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midterm_notes

# midterm_notes - Midterm Review Notes November 3 2008 1 RoR...

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Midterm Review Notes November 3, 2008 1 RoR Analysis Net Present Value (NPV) Definition? The Net Present Value of a cash flow is a quantity of money, which if received today, would be equally desirable as the cash flow. ”How much does a dollar in tomorrow worth today?” Formula? in terms of interest rate i NPV := x 0 + ( 1 1 + i ) x 1 + ( 1 1 + i ) 2 x 2 + . . . = k =0 (1 + i ) - k x k in terms of discount factor δ NPV := x 0 + δx 1 + δ 2 x 2 + . . . = k =0 δ k x k Note. (1) Actually, δ := (1 + i ) - 1 = 1 / (1 + i ) in our case (2) ”present” is at time slot 0; x 0 is the amount of money which corresponses to either negative (in- vestment) or positive (revenue) (3) The formula is discounting x 1 , x 2 , . . . , i.e. all the future cash flow, into today. 1

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Midterm Review Notes , (Bob) (4) The summation is summing over all the future cash flow. In the above 2 formulas, it supposes that the cash flow happens forever. If a project only generate revenue for n years, then the formulas will become NPV := n k =0 (1 + i ) - k x k = n k =0 δ k x k (5) Discount rate is an equivalent term of interest rate in some problems Rate of Return (RoR) Definition? The return on investment, or more commonly called the rate of return (RoR), is an inverse problem to computing the NPV. ”What would the interest rate at the bank have to be in order for me to be neutral about investing in my project?” How to compute? Formula x 0 + 1 1 + i · x 1 + ( 1 1 + i ) 2 · x 2 = 0 Meaning x 0 is the amount money of your investment of the project, usually negative x 1 , x 2 , . . . are the future revenues you’ll get from this project. x 1 is the revenue of 1st year from now, etc. By setting the NPV of this kind of cash flow to 0, we will be neutral about investing since the NPV of the cash flow incurred by this project is 0. Suppose the solution of RoR we computed is i * . 1. If the interest in the bank, i , is great than the RoR, i > i * , investing is not profitable since we could make more money by putting the money in bank; 2. If i < i * , investing in the project is preferable since the revenue generated by this project in the future is larger than the interest profit we might have by saving money in bank. 2
Midterm Review Notes , (Bob) Quadratic formula Usually, you will face a equation in the following form x 0 + (1 + i ) - 1 x 1 + (1 + i ) - 2 x 2 = 0 To solve it, following steps below: 1. Let δ = (1 + i ) - 1 , and the equation becomes x 0 + δx 1 + δ 2 x 2 = 0 2. Using the quadratic formula δ * = - x 1 ± x 2 1 - 4 x 0 x 2 2 x 2 ( ) (General form of quadratic equation/formula, ax 2 + bx + c = 0 x * = - b ± b 2 - 4 ac 2 a 3. Formula ( ) will give you 2 roots of the quadratic equation. Drop the negative root (if any) since the discount factor we are computing here won’t be negative. 4. Remember back-substituting δ * into δ = (1 + i ) - 1 and get the RoR as the REAL solution i * = 1 δ * - 1 Note. 1. The goal of the RoR problem is to compute a i * based the cash flow of a project given by the problem.

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midterm_notes - Midterm Review Notes November 3 2008 1 RoR...

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