Question

A preferred stock is expected to pay every quarter into indefinite future, the following dividend yield, dented by DY:
DY = The annual yicld on 10-year GỌC bond, prevailing at the time of payment + 4%

The par value of the preferred stock is $100. Suppose the annual yield on 10-year GOC bond is expected to be as: 1.5% at the end of the first quarter, 2% at the end of the 2 quarter, 2.5% at the end of the 3d quarter, 3% at the end of the 4th quarter and 4% at the end of the 5 this 4% per quarter will remain the same into indefinite future. Suppose the required expected rate of return on the preferred stock is 6% throughout. quarter and Calculate the current price of the preferred stock.

b. Consider the same data as in question 5. Suppose that an investor buys a share of the preferred stock today and sells this share at the end of the first quarter from today. Calculate the rate of return the investor will earn over the quarter.

Answer 1

1	2	3	Col.4=3/4	5	6=1/1.015^Qtr.n	7=5*6	Price at end of Qtr.1
End of Quarter	Annual Yield		Yield/Qtr.	$ 100*Yield /qtr.	PV F at 6%/4=1.5%	PV at 1.5%
1	1.5%+4%=	5.5%	0.01375	1.375	0.98522	1.35
2	2%+4%=	6%	0.015	1.5	0.97066	1.46	0.98522	1.48
3	2.5%+4%=	6.50%	0.01625	1.625	0.95632	1.55	0.97066	1.58
4	3%+4%=	7%	0.0175	1.75	0.94218	1.65	0.95632	1.67
5	4%+4%	8%	0.02	2	0.92826	1.86	0.94218	1.88
	Horizon value
5	$ 2/0.02=			100	0.92826	92.83	0.94218	94.22
Current price of the preferred stock =sum of PV of the qtrly. Dividends						100.70		100.83

Price at end of Qtr. 1	100.83
Price now	100.7
Gain(100.83-100.70)	0.13
ROR/Qtr.	0.13/100=
	0.13%
Rate of return p.a.	(1+0.13%)^4-1=
for the investor	0.52%