Question

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

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

Please provide detailed formula solutions

Answer 1

Solution 1) 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%

OR

YTM can also be calculated using the financial calculator as:

N = 34, PV = -1120, FV = 1000, PMT = 50

CPT -> I/Y = 4.32%

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

OR

The bond pricing formula is given as:

On putting, C = 50, N = 34, P = 1120, M = 1000, we can solve for i,

On solving we will get, i = 4.32%

1120 = 50*(1 - (1+i)^(-34)/i + 1000/(1+i)^34

On solving i = 4.32%, thus, YTM of the bond = 4.32%*2 = 8.64%

These 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 2) 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

Please comment in case of any doubts or clarifications required. Please Thumbs Up!!