Question

6. At what price should I offer to buy a $500 bond on December 11, 2008, if I want it to yield 13%, compounded quarterly? The bond matures on April 1, 2012, and bears 11.5% coupons payable on April 1 and October 1.

Answer 1

Answer on Question #38594, Math, Other

The bond's price is equal to the present value of all future cash flows.

The calculation of it can be presented as:

$$\text{Bond price} = \frac{CF1}{(1 + yield)^1} + \frac{CF2}{(1 + yield)^2} + \dots + \frac{\text{Last } CF}{(1 + yield)^n}$$

where CF1,2...n-1 means coupon payment for the period 1,2...n-1 respectively, last CF means last coupon payment plus nominal value of the bond.

Since interests are compounded quarterly, there will be 13 periods, when interests are charged.

The calculation of bond price will be as following:

\begin{array}{l} \text{Bond price} = \frac{0,115 \times 500}{(1 + 0,13)^1} + \frac{0,115 \times 500}{(1 + 0,13)^3} + \frac{0,115 \times 500}{(1 + 0,13)^5} + \frac{0,115 \times 500}{(1 + 0,13)^7} + \frac{0,115 \times 500}{(1 + 0,13)^{9}} + \frac{0,115 \times 500}{(1 + 0,13)^{11}} + \\ + \frac{0,115 \times 500}{(1 + 0,13)^{13}} = 192.255 \text{ $} \end{array}