CHP 7

Capital Gains Yield

capital gains yield is the rise or the fall in the price of a security represented by the percentage of current price.

The call provision generally states

states that the issuer must pay the bondholders an amount greater than the par value if they are called. The additional sum, which is termed a call premium, is often equal to one year's interest. Call premium declines over time as the bonds approach maturity

Will the actual realized yields be equal to the expected yields if interest rates change? If not, how will they differ?

As rates change they will cause the end-of-year price to change and thus the realized capital gains yield to change. As a result, the realized return to investors will differ from the YTM.

Current Yield

Current yield is a bond's annual return based on its annual coupon payments and current price (as opposed to its original price or face).

¬ Example on pricing a semiannual bond: What is the value of a 10-year, 10% semiannual coupon bond, if rd = 13% and par value is 1000?

Multiply number of years by 2: N = 2 x 10 = 20. Divide nominal rate by 2: I/YR = 13/2 = 6.5. Divide annual coupon by 2: PMT = 100/2 = 50. FV= 1000 CPT PV= -834.72

Par value

face amount of the bond, which is paid at maturity (assume $1,000).

**Both long-term bonds and low-coupon bonds...

get most coupons relatively later, and later coupons are more sensitive to interest rate changes, so long-term bonds and low-coupon bonds have more price risk.

Borrowers are willing to pay more...

, and lenders require more, for callable bonds.

Three conversion when calculating for semiannual bonds:

1. Multiply number of years N by 2: Number of periods [N]= 2N 2. Divide nominal rate rd by 2: Periodic rate [I/YR] = rd/2 3. Divide annual coupon by 2: Semiannual coupon [PMT] = Annual coupon/2

Example of calculating CY and CGY: Find the current yield and the capital gains yield for a 10-year, 9% annual coupon bond that sells for $887, and has a face value of $1,000.

CY= Annunal coupon payment/Current price = 90/887= .1015= 10.15% CGY= N=10 PMT=90 PV=-887 FV=1000 CPT I=YTM= 10.91% CGY=YTM-CY =10.91%-10.15%= .76%

Kaufman Enterprises has bonds outstanding with a $1,000 face value and 10 years left until maturity. They have an 11% annual coupon payment, and their current price is $1,185. The bonds may be called in 5 years at 109% of face value (Call price = $1,090). What is the yield to maturity? Round your answer to two decimal places. What is the yield to call if they are called in 5 years? Round your answer to two decimal places.

Find the YTM as follows: N = 10, PV = -1,185, PMT = 110, FV = 1,000 I/YR = YTM = 8.22%. Find the YTC, if called in Year 5 as follows: N = 5, PV = -1,185, PMT = 110, FV = 1,090 I/YR = YTC = 7.91%

Callaghan Motors' bonds have 18 years remaining to maturity. Interest is paid annually, they have a $1,000 par value, the coupon interest rate is 9.5%, and the yield to maturity is 6%. What is the bond's current market price? Round your answer to the nearest cent.

N = 18; I/YR = YTM = 6%; PMT = 0.095 x 1,000 = 95; FV = 1,000; PV = VB = ? PV = $1,378.97 PMT= coupon intrest rate times par value YTM=ir

The same company also has 10-year bonds outstanding with the same risk but a 13% annual coupon rate. This bond has an annual coupon payment of $130.

N=10 I=10 CPT PV=-1184 PMT=130 FV= 1000

Example of pricing a Discount Bond: The same company also has 10-year bonds outstanding with the same risk but a 7% annual coupon rate. This bond has an annual coupon payment of $70. Since the risk is the same the bond has the same yield to maturity as the previous bonds (10%). In this case, the bond sells at a discount because the coupon rate is less than the yield to maturity. And the bond's price is lower than its par value

N=10 I=10 PMT= 70 FV=1000 PV=? PV=-815.66

Example on YTM for Premium Bond: What is the YTM on a 10-year, 9% annual coupon, $1,000 par value bond, selling for $1,134.20?

N=10 PV= -1134 PMT=90 FV=1000 CPT I= 7.08

Example on YTM for Discount Bond: What is the YTM on a 10-year, 9% annual coupon, $1,000 par value bond, selling for $887?

N=10 PV= -887 PMT=90 FV=1000 CPT= I= 10.91

a bond with a face amount of $20,000 maturing in 20 years with a price of $6,757. At the beginning, you spend $6,757 to buy this zero coupon bond, and at the end of the 20 years, the investor will receive $20,000. What is the interest rate of this zero coupon bond?

N=20 Pv= -6757 fv= 20,000 pmt=0 I= ?

Practice on Bond Valuation: Morin Company's bonds mature in 8 years, have a par value of $1,000, and make an annual coupon interest payment of $65. The market requires an interest rate of 8.2% on these bonds. What is the bond's price?

N=8 I=8.2 PMT= 65 FV=1000 cpt PV=

Example on YTC of semiannual bond: A 10-year, 10% semiannual coupon bond with a par value of 1000 selling for $1,135.90 can be called in 4 years for $1,050, what is its yield to call (YTC)?

N=8 PV= -1135.9 PMT= 50 FV=1050 CPT I= 3.568 YTCnom= 3.568 X 2(SEMIANUNAL)= 7.137%

Bond valuation Bond X is noncallable and has 20 years to maturity, a 9% annual coupon, and a $1,000 par value. Your required return on Bond X is 8%; and if you buy it, you plan to hold it for 5 years. You (and the market) have expectations that in 5, years the yield to maturity on a 15-year bond with similar risk will be 8%. How much should you be willing to pay for Bond X today? (Hint: You will need to know how much the bond will be worth at the end of 5 years.) Round your answer to the nearest cent.

