Question

An XYZ bond has 20 years until maturity, a coupon rate of 7 percent and sells for $920.00.

1. What is the current yield on the bond?

2. What is the yield to maturity?

3. If an appropriate discount rate is 8%, what the bond price should be?

4. Considering question 3, if XYZ Company wants to issue a new 20-year bond at face value, what coupon rate must the bond offer

Answer 1

Answer 1.

Face Value = $1,000
Current Price = $920

Annual Coupon Rate = 7.00%
Annual Coupon = 7.00% * $1,000
Annual Coupon = $70

Current Yield = Annual Coupon / Current Price
Current Yield = $70 / $920
Current Yield = 7.61%

Answer 2.

Time to Maturity = 20 years

Let Annual YTM be i%

$920 = $70 * PVIFA(i%, 20) + $1,000 * PVIF(i%, 20)

Using financial calculator:
N = 20
PV = -920
PMT = 70
FV = 1000

I = 7.80%

Yield to Maturity = 7.80%

Answer 3.

Annual Discount Rate = 8%

Price of Bond = $70 * PVIFA(8%, 20) + $1,000 * PVIF(8%, 20)
Price of Bond = $70 * (1 - (1/1.08)^20) / 0.08 + $1,000 / 1.08^20
Price of Bond = $901.82

Answer 4.

If XYZ company wants to issue a new 20-year bond at face value, then it should set a coupon rate of 7.80%.