Question

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

%

Answer 1

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%