MSc 2 Finance d’entreprise & ingénierie financière

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Group :

MSc 2 Finance d’entreprise & ingénierie financière

Students :

• ABOULFADL Dalal
• MANSOURI Paul
• WAXWEILER Arthur

Answers :

3. Calculer le taux de rendement actuariel (yield-to-maturity) de l’obligation Disney avec les caractéristiques suivantes : Maturité : 13 ans, coupons 6%, paiement semestriel, valeur actuelle : $148.026, valeur nominale de l’obligation :1000$.

To calculate YTM here, the cash flows must be determined first. Every six months (semi-annually), the bondholder would receive a coupon payment of (6% x $1000)/2 = $30. In total, he or she would receive five payments of $30, in addition to the face value of the bond due at maturity, which is $148.026. Next, we incorporate this data into the formula, which would look like this:

POB = C/2 *((1-(1/1+Ytm/2) ^2n)/(Ytm/2)) + ((PP/ (1+ ((Ytm/2) ^2n)))

Now we must solve for the interest rate "YTM," which is where things get tough. Yet, we do not have to start simply guessing random numbers if we stop for a moment to consider the relationship between bond price and yield. As was mentioned earlier, when a bond is priced at a discount from par, its interest rate will be greater than the coupon rate. In this example, the par value of the bond is $1000, but it is priced below the par value at $148.026, meaning the bond is priced at a discount. As such, the annual interest rate we are seeking must necessarily be greater than the coupon rate of 6%.

With this information, we can calculate and test several bond prices by plugging various annual interest rates that are higher than 6% into the formula above. Using a few different interest rates above 6%, one would come up with the following bond prices:

Taking the interest rate up to 43% and 42% yields bond prices of $144.970 and $148.890, respectively. Because the bond price in our example is $148.026, the list indicates that the interest rate we are solving for is between 42% and 43%. Having determined the range of rates within which our interest rate lies, we can use interest rates with smaller increments, for example is we choose 42.2% as the approximative Ytm, the present value of our bond price will be equal to 148.090$ which corresponds approximatively to our bond price.