Lesson 6 of Investments: Bond Valuation Flashcards
Bond Valuation and Pricing!
- Coupon Rate
- Par Value
- Length of Time to Maturity
- Market Interest Rates
- Important Considerations
Coupon Rate
-
Coupon rate
- is the periodic interest payment received by a bond holder.
- The actual dollar amount of the coupon payment is entered as a payment on a financial calculator
For example:
- A bond with a 10% coupon pays $50 semiannually ($1, 000 par x 0. 10 coupon divide by 2)
- That is, 10% of the $1,000 par value or $100, paid semiannually at $50 each time.
Keystroke = PMT
Coupon rate is the stated rate
Par Value
Par value is the
- principal amount which is
- $1,000 on bond issues, unless stated otherwise.
The par value is the amount that
- will be repaid to bond investors at the end of the loan period.
Keystroke =FV
Length of Time to Maturity
- The length of time to maturity is the time remaining until the bond holder receives the par value.
- The length of time to maturity can be described as the “Number of periods” to maturity, or that the loan will be outstanding.
- For a bond paying semiannually, there will be 2 periods per year;
- quarterly payments will have 4 periods per year,
- and monthly, there will be 12 periods per year.
Keystroke = N
Market Interest Rates
-
Market interest rates
- is the yield that is currently being earned in the marketplace on comparable securities.
- Market interest rate is the
- rate used to discount a bond to
- determine what it is currently selling for in the market.
Keystroke = i (in some cases I/Y or I/YR).
Important Considerations
- The coupon rate, though expressed as an interest rate, is calculated as a constant dollar payment.
- Interest rate changes in the marketplace do not affect the coupon rate payments.
- Rising interest rates mean that investors can get a larger stream of cash flows
- (higher coupon) on new bonds from the corporation. Current bond holders
- selling bonds must do so at a discount.
- This makes their bond competitive with the new issue from the corporation.
- A drop in market interest rates
- means coupon rates on new bonds (constant income stream) from corporations will be
- less than previous bond issues making the older bonds worth a premium.
- Investors buying these higher coupon bonds (larger stream of cash flows) must pay a premium above par value.
Explaining Last Two Considerations
- An increase in interest rates mean the company would increase their coupon rate. The investor would buy the bond and give the money to the company. The company would pay higher coupon payments on the bond. The current bond holders would have to sell at a discount or decrease their face value so investor’s would be willing to buy from them.
- A decrease in interest rates mean the company would decrease their coupon rate. The investor would buy the bond and give the money to the company. Older bonds would become more attractive to the investors, especially if the investor is seeking a large stream of cash flows. As a result the investors are willing to pay more (than the face value or par value) to purchase older bonds. This is called a Premium.
- Investors are the ones who by the bond. They give money to company and receive stream of payments back.
Conventional Yield Measures of Bonds!
- Coupon Rate (CR) or Nominal Yield
- Current Yield (CY)
Coupon Rate (CR) or Nominal Yield
Coupon Rate is the annual payments
- amount in dollar, divided by the par value.
Coupon Rate (CR) or Nominal Yield
Not given on exam.
Coupon Rate = Coupon Payment ÷ Par
Example of Coupon Rate
A bond pays $100 per year with a par value of $1,000.00
Calculate coupon rate.
Coupon Rate =
Coupon Payment = $100 ÷ $1,000
Coupon rate = 10%
Current Yield (CY)
The current yield is the annual payment
- in dollars divided by the current price of the bond.
Current Yield Formula
Not given on exam.
Current Yield = Coupon Payment ÷ Price of the Bond
Current Yield Formula Example
A bond pays $100 per year total, with a current market price of $876.00. What is the Current Yield?
Coupon Payment = $100
÷
Price of the Bond = $876
Current Yield = 11.42%
Exam Question
Paul is considering a bond with a current yield of 8% and selling for $900. Assuming the bond pays an annual coupon, what is the coupon rate of this bond?
a) 5.5%
b) 6.0%
c) 7.2%
d) 8.2%
e) 9.0%
Answer: C
Current Yield Formula First:
Current Yield = Coupon Payment / Price of the Bond
.08 = x / 900
x = $900 x 8%
=$72
Coupon Rate =Coupon Payment / Par
=$72 / $1,000
=7.2%
Yield to Maturity (YTM)
Yield to maturity is essentially the
- compounded rate of return if an investor buys a bond today
- and holds it until maturity.
Yield to maturity assumes that an investor is
- able to reinvest the coupon payments at the yield to maturity rate.
Yield to maturity is
- useful for comparing the return on different bonds.
Calculating YTM
A bond paying 10% interest or $100 a year ($50 semiannually), the market price indicated is $876. There is a 5-year period to maturity, at which time the $1,000 par value will be paid to the investor. The calculation is as follows:
N = 10 (5x2)
I/Y= What you are trying to figure out?
