Question

The risk-free rate of return is 10.0%, the expected rate of return on the market portfolio is 17%, and the stock of Xyrong Corporation has a beta coefficient of 1.6. Xyrong pays out 30% of its earnings in dividends, and the latest earnings announced were $15 per share. Dividends were just paid and are expected to be paid annually. You expect that Xyrong will earn an ROE of 20% per year on all reinvested earnings forever.

a. What is the intrinsic value of a share of Xyrong stock? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Intrinsic value            $

b-1. If the market price of a share is currently $70, and you expect the market price to be equal to the intrinsic value one year from now, calculate the price of the share after one year from now. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Price            $

b-2. What is your expected one-year holding-period return on Xyrong stock? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Expected one-year holding-period return             %

Answer 1

Formula sheet

A	B	C	D	E	F	G	H	I	J	K
2
3		Cost of Equity Calculation:
4		As Per CAPM, Cost of equity can be calculated as
5		r(E) = rf + ?*(rm-rf)
6		Using the Following data
7		Beta (?)	1.6
8		Risk free rate ( rf )	0.1
9		Market Return (rm)	0.17
10
11		Cost of equity can be calculated as follows:
12		Cost of equity	= rf + ?*(rm-rf)
13			=D8+D7*(D9-D8)	=D8+D7*(D9-D8)
14
15		Hence Cost of Equity is	=D13
16
17		Growth rate	=ROE*(1-Payout Ratio)
18			=20%*(1-30%)
19			=20%*(1-30%)
20
21		As per dividend growth model, Price of share is the present value of all future dividends discounted at cost of equity.
22		Current Price of Share (P)	=Div0*(1+g)/(r-g)
23		Where Div0 is the dividend paid this year, r is cost of equity and g is perpetual growth rate of dividend.
24
25		Given the following data:
26		Dividend (Div0)	=15*30%
27		Cost of equity (r)	=D15
28		Growth rate (g)	=D19
29
30		From Dividend growth model,
31		Share Price, P	=Div0*(1+g)/(r-g)
32			=D26*(1+D28)/(D27-D28)	=D26*(1+D28)/(D27-D28)
33
34		Hence Intrinsic value of stock today is	=D32
35
36		b-1)
37
38		Calculation of intrinsic Value after one Year:
39
40		Given the following data for next year:
41		Dividend (Div0)	=D26*(1+D28)
42		Cost of equity (r)	=D27
43		Growth rate (g)	=D28
44
45		From Dividend growth model,
46		Share Price, P	=Div0*(1+g)/(r-g)
47			=D41*(1+D43)/(D42-D43)	=D26*(1+D28)/(D27-D28)
48
49		Hence Intrinsic value after one year is	=D47
50
51		Share Price after one year	=Intrinsic Value after one year
52			=D49
53
54		Hence Share Price after 1 Year	=D52
55
56		b-2)
57
58		Share Price Today	70
59		Share Price after one Year	=D54
60		Dividend Paid during the Year	=D41
61
62		Holding period Return	=(Final Price - Initial Price +Dividend)/Initial Price
63			=(D59-D58+D60)/D58	=(D59-D58+D60)/D58
64
65		Hence Holding period Return	=D63
66