Question

a. Wee Beastie Animal Farm bonds have 9 years to maturity and pay an annual coupon at the rate of 6 %. The face value of the bonds is $1,000.The price of the bonds is $1,082.29 to yield 4.85%.What is the capital gain yield on the​ bonds?

b. A 10​-year bond pays interest of $ 26.80 semiannually, has a face value of $1,000 and is selling for $719.86.What are its annual coupon rate and yield to​ maturity?

The annual coupon rate is %.​(Round to two decimal​ places).

The yield to maturity is ​%.​(Round to two decimal​ places).

Answer 1

Answer a.

Face Value = $1,000
Current Price = $1,064.17

Annual Coupon Rate = 6.40%
Annual Coupon = 6.40% * $1,000
Annual Coupon = $64

Dividend Yield = Annual Coupon / Current Price
Dividend Yield = $64 / $1,064.17
Dividend Yield = 0.0600 or 6.00%

Yield to Maturity = 5.23%

Capital Gain Yield = Yield to Maturity - Dividend Yield
Capital Gain Yield = 5.23% - 6.00%
Capital Gain Yield = -0.77%

Answer b.

Face Value = $1,000
Current Price = $719.86
Semiannual Coupon = $26.80

Time to Maturity = 10 years
Semiannual Period = 20

Semiannual Coupon Rate = Semiannual Coupon / Face Value
Semiannual Coupon Rate = $26.80 / $1,000
Semiannual Coupon Rate = 0.0268 or 2.68%

Annual Coupon Rate = 2 * Semiannual Coupon Rate
Annual Coupon Rate = 2 * 2.68%
Annual Coupon Rate = 5.36%

Let Semiannual YTM be i%

$719.86 = $26.80 * PVIFA(i%, 20) + $1,000 * PVIF(i%, 20)

Using financial calculator:
N = 20
PV = -719.86
PMT = 26.80
FV = 1000

I = 4.91%

Semiannual YTM = 4.91%

Annual YTM = 2 * Semiannual YTM
Annual YTM = 2 * 4.91%
Annual YTM = 9.82%