Question

HIJ Ltd. has just issued a dividend of $1.25 per share on their ordinary shares that have a face value of $1.00. Dividends have been increasing at a rate of 4%pa and this trend is expected to continue for another year. After that the growth rate is expected to be 6%pa for three years before settling down into the long term growth rate of 5%pa. If the market requires a return of 12%pa on these shares:

i. What is their current price?

ii. What is the expected price five years from now?

Three years ago, HIJ Ltd. issued 10 year $1,000 bonds with a 7% coupon rate paid semiannually, at par value. The market currently requires a 9% yield.

i. What was the price of the bond at issue?

ii. What is the current price of the bond?

iii. If the market yield falls to 6% in two years time, what will the bond's price be at that time?

iv. Explain your results in (i) - (iii)

Answer 1

As per Gordon model:

D1 = 1.25 $ * 1.04 = 1.3

r or required return by market = 12 %

g or growth rate is 1 year = 4%

i. Current price of stock = D1/(r-g) = 1.3/(0.12-0.04)=1.3/0.08 = 16.25

ii. Expected price of stock 5 years from now using the Gordon two stage model. = 19.0427

Step 1 - For each year use the growth rate to find what the dividend will be for that year. Since the 5th year onwards the dividend is going to grow at a constant rate, we find the terminal value here.

Step 2 - Discount the dividends each year and the terminal value, add it to find the price of the stock.

Please find the excel screenshots of how this is done:

Second question.

1. Bond price at issue. - 647.0288

Please find the below screenshots

ii. Current market price of bond = Annual coupon payment /Current yield = 70/0.09 = 777.78

iii. If the bond yield falls to 6 %, the bond price will be 70/0.06 = 1166.667

iv. As bond prices and yields are inversely related, as the bond yield goes down, the market value of bond goes up.