Question

1 a). KLM has a semiannual bond with a coupon rate of 11 percent. The bonds mature in 20 years and have a par value of $1000. If these bonds currently sell for $1035, what is the yield to maturity?

b). Loveday and Co. common stock is currently selling 99. Industry analysts are forecasting a dividend of 3.70 for next year and a growth rate of 5 percent per year for the foreseeable future. What is the expected annual rate of return (in percentage) for the stock?

Please show work

Answer 1

1 a) YTM = 10.64% (See explanation below)
b). Expected annual rate of return = 8.74%
1 a)
YTM = [C + {(F - P)/n}] / [{(F + P)/2}]
Where,
C = Coupon or interest payment
F = Face value
P = Price
n = Years to maturity
Given,
Coupon rate = 11%
F = $1000
P = $1035
n = 20years
Since bond is paying semiannual coupon, so
Coupon rate = 11/2 = 5.5%
n = 20 * 2 = 40 period
Now,
C = $1000 * 5.5% = $55
Now by applying the above formula
Semiannual YTM = [$55 + {($1000 - $1035)/40}] / [{($1000 + $1035)/2}]
Semiannual YTM = {$55 + (-$0.875)} / $1017.5
Semiannual YTM = ($55 - $0.875) / $1017.5
Semiannual YTM = $54.125 / $1017.5
Semiannual YTM = 0.053194
Now, YTM = Semiannual YTM * 2
YTM = 0.053194 * 2
YTM = 0.106388
YTM = 10.64%
Alternatively,
YTM = (1 + Semiannual YTM)^2 - 1
YTM = (1 + 0.053194)^2 - 1
YTM = 1.1092176 - 1
YTM = 10.92%
b).
By using Gordon growth model (GGM) we can calculate expected annual rate of return.
As per GGM,
Price per share = D1/(Re-g)
Where,
D1 = The estimated value of next year’s dividend
Re = The company’s cost of capital equity (expected annual rate of return)
g = The constant growth rate for dividends, in perpetuity​
Given,
Price = 99
D1 = 3.70
g = 5%
Now according to above formula
99 = 3.70/(Re - 0.05)
or, (Re - 0.05) = 3.70/99
or, (Re - 0.05) = 0.0373737
or, Re = 0.0373737 + 0.05
or, Re = 0.0873737
or, Re= 8.74%