Question

You have been hired to value a new 20-year callable, convertible bond. The bond has a 5 percent coupon, payable semi-annually, and its face value is $1,000. The conversion price is $55, and the stock currently sells for $45. |

What is the minimum value of the bond? Comparable nonconvertible bonds are priced to yield 6 percent. |

What is the conversion premium for this bond? |

Answer #1

**The minimum value is computed as shown
below:**

**The coupon payment is computed as follows:**

= 5% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

**= $ 25**

**The YTM will be as follows:**

= 6% / 2 (Since the payments are semi annually, hence divided by 2)

**= 3% or 0.03**

**N will be as follows:**

= 20 x 2 (Since the payments are semi annually, hence multiplied by 2)

**= 40**

**So, the price of the bond is computed as
follows:**

**Bonds Price = Coupon payment x [ [ (1 - 1 / (1 +
r) ^{n} ] / r ] + Par value / (1 +
r)^{n}**

= $ 25 x [ [ (1 - 1 / (1 + 0.03)^{40} ] / 0.03 ] + $
1,000 / 1.03^{40}

= $ 25 x 23.11477197 + $ 306.5568408

**= $ 884.43 Approximately**

**b. The conversion premium is computed as shown
below:**

**= (Conversion price - current price) / current
price**

= ($ 55 - $ 45) / $ 45

**= 22.22% Approximately**

Feel free to ask in case of any query relating to this question

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