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

# Valuing bonds based on the yield curve 13 / 13

### The spot yield curve can be used to estimate the price or value of a bond

#### Example

A company wants to issue a bond that is redeemable in four years for its par value or face value of \$100, and wants to pay an annual coupon of 5% on the par value.

Estimate the price at which the bond should be issued and the gross redemption yield.

The annual spot yield curve for a bond of this risk class is as follows:

Year  Rate
1 3.5%
2 4.0%
3 4.7%
4 5.5%

#### Solution

The market price of the bond should be the present value of the cash flows from the bond (interest and redemption value) using the relevant yearâ€™s yield curve spot rate as the discount factor.

Year  1 2 3 4
Cash flows  5 5 5 105
Df  1.035^-1  1.04^-2  1.047^-3  1.055^-4
Present value  4.83  4.62  4.36  84.76
The market price = \$98.57

Given a market price of \$98.57, the gross yield to maturity is calculated as follows:

Year CF   DF10%  PV  DF5%  PV
0 MP (98.57)  1 (98.57) 1 (98.57)
1-4 gross interest 3.170   15.85  3.546  17.73
4 Redemption value  100 0.683  68.3  0.823  82.3
NPV (14.42) 1.46

IRR or to maturity = 5% + (1.46 / 1.46 + 14.42) X(10% - 5%) = 5.46%

Note that the yield to maturity of 5.46% is not the same as the four year spot yield curve rate of 5.5%.

#### The reasons for the difference are as follows:

1. The yield to maturity is a weighted average of the term structure of interest rates.

2. The returns from the bond come in earlier years, when the interest rates on the yield curve are lower, but the largest proportion comes in Year 4.