### Valuation of bonds

A ‘plain vanilla’ bond will make regular interest payments to the investors and pay the capital to buy back the bond on the redemption date when it reaches maturity.

Therefore the value of a redeemable bond is the present value of the future income stream discounted at the required rate of return (or yield or the internal rate of return)

#### Example

A company has issued 11% bonds, which are redeemable at par in 3 years’ time.

Investors require an interest yield of 10%.

**Required**

What will be the current market value of £100 of bond?

#### Solution

Year | Cash flow | 10% discount factor | PV | |
---|---|---|---|---|

1-3 | NET Interest | 11 | 2.487 | 27.357 |

3 | redemption value | 100 | 0.751 | 75.10 |

Market value | 102.457 |

This means that £100 of bonds will have a market value of £102.457.

Remember that there is an inverse relationship between the yield of a bond and its price or value.

The higher rate of return (or yield) required, the lower the price of the bond, and vice versa.

### Gross redemption yield or yield to maturity or required rate of return

The cost of redeemable bond is the internal rate of return or required rate of return or redemption yield or yield to maturity of the cash flows of the bond.

#### Example

A 5.6% bond is currently quoted at £95 ex-int. It is redeemable at the end of 5 years at par. Corporation tax is 30%.

**Required**

Calculate gross cost of the bond.

#### Solution

Year | Cash flow | 10% discount factor | PV | DF5% | PV | |
---|---|---|---|---|---|---|

0 | MP | (95) | 1 | (95) | 1 | (95) |

1-5 | gross interest | 5.6 | 3.791 | 21.23 | 4.329 | 24.24 |

5 | redemption value | 100 | 0.621 | 62.1 | 0.784 | 78.4 |

NPV | (11.67) | 7.64 |

IRR = 5% + (7.64 / 7.64 + 11.67) X(10% - 5%) = 7%

#### Standard exam question (extract)

The current $250 million borrowing is in the form of a 4% bond which is trading at $98•71 per $100 and is due to be redeemed at par in three years. The issued bond has a credit rating of AA.

Year | 1 | 2 | 3 |
---|---|---|---|

3.2% | 3.7% | 4.2% |

**Yield spreads (in basis points)**

Bond Rating | 1 year | 2 years | 3 years | 4 years | 5 years |
---|---|---|---|---|---|

AAA | 5 | 9 | 14 | 19 | 25 |

AA | 16 | 22 | 30 | 40 | 47 |

A | 65 | 76 | 87 | 100 | 112 |

**Required**

Calculate the expected percentage fall in the market value of the existing bond if Levante Co’s bond credit rating falls from AA to A.

#### Solution

Spot yield rates applicable to Levante Co (based on A credit rating)

1 year (3.2 + 0.65) = 3·85%

2 year (3.7 + 0.76) = 4·46%

3 year (4.2 + 0.87) = 5·07%

Bond value based on A rating =

Interest $((4% x $100) = 4) x 1·0385^–1 + $4 x 1·0446^–2 + $104 x 1·0507^–3 = $97·18 per $100

Current price based on AA rating = $98·71

Fall in value = (97·18 – 98·71)/98·71 x 100% = 1·55%