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FINC3240 International Finance

FINC3240 International Finance. Capital Budgeting (1). 0. 1. 2. N. r%. . Value. CF 1. CF 2. CF N. The value of financial assets. Question. You are asked to choose from the following: Receive $100 today Receive $100 one year from now Would you choose 1 or 2?.

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FINC3240 International Finance

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  1. FINC3240International Finance Capital Budgeting (1)

  2. 0 1 2 N r% ... Value CF1 CF2 CFN The value of financial assets

  3. Question You are asked to choose from the following: • Receive $100 today • Receive $100 one year from now Would you choose 1 or 2?

  4. Important observations 1 • Money has time value--People prefer to receive (and spend) it sooner rather than later. You prefer receiving $100 today to receiving $100 one year from now because you place a LOWER value on cash flow received at a later date.

  5. Important observations 2 You cannot simply add sums of money received at different points in time because the same face amount of money at different points of time have different value. Money received (or paid) at different times must first be converted to a common basis, the same point in time, for comparison.

  6. Time Value Basics Deposit problem: If you put $100 in a bank deposit account earning 10% annually, how much will be in the account after one year? + 10 = 110 100 + Interest = Principal Future Value + 100(.10) = 110 100 x (1+.10) = 110 100

  7. Time Value Basics What would it be worth after two years? x 1.1 = 121 110 But, since 110 = 100(1+.10)… x (1+.10) x (1+.10) = 121 100 or x (1+.10)2 = 121 100

  8. The Formula for Future Value Future Value Number of periods Rate of return or discount rate or interest rate or growth per period Present Value

  9. The Formula for Future Value • The formula lets you convert a current cash flow into its future value. • This process is called compounding.

  10. The Formula for Present Value From before, we know that Solving for PV, we get Unless otherwise stated, r stated on an annual basis.

  11. The Formula for Present Value • The formula lets you convert future cash flows into their present values. • This process is called discounting.

  12. Discount rate and PV • If FV is fixed, then as the discount rate increases, PV decreases.

  13. FV and PV formulas • These are the basic building blocks which we will use to construct bigger and more complex ideas & concepts. • Not surprisingly, we will use these basic building blocks to solve complicated capital budgeting problems.

  14. 1-period, find FV You require $1,700 to buy a computer and the bank is offering a loan at an interest rate of 14 percent. If you plan to repay the loan after one year, how much will you have to pay the bank? Use FV = PV(1 + r)

  15. 1-period, find PV What is the present value of $16,000 to be received at the end of one year if the discount rate is 10 percent? Use PV = FV/(1 + r)

  16. 2-period, find FV You plan to loan $11,000 to your friend at an interest rate of 8 percent per year compounded annually. The loan is to be repaid in two years. How much will your friend pay you at t = 2? Use FV = PV(1+r)2

  17. 2-period, find PV You are offered the chance to buy into an investment that promises to pay you $28,650 at the end of two years. If your required rate of return is 12 percent, what is the maximum amount that you would pay for this investment? Use PV = FV/(1+r)2

  18. Time line: visualizing cash flows • For a problem with 2 or more periods, a time line helps you to understand the problem better. • A time line is a graphical representation of a problem. For the previous problem, the time line would look like this: -$ 5,000 -$ 4,000 t = 1 t = 2 t = 0

  19. Capital Budgeting Decision 1 • Capital budgeting: the process of analyzing projects and decide which ones to invest in. • Project: any investment that involves cash outflows (costs) made in order to receive cash inflows (benefits). E.g.,: new product, new plant & machinery, cost saving technologies, new accounting software.

  20. Capital Budgeting Decision 2 • Let’s be more specific about the decision to be made: • Given the cash inflows and outflows of a project, should the firm accept or reject the project. • If the firm accepts, it will invest in the project. If the firm rejects, it will not invest in the project. • This type of decision is known as a capital budgeting decision.

  21. Capital Budgeting Decision 3 • If the firm makes a wrong capital budgeting decision, e.g., invest in the wrong project, then scarce resources are wasted. It also means that firm value and shareholder wealth will be reduced.

  22. The Value of a Project • Determined by the present value of its expected investment cost and future cash flows.

  23. Net present value (NPV) rule Accept project if Net present value > 0 What is Net present value? Net present value = Benefits minus Costs

  24. How do we measure benefits & costs? Benefits, B = Present value of all cash inflows from the project = Cash inflow at the end of period t Number of years in the project’s life Discount rate for the project’s cash flows

  25. How do we measure benefits & costs? Costs, C = Present value of all cash outflows from the project = Cash outflow at the end of period t Number of years in the project’s life Discount rate for the project’s cash flows

  26. NPV NPV = B – C =

  27. NPV Profile NPV profile is a graph showing the NPV values for different discount rates.

  28. NPV Profile

  29. Example 1 A firm is considering investment in a project that costs $1,200 and yields cash flows of $500 in the first year, $600 in the second year and $700 in the third year. The appropriate discount rate for this project is 10%. Compute the NPV of this project.

  30. By Math

  31. Computing NPV using BA II Plus • Press CF, press -1200 and then press ENTER for CF0. • Next press “” and enter 500 for C01. • Press “” and enter 1 for F01. • Similarly enter C02 = 600, F02 = 1, C03 = 700, and F03 = 1. Make sure that all the cash flows later than C03 are zero. • Press NPV. Enter the discount rate of 10 percent by pressing 10 and then ENTER. • The display will show that I = 10. • Next press the “” and press CPT. • The calculator will display the NPV of 276.33. • Decision: Accept project

  32. Example 2 Project K costs $52,125, its expected net cash inflows are $12,000 per year for 8 years, and its cost of capital is 12%. Shall we reject the project or not? NPV = $7,486.68.

  33. Homework 1. Your division is considering a projects with the following net cash flows (in millions). The initial investment cost is 25, the cash flows at the end of year 1, 2, 3 are 5,10,17, respectively. What are the projects’ NPV assuming the cost of capital is 5%? 10%? 15%? 2. Your division is considering a projects with the following net cash flows (in millions). The initial investment cost is -20, the cash flows at the end of year 1, 2, 3 are 10,9,6, respectively. What are the projects’ NPV assuming the cost of capital is 5%? 10%? 15%? 3. A firm with a 14% capital cost is evaluating a project. The project needs 6000 as the initial investment and has 2,000 cash inflows for the following 5 years. Calculate NPV.

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