## Determining the value at a node or backward induction, Financial Management

Assignment Help:

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 TH and TL and to find the value of bond at node TH; also, we need to first calculate the value of the bond at nodes THH and THL 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 THH plus coupon rate or the bond rate at THL 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.

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

VL       =       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

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

VL+ 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 #### Leverage, evaluate the importace of leverage in financial management of a s...

evaluate the importace of leverage in financial management of a small scale company

#### Discount Pricing, Discount Pricing The T-bills are issued at a discount...

Discount Pricing The T-bills are issued at a discount to face value and hence have no coupon. Commission rates on round lots generally range from \$12.50 to \$25.00 per \$1 mil

#### Financial system, Financial System: The economic development of a natio...

Financial System: The economic development of a nation is reflected by the progress of the various economic units, broadly classified into corporate sector, government and hous

#### Factors affecting investment decisions, I have a question for my homework, ...

I have a question for my homework, which is: Explain, using relevant instances, how investment decisions are affected by different factors. Help please?

#### What are assumptions of walters dividend model, Q. What are assumptions of ...

Q. What are assumptions of Walters dividend model? 1. Constant Return and Cost of Capital: - The Walter' model presume that the firm's rate of return and its cost of capital ar

#### Accounting or average rate of return , I need a report on Accounting or Ave...

I need a report on Accounting or Average Rate of Return. Can you please assist me for Accounting or Average Rate of Return report for about 2500 words?

#### What are the misstatements, Q. What are the misstatements? A Misstatem...

Q. What are the misstatements? A Misstatement is Inconsequential - If a reasonable person would determine after considering the possibility of further undetected misstatement

Examine about Environmental (external) analysis "A study that considers potential environmental effects during planning phase before an investment is made or an operation start

#### Investment decision and financing decision, The Investment Decision: - Inv...

The Investment Decision: - Investment decision as well known as 'Capital Budgeting' is related to the selection of long-term assets or else projects in which investments will be m

#### Selection of a project in financial management, Q. Selection of a project i...

Q. Selection of a project in Financial Management ? The selection of a project is typically made on the following line: (i) In general a project becomes acceptable if it has  