Bond Valuation Flashcards
Calculate YTM for a bond paying 10% interest or $100/yr, market price is $876, 5-year period to maturity, matures at par or $1000
- EXAM TIP: Always assume semi-annual compounding unless told otherwise in the question
- Answer: I/YR = 13.49%
- PV: -876
- N: 10
- PMT: 50
- FV: 1000
What is the YTM of a bond selling at a 5% discount to par, paying 11.25% interest, and maturing in 7 years?
- i = 12.34%
- N: 14
- PV: -950
- PMT: (1000 x 0.1125) ÷ 2
- FV: 1000
Joe purchased a bond for $880 with a 9% coupon. He sold the bond after one year when it was paying a current yield of 10%. What is the holding period return?
- 12.5%
- Step 1:
- Current Yield: 0.10 = $90 / Purchase Price
- Price = $90/.10 = $900
- Current Yield: 0.10 = $90 / Purchase Price
- HPR = SP - PP +- Cash Flows ÷ Purchase price
- $900 - $880 + $90 / $880 = 12.5%
- Step 1:
- EXAM TIP: similar questions on CFP exam frequently!
- What is the relationship between Current Rate, Current Yield, YTM and YTC when a 20 year bond is trading at a current price of $1200 with a CR of 10% callable in 5 years at $1050?
- CR, CY, YTM, YTC
- CR: 10%
- CY: 8.3%
- YTM: 7.98%
- YTC: 6.16%
What is the relationship between Current Rate, Current Yield, YTM and YTC when a 20 year bond is trading at a current price of $1000 with a CR of 10% callable in 5 years at $1050?
- YTM,CY,CR,YTC
- YTM: 10%
- CY: 10%
- CR: 10%
- YTC: 10.78%
What is the relationship between Current Rate, Current Yield, YTM and YTC when a 20 year bond is trading at a current price of $800 with a CR of 10% callable in 5 years at $1050?
- CR: 10%
- CY: 12.50%
- YTM: 12.79%
- YTC: 16.74%
- What is the Exam Tip for the yield ladder or order of yields for a bond selling at a discount?
- “When shopping, if you see a discount “Call Mom’s Cell Now”
- Yield to Call
- Yield to Maturity
- Current Yield
- Nominal Yield
- What is the Liquidity Preference Yield Curve Theory?
- Lower yields for shorter maturities because investors prefer liquidity and are willing to pay for that in the form of lower yields
- Also, longer-term yields have more risk and should be higher
What is the Market Segmentation Yield Curve Theory?
- yield curve depends on supply and demand at a given maturity
- supply > demand at a given maturity, rates are low; rates will have to increase for demand to increase
- supply < demand at a given maturity, rates are high; rates will have to decrease for demand to drive demand down
What is the Expectations Yield Curve Theory?
- Yield curve reflects investors inflation expectations
- Typically, investors are uncertain or believe inflation will be higher in the future, long-term yields are higher than short-term yields
- If inflation is expected to be lower in the future long-term rates will be lower than short-term rates, resulting in an inverted yield curve
What is the Unbiased Expectations Theory?
- Related to the term structure of interest rates
- Today’s longer term rates have imbedded in them expecations about future short term interest rates
- Long term rates are geometric averages of current and expected future shorter-term interest rates
- Formula (on exam sheet)
- 1RN = [(1+1R1)(1+E(2r1))…(1+E(Nr1))]1/N - 1
- example on page 101
Describe Bond Duration:
- The weighted average maturity of all cash flows
- The bigger the duration, the more price sensitive/volatile the bond is to interest rate changes
- Duration is the moment in time the investor is immunized from interest rate risk and reinvestment rate risk
- Modified Duration: a bond’s price sensitivity to changes in interest rates
- A bond portfolio should have a duration equal to the investor’s time horizon to be effectively immunized
Q1: What is the relationship between a bonds term and duration?
Q2: What is the relationship between a bonds coupon rate/YTM and duration?
- A1: DIRECT: is term increases/decreases, duration will increase/decrease
- A2: INVERSE: as CR/YTM increase, duration will decrease; as CR/YTM decrease, duration will increase
- EXAM TIP: “Coupon rate and yield are INterest rates and there is an INverse relationship.”
How do you calculate a bonds duration using the two methods?
