Question

The Sisyphean Company has a bond outstanding with a face value of $ 1,000 that reaches maturity in 15 years. The bond certificate indicates that the stated coupon rate for this bond is 8.1​% and that the coupon payments are to be made semiannually. Assuming that this bond trades for $ 876​, then the YTM for this bond is closest​ to:

Answer 1

The yield to maturity can be calculated by the following formula:

Yield to maturity = Coupon payments + (Face value - Price / n) / Face value + Price / 2

where, n is the no. of periods to maturity

Here in this question, interest is paid semi annually. So, we will take n as 15 *2 = 30 semi annual periods. We have to calculate the semi annual interest for calculating the yield to maturity.

Interest amount = 8.1% * Face value

Interest amount = 8.1% * $1000 = $81

Semi annual interest = $81 /2 = $40.5

Now, putting these values in the yield to maturity formula above, we get,

Yield to maturity = $40.5 + ($1000 - $876) / 30 / ($1000 + $876) / 2

Yield to maturity = $40.5 + ($124 / 30) / ($1876 / 2)

Yield to maturity = $40.5 + $4.1333 / $938

Yield to maturity = $44.6333 / $938

Yield to maturity = 0.0475 or 4.8%