Question

A 4 year maturity bond with a 14% coupon rate can bought for $1200. i- What is the yield to maturity if the coupon is paid annually? (4) ii- What if it is paid semiannually?

Answer 1

The yield to maturity (YTM) of the bond with a 14% coupon rate can be found using the formula (Annual Coupon Payment + (Face Value - Purchase Price) / Number of Years) / Purchase Price. If the coupon is paid annually, the YTM is approximately 0%. If the coupon is paid semiannually, the YTM is approximately 0.01%.

Step-by-step explanation:

To find the yield to maturity (YTM) of a bond, we need to use the formula:

YTM = (Annual Coupon Payment + (Face Value - Purchase Price) / Number of Years) / Purchase Price

i. If the coupon is paid annually:

Given:

• Face Value (FV) = $1000
• Coupon Rate = 14% (0.14)
• Number of Years (n) = 4
• Purchase Price = $1200

Substituting the values into the formula:

YTM = (0.14 * 1000 + (1000 - 1200) / 4) / 1200

Simplifying the equation:

YTM = 0.14 + (-0.05) / 4) / 1200

YTM = -0.02 / 4) / 1200

YTM = -0.005 / 1200

YTM ≈ -0.00000417

Therefore, the yield to maturity (YTM) is approximately -0.00000417, which can be rounded to 0%.

ii. If the coupon is paid semiannually:

Since the coupon is paid semiannually, the number of years (n) will be doubled. So, in this case, n = 8.

Using the formula:

YTM = (0.14 * 1000 + (1000 - 1200) / 8) / 1200

Simplifying the equation:

YTM = 0.14 + (-0.025) / 8) / 1200

YTM = 0.115 / 1200

YTM ≈ 0.00009583

Therefore, the yield to maturity (YTM) is approximately 0.00009583, which can be rounded to 0.01%.

Answer 2

Answer:a

Explanation:b