PV = -876
PMT = 50
FV =1,000
I/Y = 6.744% x 2
=13.49%
When a company buys a bond, the investor loses the market price of the bond but receives the Face value and the periodic interest payments back. That’s why PV is negative and PMT and FV are positive.
Exam Question
What is the yield to maturity of a bond that is selling at a 5% discount to par, paying 11.25% interest, and maturing in 7 years.
a) 11.23%
b) 12.34%
c) 13.10%
d) 13.79%
Answer: B
5% discount to par = $1,000 par x 0.95 = $950.00
N = 7 x 2
i = ?
PV = -950
PMT = (1,000 x .1125) ÷ 2
FV = 1,000
i = 6.16 x 2 = 13.4%
Exam Tip
- Always assume semiannual compounding on the CFP Exam, unless told otherwise!
Exam Question
Joe purchased a bond for $800 with a 9% coupon. He told the bond after one year when it was paying him a current yield of 10%. What is the holding period return?
Current Yield = Coupon Payment / Price of the Payment
Step 1: Calculate Selling Price
0.10 = $90 / Price
Price = $900
Step 2 Calculate HPR
HPR = (SP - PP +/- Cash Flows) ÷ Purchase Price
= ( $900 - $880 +$90 ) / $880
=12.5%
Yield to Call (YTC)
Yield to call
- is the compounded rate of return if
- an investor buys a bond today and
- the bond is called (retired) by the issuer.
When calculating YTC,
- be sure to use the number of periods until the bond is called,
- not the time until maturity.
In addition, be sure to use the call price,
- not the par value as the FV.
Calculating YTC
A bond paying 10% interest or $100 a year ($50 semiannually), the market price indicated is $876. There is a 5-year period to maturity, at which time the $1,000 par value will be paid to the investor. The bond is callable in 3 years at $1,050. What is the YTC?
N = 6 (3x2)
I/Y = ?
PV = -$876
PMT = 50
FV = $1,050
I/Y = 16.78% (8.39 x2)
Exam Question
What is the yield to call of a bond that is selling at $1,200 paying 12% interest, semi-annually, and maturing in 10 years, if the bond is callable in 5 years at $1,050?
a) 3.96%
b) 7.91%
c) 10%
d) 12.91%
Answer: B
N = 10 (5x2)
PV = -$1,200
PMT = $60 = (($1,000 x 0.12) ÷2)
FV = $1,050
Yield Summary 1!
Comparing Premium, Par, and Discount:
- Par: will always be the same level for Coupon Rate, Current Yield, Yield to Maturity and Yield to Call
- Premium: Coupon Rate will always be the highest, followed by Current Yield, Yield to Maturity and Yield to Call.
- Discount: Yield to Call will always be highest followed by, Yield to Maturity, Current Yield and then Coupon Rate.
Explanation
Conversely, if a callable bond is trading at a premium (above its face value), the issuer is less likely to call the bond before maturity because it would have to pay a premium over the face value to retire the debt.
- In this case, the YTC for the investor is lower because the investor is less likely to experience an early call, and therefore, they are more likely to receive interest payments for a longer period, potentially until the original maturity date.
- The current price increased, which is why all the other ratings decreased.
If a callable bond is trading at a discount (below its face value), the issuer has an incentive to call the bond when market interest rates have fallen. This is because the issuer can retire the existing debt and reissue new debt at a lower interest rate, resulting in cost savings.
- In this scenario, the YTC would be higher for the investor because the investor may receive the call price, which is usually the face value of the bond, sooner than the maturity date. This results in a higher yield compared to holding the bond until maturity.
- The current price decreased, which is why all the ratings increased.
Yield Summary 2!
Yield Summary 3!
Accrued Interest!
- When purchasing a bond, the buyer
- pays the seller interest that has accrued since the last interest payment.
- The new buyer then receives the full amount of interest due
- at the next interest payment.
- The buyer will receive a 1099-INT
- that reflects the full period interest received, however,
- the buyer is entitled to a deduction equal to the amount of accrued interest paid to the seller.
Exam Tip:
- The buyer is not the original owner. Initial buyer is selling bond. They are compensated for when they had the bond,
Example of Accrued Interest
Taylor buys ten bonds listed as MSFT 6.00s 07/01/10 on September 30th. The bond pays interest semiannually. The price of the bond was $9,500 plus $100 commission. Taylor actually had to pay his broker the following:
Bond Price: $9,500
Commission: $100
Accrued Interest: $150 (6% × 10,000 × (3 ÷ 12))
(The 10,000 comes from par value)
- Note: July - September is three months of interest that Taylor will receive when the bond pays interest at the end of the year. Since he did not own the bond during this period, he must pay the accrued interest to the bond seller.
Total Payment to Broker = $9,750 (150+9,500+100) - Taylor will receive a 1099-INT with $300 ($10,000 × 6% × (6 ÷ 12)) as taxable interest; however, he is entitled to a deduction of $150 for the accrued interest he paid
Yield Curve
UET Formula
Ptovided on the exam.
