Question

Kurt owns a convertible bond that matures in three years. The bond has an 8 percent coupon and pays interest semi-annually. The face value of the bond is $1,000 and the conversion price is $25. Similar bonds have a market return of 9.25 percent. The current price of the stock is $26.50 per share. What is the minimum value of the convertible bond? what is the minimum value of the option to convert?

Answer 1

Given:

Bond Face Value = $1,000

Coupon rate = 8%

Interest Payment -> Semi annual

Maturity = 3 years

Market rate of return =yield to maturity (ytm) = 9.25%

Current stock price = $26.5

Conversion price = $25

Things to be calculated:

Coupon value = (Coupon rate) x (bond face value)

                   = 8% x $1,000

                   = $80

Since the coupon payments are semi- annual, so semi- annual coupon value = $80/2 = $40

Conversion ratio = Bond face value / Conversion price

                                = $1,000/$25

                                = 40

(The value 40 indicates the total number of stocks for which one can exchange a single convertible bond)

Conversion value of the bond = (Conversion ratio) x (current stock price)

                                                       = (40) x ($26.5)

                                                       = $1,060

Straight bond value = $[coupon value/ytm] x [1-{1/(1+ytm)^year}] + [face value/(1+ytm)^year]

                                     = $[40/4.625%] x [1 – {1/(1+4.625%)⁶}] + [1,000/(1+4.625%)⁶]

                                     = $[864.86] x [0.24] + [762.41]

                                     = $207.57 + 762.41

                                     = $969.98

[Since the coupon payments are semi- annual, in the above calculation, we have considered the market rate of return to be (9.25%/2) i.e., 4.625% and, the number of years to be (3 x 2) i.e., 6]

Part 1 answer:

Minimum value of the convertible bond = Maximum value (Conversion value of the bond,

                                                                            Straight bond value)

                                                                         = max ($1060, $969.98)

                                                                         = $1,060

Part 2 answer:

Minimum value of the option to convert = |Conversion value of the bond – Straight bond

                                                                             value|

                                                                = $|1060 – 969.98|

                                                                          = $90.02