- Formula provided on CFP exam sheet, p102
- Calculate Duration using Present Value of Cash Flows Chart
- Create chart with headings Payment Period (N), Amount of Payment, Period x Payement (FV) and PV of (period x payment)
- Calculate the PV for each year, years X payment amount, in last year include bond maturing plus interest payment
- Total all years
- Add total to bond current value to find duration
- on page 103 of IP book
Consider a bond with a $1000 par value, five years to maturity, with a 6% annual coupon. The YTM is 8% and the bond is selling for $920.15. What is the duration of the bond?
- Use formula from exam sheet, Answer: 4.4 years
- Calculate Duration using the PV of Cash Flows Chart
Payment Period (Amount of Period x PV of
(N) Payment) Payment (FV) (Period x PMT) calculator:
1 $60 $60 $55.56 N=Payment Period
2 $60 $120 $102.88 i=8
3 $60 $180 $142.89 PV=?
4 $60 $240 $176.41 PMT=0
5 $1060 $5300 $3607.49 FV={period x pmt)
$4084.83
$4084.83 ÷ $920.15 = 4.4 years
- What is the Duration assumption?
- Is it accurate?
- That there is a linear relationship between a change in interest rates and a bond’s price change.
- No, the actual price change of a bond is NOT linear, it’s curve-linear
What is convexity?
- A concept that actually measures the difference in price between what Duration “estimates” and the “actual” price change of the bond
- What does Duration to a good job of estimating?
- What does Duration to a bad job of estimating?
- The price change of a bond for small changes in interest rates
- The price change of a bond for large changes in interest rates
- What does Duration do when interest rates decrease?
- What does Duration do when interest rates increase?
- Understates the price appreciation when interest rates decrease
- Overstates the price depreciation when interest rates increase
- Describe various Bond Strategies:
- Tax Swap
- sell a bond with a gain and a bond with a loss to offset
- Sell a bond with a loss and buy a replacement
- Barbells
- Own both short-term and long-term bonds
- When interest rates move, only one set of positions need to be sold and restructured
- Laddered Bonds
- Purchasing bonds with varying maturities
- As bonds mature, new bonds are purchased with longer maturities than what is outstanding in the portfolio
- Bullets
- Have very little payments during interim period, then a lump sum at a specified date in the future
- Bost bonds will mature around the same time period
- Zero-coupon, Treasuries, and corporates most likely candidates since they have little or no coupon during period and payoff comes at a date in the future
- Typically used when an investor has a baloon payment due on a liability at some future date
Describe Preferred Stock:
- Has both equity and debt features
- Debt:
- Stated par value
- Stated dividend as a percentage of par
- ex. 5% dividend with par value of $20=20X5%=$1 per sh
- Equity
- Price of preferred stock may move with price of common stock
- Debt:
- Q1: What are the unique features of preferred stock?
- Q2: What is a tax advantage?
A1:
- Dividend does not fluctuate like a common stock dividend
- No maturity date like a bond
- Price more closely tied to interest rates than common stock
A2:
- Corporations receive a 50 or 65% deduction of dividends (preferred or common stock) based on percentage ownership of the company paying the dividends for tax years beginning after December 31, 2017 (covered in tax module)
- Q1: Describe Convertible Bonds:
- What is the formula for Conversion Value?
- A1: One of the primary benefits of convertible bonds is that even if the stock does not perform well, the investor has a floor built in.
- The floor is the par value of the bond if held to maturity
- A2:
- CV = PAR/CP X Ps
- Ps = the price of the common stock
- CP is the conversion price
- (1000 ÷ CP) is the conversion ratio or the number of shares the convertible can be converted into
- CV = PAR/CP X Ps
- EXAM TIP: Formula no longer on CFP Exam Sheet
Describe Property Valuation:
- A formula to determine how much an investor is willing to pay for a piece of property
- Just a restatement of the dividend yield formula
- FORMULA
- Capitalized Value = Net Operating Income (NOI) / Capitalization rate
- Capitalized rate = NOI ÷ Cost
How do you calculate Net Operating Income (NOI)
Gross Rental Receipts
+ Non-Rental Income
= Potential Grosss Income (PGI)
- Vacancy & Collection Losses
= Effective Gross Income (EGI)
- Total (Cash Operating) Expenses
= Net Income
+ Interest Expense
+ Depreciation Expense
= Net Operating Income
- Cash operating expenses does not include depreciation or amortization, which are not cash expenses. It also excludes payments on debt service since this is a financing expense, not an operating one
