Question

ABC Corp. just issued some new preferred stock. The issue will pay a $3 quarterly dividend in perpetuity, begining 12 years from now. If the market requires a 8% return on this investment, how much does a share of preferred stock cost today?

Suppose that you buy a semi-annual coupon bond with coupon rate of 10%; the market price of $1,120, and the time to maturity of 17 years. Seven years from now, the YTM on your bond is expected to decline by 2%, and you plan to sell. What is the holding period yield (HPY) on your investment?

Consider the following bond quotes for ABC and XYZ Corp.

It is June 27, 2020. You must provide equations for each of the questions.

Issuer Name	Coupon	Maturity	Last	Change	Yield%
ABC Corp.	4.375	12/27/2038	92.5133	-0.315	?????
XYZ Corp	0.000	06/27/ 2031	46.9150	+0.234	?????

Note that yields for ABC and XYZ Corp bonds are all semiannually compounded.

1. (6 points) Supply the missing information (yield%) for each of the bonds.

2. (6 points) What are the current yield and expected capital gains yield for the next year for ABC Corp bond?

3. (2 points) What was the yesterday’s price for ABC Corp bond?

Answer 1

Solution 1) According to the Gordon Growth Model, the present value of the perpetuity = Expected Dividend/Required Rate of Return

Annual stated rate = 8%

Since the dividend is paid on a quarterly basis, hence, rate = 8%/4 = 2%

The present value of perpetuity with $3 quarterly dividend starting 12 years from now = $3/2% = $150

Since this present value is at t=12 years, hence, the present value of this cash flow today is:

= 150/(1+8%)^12

= $59.567 = $59.57

Solution 2) Coupon rate (C) = 10%

Since the coupon is paid semi-annually, thus, coupon per period = 10%*1000/2 = $50

Original time-to-maturity = 17 years

Total number of periods (n) = 17*2 = 34

The current market price at which bond is bought (P) = $1120

The YTM of the bond can be calculated using the Rate function in Excel = RATE(Nper, PMT, PV, FV, TYPE)

= RATE(34, 50,-1120,1000,0)

= 4.32%

On an annual basis, YTM of the bond = 2*4.32% = 8.64%

The coupons will be reinvested at the YTM

The reinvestment income by investing the coupons is calculated as:

= C*[(1+r)^n - 1]/r

= 50*[(1+4.32%)^14 - 1]/4.32%

= 50*[(1.0432)^14 - 1]/4.32%

= 50*[1.807782 - 1]/4.32%

= 50*0.807782/4.32%

= 934.9329

= $934.93

YTM of the bond after 7 years = 8.64% - 2% = 6.64%

YTM per period (i) = 6.64%/2 = 3.32%

Years left to maturity = 17 -7 =10 years

Number of periods on semi-annual basis = 10*2 = 20

Coupon (PMT) = 50

Price of the bond is calculated as follows:

P = 50*[1 - (1+3.32%)^(-20)]/3.32% + 1000/(1+3.32%)^20

P = 50*[1 - 0.532606]/3.32% + 1000/1.877561

P = 50*0.467394/3.32% + 532.606

P = 703.9066 + 532.606

P = $1236.513

Holding period yield is calculated as:

1120 = (1236.513 + 934.93)/(1 + r)^14

1120 = 2171.443/(1+r)^14

r = (2171.443/1120)^(1/14) - 1

r = 1.048426 - 1

r = 0.048426 = 4.8426%

On an annual basis, the Holding Period Yield is = 4.8426%*2 = 9.685% = 9.69%

Solution 3) a)

For ABC Corp.

Let the Face Value = 100

Bond Price = Last trading price = 92.5133

Coupon = 4.375

Number of years = 18.5 years

Since it is semi-annual compounding, thus, number of periods = 18.5*2 = 37

Coupon per period = 4.375/2 = 2.1875

Yield of the bond can be calculated using the RATE function in Excel = RATE(Nper, PMT, PV, FV, TYPE)

= RATE(37,2.1875,-92.5133,100,0)

= 2.5000%

On the annual basis, Yield on the bond is = 2.5000%*2 = 5.0000%

For XYZ Corp.:

Let the Face Value = 100

Bond Price = Last trading price = 46.9150

Coupon = 0

Number of years = 11 years

Since it is semi-annual compounding, thus, number of periods = 11*2 = 22

Coupon per period = 0

Yield of the bond can be calculated using the RATE function in Excel = RATE(Nper, PMT, PV, FV, TYPE)

= RATE(22,0,-46.9150,100,0)

= 3.5000%

On the annual basis, Yield on the bond is = 3.5000%*2 = 7.0000%

Solution 3) b) Current Yield of the bond = Annual Coupon payment/Price of the bond

For ABC Corp.

Current yield = 4.375/92.5133 = 4.7290%

For XYZ Corp.

Since it is a zero-coupon bond, thus, current yield = 0

To calculate the expected capital gains yield, the bond price for the next year is calculated.

For ABC Corp.

Nper = 35, Rate = 2.5%, PMT = 2.1875, FV = 100,

Price can be calculate as = PV(Rate, Nper, PMT,FV,Type)

= PV(2.5%,35,2.1875,100,0)

= $92.7671

Expected capital gains yield = (P1 - P0)/P0 = P1/P0 - 1 = 92.7671/ 92.5133 -1 = 0.2743%

For XYZ Corp.

Nper = 20, Rate = 3.5%, PMT = 0, FV = 100,

Price can be calculate as = PV(Rate, Nper, PMT,FV,Type)

= PV(3.5%,20,0,100,0)

= $50.2566

Expected capital gains yield = (P1 - P0)/P0 = P1/P0 - 1 = 50.2566/ 46.9150 -1 = 7.123%