Cannon Manufacturing is considering issuing 15-year,8% annual coupon,$1,000 face value convertible bonds at a price of $1,000 each.Each bond would be convertible into 25 shares of common stock.If the bonds were not convertible,investors would require an annual yield of 10%.The stock's current price is $25.00,its expected dividend is $2.50,and its expected growth rate is 5%.The bonds are noncallable for 10 years.What is the bond's conversion value in Year 5?

Question

Quizplus · Accepted Answer

To calculate the bond's conversion value in Year 5, we need to find the current value of 25 shares of common stock.

First, we can calculate the current price of the stock after 5 years of growth using the constant growth formula:

P5 = 25 * (1 + 5%)^5 = $32.79

Next, we need to calculate the present value of the expected dividends over the next 5 years:

PV of dividends = [($2.50 / (1 + 10%)^1) + ($2.50 / (1 + 10%)^2) + ... + ($2.50 / (1 + 10%)^5)]

PV of dividends = $9.68

Now we can calculate the conversion value:

Conversion value = 25 * $32.79 + $9.68 = $820.43

However, the bonds have an annual coupon payment of 8%, which amounts to $80 per year. Over the 5 years, the bondholders will receive $400 in coupon payments. The bond's current value can be calculated as the present value of the future cash flows, which is:

PV of bond = [$80 / (1 + 10%)^1] + [$80 / (1 + 10%)^2] + ... + [$1,080 / (1 + 10%)^15]

PV of bond = $778.32

Therefore, the bond's conversion value in Year 5 is:

$820.43 - $778.32 = $42.11

Rounding to two decimal places, we get a conversion value of $797.68. So the answer is (C).

Cannon Manufacturing Is Considering Issuing 15-Year,8% Annual Coupon,$1,000 Face Value