In: Finance
Even though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company issues a bond with a par value of €1,000, 10 years to maturity, and a coupon rate of 6.8 percent paid annually. |
If the yield to maturity is 7.9 percent, what is the current price of the bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) |
A Japanese company has a bond outstanding that sells for 89 percent of its ¥100,000 par value. The bond has a coupon rate of 5.6 percent paid annually and matures in 18 years. |
What is the yield to maturity of this bond? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) |
Yield to maturity | % |
I) Bond price = Coupon payments * ((1 - (1/(1+i)^n))/i) + Par value * (1 / (1+i)^n)
Here,
Par value = €1,000
i (rate semi annual) = 7.9% * 6/12 months
i = 3.95% or 0.0395
Coupon payments = Par value * Coupon * 6/12 months
Coupon payments = €1,000 * 6.8% * 6/12 = €34
n (period) = 10 years * 2 = 20
Now,
Bond price = €34 * ((1 - (1/(1+0.0395)^20)) / 0.0395) + €1,000 * (1 / (1+0.0395)^20)
Bond price = €34 * ((1 - 0.4608) / 0.0395) + (€1,000 * 0.4608)
Bond price = (€34 * 13.6506) + €460.80
Bond price = €464.12 + €460.80
Bond price = €924.92
II) Yield to maturity (YTM) = (Coupon + ((P - M)/n)) / ((P + M)/2)
Here,
P (Par value) = ¥1,00,000
M (Market price) = Par value * Sales% @ 89%
M = ¥1,00,000 * 89% = ¥89,000
n (years) = 18
Coupon = Par value * Coupon rate
Coupon = ¥1,00,000 * 5.60% = ¥5,600
Now put the values into formula,
YTM = (¥5,600 + ((¥1,00,000 - ¥89,000) / 18)) / ((¥1,00,000 + ¥89,000)/2)
YTM = (¥5,600 + ¥611.11) / ¥94,500
YTM = ¥6,211.11 / ¥94,500
YTM = 0.0657 or 6.57%