YNB Ltd. acquired Pty Ltd. 10 years ago. In order to fund this acquisition, YNB Ltd issued a bond. Currently it has an outstanding amount of $50,000,000 with maturity in 2 years. The bond has a coupon rate of 5% (payable annually). Which of the following is closest to the current price of the bond given the YTM is 7%?
$45,948,555
$48,191,982
$50,000,000
$49,000,000
???
To calculate the current price of a bond, we need to use the formula:
Bond Price = (C1 / (1+YTM)1) + (C2 / (1+YTM)2) + ... + (Cn / (1+YTM)n) + (F / (1+YTM)n)
Where:
C = Annual coupon payment
YTM = Yield to maturity
F = Face value of the bond
In this case:
C = ($50,000,000 × 5%) = $2,500,000 (since the coupon rate is payable annually)
YTM = 7%
F = $50,000,000
Now, let's calculate the bond price:
Bond Price = ($2,500,000 / (1+0.07)^1) + ($2,500,000 / (1+0.07)^2) + ($50,000,000 / (1+0.07)^2)
= ($2,500,000 / 1.07) + ($2,500,000 / 1.1449) + ($50,000,000 / 1.1449)
= $2,336,448 + $2,182,250 + $43,551,506
= $48,070,204
Thus, the closest option to the current price of the bond is $48,191,982.