The value of node is determined using a methodology called backward induction. The value at any node depends on the future cash flows; therefore, we need to start from the last year in the tree and work backwards to get the required solution. For example, if we want to find the value at node T, we need to first calculate the value at node T_H and T_L and to find the value of bond at node T_H; also, we need to first calculate the value of the bond at nodes T_HH and T_HL which is nothing but the future cash flows. The future cash flows depend on two factors. First, the coupon payment one year from now; and second, the bonds value one year from now. We have already seen that at every node there are two options and the node can take a higher or lower value. Therefore, the cash flow at a node can either be the bond value if the 1-year rate is higher rate plus the coupon payment or the bond value if the 1-year rate is lower rate plus the coupon payments. Coming back to our example, the cash flow at T will either be bond rate at T_HH plus coupon rate or the bond rate at T_HL plus coupon payment.

We need to calculate the present value of the expected cash flow to get the bond value at a node. We get two present values in each case, one is the present value if the 1-year rate is higher and the other if it is lower. As we have two options with equal probability, an average of the two present values is computed.

V_H     =       Higher 1-year rate value of the bond.

V_L       =       Lower 1-year rate of the bond.

P       =       Coupon payment.

r*      =       1-year rate at the node where the valuation is sought.

Therefore, the cash flow at a node is

V_H + P for the higher 1-year rate (or)

V_L+ P for the lower 1-year rate.

Present value of the cash flows using the 1-year rate at the node, is calculated as follows:

Present value for the higher rate = 

Present value for the lower rate = 

The value of the bond at the node is 

Posted Date: 9/10/2012 6:47:35 AM | Location : United States

Ask an Expert

Related Discussions:- Determining the value at a node or backward induction, Assignment Help, Ask Question on Determining the value at a node or backward induction, Get Answer, Expert's Help, Determining the value at a node or backward induction Discussions

Write discussion on Determining the value at a node or backward induction
Your posts are moderated

Write your message here..

Related Questions

Viability of project - syringe management, The syringe management program t... The syringe management program tries to educate society by increasing the capacity and quantity of the syringe disposable centers , providing timely responses to all syringe compla

Fixed costs, Fixed Costs The costs a rigid incurs doing business that d... Fixed Costs The costs a rigid incurs doing business that do not change in relation to production. Rent, for example, is a fixed cost because it remains constant whether product

Calculate the price of commonwealth bonds, Calculate the Price of Commonwea... Calculate the Price of Commonwealth bonds Commonwealth Company has a 10% coupon bond with a par value of $1000, The current yield to maturity on new bonds is 8%. If interest is

What are free cash flows, What are "free cash flows?" Free cash flows s... What are "free cash flows?" Free cash flows signify the total cash flows from business operations that are available to be distributed to the suppliers of a firm's capital each

financial crisis, Hedge funds are short two types of funding options. Desc... Hedge funds are short two types of funding options. Describe in detail what these options are.   Describe why these options become more valuable during a financial crisis.   During

find the weighted average cost of capital, Given the following information... Given the following information, find the Weighted Average Cost of Capital (WACC).  Assume the corporate tax rate is 35%, and give an answer based on market values of debt and equi

Explain the risk-return relationship, Explain the risk-return relationship.... Explain the risk-return relationship. The relationship among risk and required rate of return is known as the risk-return relationship.  It is a positive relationship for the r

efficient variance reduction, Assume we are in the midst of the financial ... Assume we are in the midst of the financial crisis in October 2008. Your firm is considering the purchase of a 10 year put option on the S&P 500 Index. You are analyzing the pricin

Minimum value, The minimum value is the lower limit for the market va... The minimum value is the lower limit for the market value of a convertible bond. It is equal to the greater of the conversion value and the straight value. We can

Determine about the risk management systems, Determine about the risk manag... Determine about the risk management systems Management must report to board their review and implementation of internal controls and risk management systems. The board must rev