Question

You are looking into a bond for investment which pays $1000 at maturity (par-value). This bond has an 8% annual coupon, interest paid annually and 20 years to maturity. You require 12% on this bond.

a) What is the maximum price you are willing to pay on this bond today?

b) What is its price 1 year from now?

c) Is it a discount bond, premium bond, or a par bond? Why?

d) What are the total yield, current yield and capital gain yield on this bond?

e) If this bond has a call clause to be called in 5 years for a price of $1,050, what is the yield to call on this bond if it is called? Will the investor be satisfied with this clause?

Please answer all questions and show all steps.

Answer 1

Answer a.

Par Value = $1,000
Annual Coupon = 8%*$1,000 = $80
Annual Yield = 12%
Time to Maturity = 20 years

Current Price = $80 * PVIFA(12%, 20) + $1,000 * PVIF(12%, 20)
Current Price = $80 * (1 - (1/1.12)^20) / 0.12 + $1,000 / 1.12^20
Current Price = $701.22

Answer b.

Par Value = $1,000
Annual Coupon = 8%*$1,000 = $80
Annual Yield = 12%
Time to Maturity = 19 years

Price after 1 year = $80 * PVIFA(12%, 19) + $1,000 * PVIF(12%, 19)
Price after 1 year = $80 * (1 - (1/1.12)^19) / 0.12 + $1,000 / 1.12^19
Price after 1 year = $705.37

Answer c.

This bond is discount bond as its current price is lower than its par value

Answer d.

Total Yield = 12%

Current Yield = Annual Coupon / Current Price
Current Yield = $80 / $701.22
Current Yield = 11.41%

Capital Gain Yield = (Price after 1 year - Current Price) / Current Price
Capital Gain Yield = ($705.37 - $701.22) / $701.22
Capital Gain Yield = 0.59%

Answer e.

Current Price = $701.22
Call Price = $1,050
Annual Coupon = $80
Time to Call = 5 years

Let Annual YTC be i%

$701.22 = $80 * PVIFA(i%, 5) + $1,050 * PVIF(i%, 5)

Using financial calculator, i = 18.32%

Annual YTC = 18.32%

Yes, investor should invest in this discount bond and should earn YTC.