1Rn = Actual N-period rate today
N = term to maturity, N = 1, 2, 3,
1R1 = Current one-year rate today
E(iR1) = expected one-year rate at period i,
where i = 1 to N.
- For examples the one-year rate expected at year three would be: E(3r1)
Example of UET
A simple two-year example may shed light on this complicated-looking formula.
Assume that the one-year rate today is 4%. Also assume that rates are expected to rise in the future, and that the one-year rate, next year, is predicted to be 4.5%.
According to the UET, the two-year rate being quoted today must reflect both one year rates: 4% for one a one-year loan today, and 4.5% for a one-year loan this time next year. According to the theory, the two-year rate today (¡Ry) should be equal to:
1R2 = [(1+1R1)(I+E(2r1))]^(1/N) -1
1R2 - [(1.04)(1.045)^(1/2)] -1
1R2 =.042497 = 4.249%
So, borrowing money for two years at the two-year rate today should be equivalent to borrowing money for one year (and paying the one-year rates) for two consecutive years.
Duration Formula
Formula given
Where:
y = Yield to maturity of the Bond
c = Coupon rate of the bond
t = Number of periods to Maturity.
Note: Adjust the y,c, and t if compounding is semiannual. Simply divide by 2 for y and c. Multiply by 2 for t.
Example of Duration
Consider a bond with a $1,000 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?
Calculate Duration using PV of Cash Flow Charts
Consider a bond with a $1,000 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?
- You would make a chart.
- First column would have Payment Period 1 to 5, not semiannual though.
- Second column would have Amount of Payment. Rows 1-4 would be $60 and then the fifth column would be $1,060 because you would take 6% annual coupon rate and multiply by (1+.06) and 1,000.
- Third column would be Period x Payment (FV).
- Fourth column would be PV of (Period x PMT). Use YTM for rate, and
- Add the fourth column up.
- Take that number and divide it by the market price to get duration.
Estimating Bond Price Formula
Formula on CFP Exam
Where D = Duration
y = Yield to Maturity
Δy = Change in Interest rates
(ΔP/P) = % Price Change
Exam Question
If an investor expects interest rates to increase, which type of bond would the investor prefer?
Bond A: AAA rate, 10-year maturity, 8.86 duration, 11% coupon, selling for $954.
Bond B: AA rated, S-year maturity, 4.2 duration, 12.5% coupon selling for $982.
Bond C: AA rated, zero-coupon, 30 year maturity, selling for $575.
a) Bond A.
b) Bond B.
c) Bond C.
Answer: B
The bond with the smallest duration will be the least sensitive to changes in interest rates. The bond with the smallest duration will have the shortest term and highest coupon/YTM.
Think back to the price of the bond formula, the capital gains will decrease but the smallest with Bond B as versus Bond A or C.
Exam Question
An investor expects interest rates to decrease, which type of bond would the investor prefer if the investor wants to maximize his capital gains?
Bond A: AAA rate, 10-year maturity, 8.86 duration, 11% coupon, selling for $954.
Bond B: AA rated, 5-year maturity, 4.2 duration, 12.5% coupon selling for $982.
Bond C: AA rated, zero-coupon, 30 year maturity, selling for $575.
a) Bond A.
b) Bond B.
c) Bond C.
Answer: C
The bigger duration of a bond, the more sensitive to changes in interest rates. By choosing the bond with the biggest duration, an investor will experience the biggest capital gain. The bond with the longest term and smallest coupon/YTM.
The 30-year bond will lead to the biggest increase in bond price. So because of this the investor would want this. Think back to the price of the bond formula. The percent change in bond price would increase by 55%.
Duration Assumptions:
- Duration assumes that there is a linear relationship between
- In fact, the actual price change of a bond is
- Convexity is a concept that actually measures the difference
- Duration does a good job of estimating the price change of a bond for
- Duration does NOT do a good job of estimating the price change of a bond for
- Duration understates
- Duration overstates
- a change in interest rates and a bond’s price change.
- NOT linear, it’s curve-linear.
- in price between what duration estimates and the actual price change of a bond.
- small changes in interest rates.
- large changes in interest rates.
- the price appreciation when interest rates decrease.
- the price depreciation when interest rates increase.
Calculating NOI
Not given on exam
Cash operating expenses does
- NOT include depreciation or amortization,
- which are not cash expenses.
- It also excludes payment on debt services
- since this is a financing expense, not an operating one.
Exam Question
Trippy owns 20 condominiums on the Gulf Coast of Florida. The condominiums rent for $9,167 per month. Trippy has a 10% vacancy rate and his total expenses for the year are $1,500,000. He pays $250,000 on his mortgage where $50,000 represents the interest. Assuming a 10% required rate of return, how much would an investor be willing to pay for the property?
The total $1,500,000 expenses includes the interest expense which is why you have to add that back in. Could also be for depreciation.
