Question

Question 4

A bond has the following characteristics:

Maturity 12 years

Coupon 10%

YTM 9.5%

Noncallable

a) Calculate the price now. Evaluate the price if yield was to increase by 150 bps.

b) Evaluate if the yield fell by 300bps? How would the outcome be changed with a callable bond? Specifically, from point of view of both issuer and buyer.

Answer 1

Assume semi annual coupon payment convention

Assume Face Value, FV = 1,000

Annual coupon =10%

Coupon per period (of 6 months), C = 10% / 2 = 5% x 1000 = 50

Maturity = 12 years

N, nos. of periods in time to maturity = nos. of 6 months period in 12 years = 2 x 12 = 24

YTM = 9.50%

Semi annual YTM, y = 9.50% / 2 = 4.75%

Part (a)

Price of the bond = Present value of all future coupons + Present value of repayment

$=\frac{C}{y}\times (1 - (1 + y)^{-N}) + FV\times {(1 + y)^{-N}}= \frac{50}{0.0475}\times (1 - (1 + 0.0475)^{-24}) + 1000\times {(1 + 0.0475)^{-24}}$

= 1,035.35

If yield increase by 150 bps = 1.5%

YTM = 9.5% + 1.5% = 11%

y = YTM / 2 = 11% / 2 = 5.50%

Price of the bond

$=\frac{C}{y}\times (1 - (1 + y)^{-N}) + FV\times {(1 + y)^{-N}}= \frac{50}{0.055}\times (1 - (1 + 0.055)^{-24}) + 1000\times {(1 + 0.055)^{-24}}$

= 934.24

Part (b)

Yield falls by 300 bps = 3%

YTM = 9.5% - 3% = 6.5%

y = YTM / 2 = 6.5% / 2 = 3.25%

$=\frac{C}{y}\times (1 - (1 + y)^{-N}) + FV\times {(1 + y)^{-N}}= \frac{50}{0.0325}\times (1 - (1 + 0.0325)^{-24}) + 1000\times {(1 + 0.0325)^{-24}}$

= 1,288.55

Issuer's perspective:

If it's a callable bond,

• the bond will not be called if there is an increase in the market interest rate, i.e. yield; the Issuer is in a relatively advantageous position.
• the bond may be called if there is a decline in the market interest rate i.e. yield. By doing so, the issuer refinance the existing high coupon paying bonds by the relatively lower coupon paying bonds.

Buyer's perspective

• The buyer of the bond will never want such a bond to be called back when there is a decline in the market interest rate i.e. yield. Hence they demand a call premium at the time of redemption.So, a callable bond is usually called at some premium to face value.