You are called in as a financial analyst to apprise the bonds of in a super Stor

Question

You are called in as a financial analyst to apprise the bonds of in a super Stores. The $1,000 par value bonds have quoted annual interest rate of 10 percent, which is paid semiannually. The yield to maturity on the bonds is 10 percent annual interest. There are 15 years to maturity. a) Compute the price of the bonds based on semiannual analysis. b) With 10 years to maturity, if yield to maturity goes down substantially to 8 percent, what will be the new price of the bonds? X-Tech Company issued preferred stock many years ago. It carries a fixed dividend of $12.00 per share. With the passage of time, yields have soared from the original 10 percent to 17 percent (yield is the same as required rate of return.) a) What was the original issue price? b) What is the current value of this preferred stock? c) If the yield on the Standard & Poor's Preferred Stock Index declines, how will the price of the preferred stock be affected?

Explanation / Answer

5) Present Value of an Annuity of $1; 1/ r {1 - [1 / (1 + r)^n]}

1/ 5% {1 - [1 / (1 + 5%)^ 30]} = 15.3724
$100 x 15.3724 = $1537.24

Present Value of $1; 1 / (1 + r)^n

1 / (1 + 5%)^30 = 0.2313
PV = $1,000 x 0.2313 = $231.3

$1537.24 + 231.3= $1768.5

(b) With 10 years to maturity, if yield to maturity goes down substantially to 8 percent, what will be the new price of the bonds?

1/ 4% {1 - [1 / (1 + 4%)^ 20]}
$100 x 13.6 = $1360

1 / (1 + 4%)^20 = 0.456
$1,000 x 0.456 = $456

$1360+ $456 = $1816

6) A) Use perpetuity valuation: Price = Dividend / r
Price = $12 / 0.10 = $120

B) same formula with the higher current rate
Price = $12 / 0.17 = $70.58824, round to $70.59

C.) As you can see from the answers to A and B, when required rates of return decline, the value of the preferred stock increases...at 17% the value is $70.59, at 10% the value is $120. This assumes that the particular stock moves in tandem with the rest of the preferred stock market, e.g. it is positively correlated with other preferred stocks

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