Question

West Corp. issued 20-year bonds two years ago at a coupon rate of 8 percent. The bonds make semiannual payments. If these bonds currently sell for 110 percent of par value, what is the YTM? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

7.01%

Explanation:

20-years bond with semiannual payments have 40 coupon payments. Because the bond was issued 2 years ago, there're going to be 36 coupon payments from now until maturity.

For fast calculation, we can assume a dummy par value of 100 (yields are not dependent on the absolute value of par value).

Current bond prices are discounted value of remaining coupon payments plus par value at maturity, or:

P = C/[1+(YTM/2)] + C/[1+(YTM/2)]^2 + … + [(C + Par)/(1+(YTM/2))]^36, where:

P: Current market bond price.

C: Coupon payment, calculated as = Par value x (Coupon rate/2) = 100 x (8%/2) = 4

YTM: Yield to maturity

Par: Par value

Putting all the numbers together, we have:

110 = 4/[1+(YTM/2)] + 4/[1+(YTM/2)]^2 + … + [(4 + 100)/(1+(YTM/2))]^36

Solve the equation, we get YTM/2 = 3.51% or YTM = 7.01%.

Note: The equation can be easity solved using Excel or BA II Plus Calculator.