AFMP4
Syllabus E. Treasury And Advanced Risk Management Techniques E3. The use of financial derivatives to hedge against interest rate risk

# Market value of bonds - calculation 12 / 13

### 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
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)  (95)  (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%

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%