N=Years to maturity - the years you are going to hold onto Step 1: N = 15, I/YR = 8%, PMT = 90, FV = 1,000 PV = -$1,085.59. VB = $1,085.59 Step 2: N = 5, I/YR = 8%, PMT = 90, FV = 1,085.59 PV = -$1,098.18. VB = $1,098.18. You would be willing to pay up to $1,098.18 for this bond today.

Yield to maturity

Rate of Return earned on a bond held until maturity (also called the "promised yield").

Bond Valuation

The market value of any real or financial asset, including stocks, bonds, or real estate purchased in hope of selling it at a profit, may be estimated by determining future cash flows and then discounting them back to the present

Yield to Maturity (YTM)

The rate of return earned on a bond if it is held to maturity. Yield to maturity is considered a long-term bond yield, but is expressed as an annual rate. In other words, it is the return of an investment in a bond if the investor holds the bond until maturity and if all payments are made as scheduled.

Yield to Call (YTC)

The rate of return earned on a bond when it is called before its maturity (on the call date).

Seven years ago the Singleton Company issued 29-year bonds with a 11% annual coupon rate at their $1,000 par value. The bonds had a 6% call premium, with 5 years of call protection. Today Singleton called the bonds. Compute the realized rate of return for an investor who purchased the bonds when they were issued and held them until they were called. Round your answer to two decimal places. Explain why the investor should or should not be happy that Singleton called them.

The rate of return is approximately 11.60%, found with a calculator using the following inputs: N = 7; PV = -1000; PMT = 110; FV = 1,060; I/YR = ? Solve for I/YR = 11.60%. N=7 because it was issued 7 years ago

What is the value of a 10-year, 10% annual coupon bond with par value of 1000, if cost of debt rd = 10%?

This bond has a $1,000 lump sum (the par value) due at maturity (t = 10), and annual $100 coupon payments beginning at t = 1 and continuing through t = 10, the price of the bond can be found by solving for the PV of these cash flows.

True or False？A call provision gives bondholders the right to demand, or "call for," repayment of a bond

Typically, companies call bonds if interest rates rise and do not call them if interest rates decline.

Yield to maturity and future price 1. A bond has a $1,000 par value, 8 years to maturity, and a 7% annual coupon and sells for $980. What is its yield to maturity (YTM)? Round your answer to two decimal places. 2. Assume that the yield to maturity remains constant for the next 2 years. What will the price be 2 years from today? Round your answer to the nearest cent.

VB = $980; M = $1,000; Int = 0.07 × $1,000 = $70. a. N = 8; PV = -980; PMT = 70; FV = 1,000; YTM = ? Solve for I/YR = YTM = 7.3394% ≈ 7.34%. b. N = 6; I/YR = 7.3394%; PMT = 70; FV = 1,000; PV = ? Solve for VB = PV = $983.99. n=6 because 8-2=6

Example on YTM and YTC: Radoski Corporation's bonds make an annual coupon interest payment of 7.35%. The bonds have a par value of $1,000, a current price of $1,130, and mature in 12 years, but they can be called in 5 years at $1,100. What is the yield to maturity on these bonds? What is their yield to call if the bonds are called by the firm in the fifth year

YTM: N=12 PV= -1130 PMT= 73.5 FV=1000 CPT I= 5.82 YTC: N=5 PV= -1130 PMT= 73.5 FV= 1100 CPT= I= 6.03

Zero Coupon Bond (Accrual Bond)

a debt security that doesn't pay interest (a coupon) but is traded at a deep discount (price is much lower than par value), rendering profit at maturity when the bond is redeemed for its full face value.

Current yield, capital gains yield, and yield to maturity Hooper Printing Inc. has bonds outstanding with 10 years left to maturity. The bonds have an 7% annual coupon rate and were issued 1 year ago at their par value of $1,000. However, due to changes in interest rates, the bond's market price has fallen to $810.40. The capital gains yield last year was - 18.96%. 1. What is the yield to maturity? Round your answer to two decimal places. For the coming year, what is the expected current yield? (Hint: Refer to Footnote 7 for the definition of the current yield and to Table 7.1.) Round your answer to two decimal places. 2. For the coming year, what is the expected capital gains yield? (Hint: Refer to Footnote 7 for the definition of the current yield and to Table 7.1.) Round your answer to two decimal places.

a. Solving for YTM: N = 10, PV = -810.40, PMT = 70.00, FV = 1,000 I/YR = YTM = 10.099%. N=10 is 10 years left of maturity b. The current yield is defined as the annual coupon payment divided by the current price. CY = $70.00/$810.40 = 8.638%. N = 9, I/YR = 10.099, PMT = 70.00, FV = 1,000 PV = -$822.24. VB = $822.24. Hence, the capital gains yield is the percentage price appreciation over the next year. CGY = (P1 - P0)/P0 = ($822.24 - $810.40)/$810.40 = 1.461%.

Reinvestment Rate Risk

rd will fall, and future CFs will have to be reinvested at lower rates, hence reducing income.

Coupon interest rate

stated interest rate (generally fixed) paid by the issuer. Multiply by par value to get dollar payment of interest.

Price Risk/Interest Rate Risk

the risk that rising rd will cause the value/price of a bond to fall

Issue date

when the bond was issued

Maturity date

years until the bond must be repaid