond Investment Strategies. Retrieved from: https://investinginbonds.com/learnmore.asp?catid=6&id=386
Finra, 2018. Smart Bond Investing. Retrieved from: https://www.azinvestor.gov/Documents/Smart_Bond_Investing-FINRA.pdf
Leach, 2018. Are There Better Strategies Than Dollar Cost Averaging? Retrieved from: https://www.suredividend.com/better-than-dollar-cost-averaging/
Carlson, B., 2018. The Lump Sum vs. Dollar Cost Averaging Decision. Retrieved from: https://awealthofcommonsense.com/2018/05/the-lump-sum-vs-dollar-cost-averaging-decision/
Anspach, D. 2018. The Difference Between ETFs and Open-Ended Mutual Funds. Retrieved from: https://www.thebalance.com/differences-between-etf-s-and-open-ended-mutual-funds-2388639
Fidelity. 2018. How interest rates affect bonds. Retrieved from: https://www.fidelity.com.sg/beginners/bond-investing-made-simple/how-interest-rates-affect-bonds
Bieri, D. S., & Chincarini, L. B. (2005). Riding the yield curve: a variety of strategies. Journal of Fixed Income, 15(2), 6.