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You have a convertible bond with a par value of 100,000 with a 10% coupon. It can

be converted into shares at a conversion price of 5,000€. The current price is of 4,300€.
If the dividends of the share are currently 200€, and if these grow at a rate of 6% per
year, would you, as a bondholder, convert or not in 5 years time? Suppose that the share
price coincides with its intrinsic value/objective price and that the re is 10.93%.

User Raphnguyen
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1 Answer

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To determine whether it is favorable to convert the convertible bond into shares in 5 years, we need to compare the future cash flows from holding the bond with the future cash flows from converting it into shares.

Future cash flows from holding the bond:

The bond has a par value of €100,000 and a 10% coupon rate. The coupon payment each year would be €10,000 (10% of €100,000).

Therefore, the cash flow from holding the bond for 5 years would be:

€10,000 × 5 = €50,000

Future cash flows from converting into shares:

The conversion price is €5,000 per share, and the current share price is €4,300. This means that for each bond, you can convert €5,000/€4,300 = 1.16 shares.

After 5 years, the dividend per share would be €200, growing at a rate of 6% per year.

The cash flow from converting the bond into shares after 5 years would be:

1.16 shares × (€200 × (1 + 6%)^5) = 1.16 shares × (€200 × 1.338225) = €313.38

Determine the present value of the cash flows:

To make a fair comparison, we need to discount the cash flows to present value using the given required rate of return of 10.93%.

The present value of holding the bond for 5 years:

PV_holding = €50,000 / (1 + 10.93%)^5 = €31,262.46

The present value of converting into shares after 5 years:

PV_converting = €313.38 / (1 + 10.93%)^5 = €199.81

Comparing the present values, we find that PV_holding > PV_converting. This means that the present value of holding the bond for 5 years is greater than the present value of converting into shares. Therefore, as a bondholder, it would be more favorable to hold the bond rather than convert it into shares in 5 years time.

User Reox
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