Question

The Borrow and Build Inc. has an outstanding bond with the par value of $1,000, 10 years to maturity and annual coupon rate of 9%. The required rate of return on this particular class of bonds is 8%

a) what is the maximum price you are willing to pay for this bond?

b) what are teh current (interest) yield and capital gain yield on this bond? what happens to yield-to-maturity current-yield and capital gain-yield when this bond approaches its maturity?

c) this bond has a clause that it may be recalled in 3 years for $1,1150. What is the yield to call on this bond today? interpret it. Explain why this bond may be recalled

Answer 1

A. FV = $1000, C = 9% = $90, n = 10 years, r = 8%

Price = C×PVIFA_{8%,10 yrs} + FV×PVIF_8%,10yrs

Maximum price = $ 1067.10

B. Current yield = Annual coupon / price of bond

= 90 / 1067.1 = 0.0843

Current yield = 8.43%

Capital gain yield

Price at the end of year 1 = P₁

P₁ = C×PVIFA_8%,9yrs + FV×PVIF_{8%, 9 yrs}

= 90× 6.247 + 1000 × 0.50024

= 562.23 + 500.24 = $ 1062.47

Capital gain yield = ($1062.47 - $1067) / $1067 = -4.53/1067 = - 0.004

Capital gain yield = - 0.4%

YTM = Current Yield + Capital Gain Yield

As soon as bond will approach its price will reduce hence capital gain yield will be tending towards zero.

Due to reduction in price the current yield will increase and hence YTM will be stable and will remain same.

C.

YTC = 9.67%

Issuers call a bond when interest rate drops below where they were when bond was issued.

Here YTC>YTM hence it is advantegeous to the investors to redeem it on the call date.