Question

16)

A) A company is planning to issue an annual-pay $500 face value bond that matures in 10 years with a coupon rate of 7.5%. If similar bonds are currently priced to yield 9.25%, what is the price of the bond?

B)

After a recent IPO, SOME Co. has a unique dividend policy. Next year they anticipate paying out a $2 dividend. In year 2, they will increase the dividend to $2.50. In year 3, the dividend will increase to $3.50. After year 3, the dividend will grow at a constant rate of 4%. What is the current stock price? Assume that the required rate of return by shareholders is 10%.

C)Suppose a company just paid a dividend of $1.00 and plans on increasing the dividend each year at a constant rate of 5%. If the current rate required by share holders equals 12%, what is the current stock price?

Answer 1

a)

Coupon = 500 * 0.075 = 37.5

Price = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Price = 37.5 * [1 - 1 / (1 + 0.0925)¹⁰] / 0.0925 + 500 / (1 + 0.0925)¹⁰

Price = 37.5 * 6.34764 + 206.42179

Price = $444.46

b)

Year 4 dividend = 3.5 * 1.04 = 3.64

Value at year 3 = D4 / required rate - growth rate

Value at year 3 = 3.64 / 0.1 - 0.04

Value at year 3 = 3.64 / 0.06

Value at year 3 = 60.6667

Current stock price = 2 / (1 + 0.1)¹ + 2.5 / (1 + 0.1)² + 3.5 / (1 + 0.1)³ + 60.6667 / (1 + 0.1)³

Current stock price = $52.09

c)

Current stock price = D1 / required rate - growth rate

Current stock price = (1 * 1.05) / 0.12 - 0.05

Current stock price = 1.05 / 0.07

Current stock price = $15.00