An Introduction to Capital Budgeting Methods

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1 An Introduction to Capital Budgeting Methods Econ 466 Spring, 2010 Chapters 9 and 10

2 Consider the following choice You have an opportunity to invest $20,000 in one of the following capital assets. You have estimated the annual cash flows for each option (in $1000) Year A B C Which option would you select?

3 Simple rate of return Calculate the average return to each investment and then compare. Select the investment with the highest simple rate of return SRR = Y/I Where SRR = simple rate of return Y = annual profit (less depreciation) I = original investment

4 SRR calculations Project Total Gross Returns Total Depreciation Average Annual Profits Simple rate of return Original Investment Average Investment A 30,000 20,000 2,000 10% 20% B 29,000 20,000 1,800 9% 18% C 28,000 20,000 1,600 8% 16%

5 SRR analysis How would you rank the investments? A>B>C Good points Simple because you are working with an average (annualized) budget Weak points Timing of returns is not considered

6 Payback period Key question: How long before I get my investment back? Simple, intuitive Widely used If the cash flows are uniform, the calculation is easy P = I/E Where P= payback period I = investment E= income per period Otherwise you need to add up the cash flows until the investment is recaptured

7 Calculate the payback period for these investments Year A B C Project A B C Payback Period 4 years ~ 3.4 years ~ 2.3 years

8 Payback period analysis How would you rank the investments? C>B>A In terms of payback period Good points Very simple Reflects liquidity needs Assumes future returns are too risky to trust Weak points Does not consider earnings beyond payback date Does not consider differences in timing of cash flows Does not measure profitability

9 Signal check on compounding and discounting Suppose you had $1,000 to invest in an investment that earned 10% per year After one year, how much would you have? FV = (1+.10)x$1,000 = $1,100 And after two years, at 10%? FV = (1.10)x$1,100) = $1,210 = 1,000x(1.10) 2

10 Buying the rights to an income stream How much would you pay me for a bond that would pay you $1,100 in a year? If the opportunity cost of your money was 10%? PV = $1,100/(1.10) = $1,000 What if the payout was in two years? PV = $1,210/(1.10) 2 = $1,000 OK??

11 Net present value Determine the value of the cash flows in a way that reflects timing and the time value of money NPV = -INV + P 1 /(1+i) + P 2 /(1=i) 2 + P 3 /(1+i) (P N + V N )/(1+i) N Where NPV = net present value INV = initial investment P t = cash flow in period t V N = salvage value of the investment i = discount rate, required rate of return, opportunity cost of capital

12 Calculate the NVP for the three investments Assuming a discount rate of 8% Year Discount Factor Project A Cashflow PV ,000-20, ,000 1, ,000 3, ,000 4, ,000 5, ,000 6, Net Present Value for A 2,730.27

13 Calculate the NVP for the three investments Assuming a discount rate of 8% Year Discount Factor Project B Cashflow PV ,000-20, , , , , , Net Present Value for B 3,157.72

14 Calculate the NVP for the three investments Assuming a discount rate of 8% Year Discount Factor Project C Cashflow PV ,000-20, , , , , Net Present Value for C $3,766.64

15 NVP analysis summary Project NPV A 2,730 B 3,158 C 3,766

16 NPV summary Decision rule for income earning investments Specify required rate of return (discount rate) Select or rank projects based on their NPV (if positive) Ranking by NPV C>B>A What about cost reducing investments such as machinery?

17 Internal rate of return Consider the following problem. You have an opportunity to invest $1,000 in a one year project that returns $1,100 at the end. What is the minimum opportunity cost of capital that would be acceptable to invest in this project? NPV = 0 = $1,000 - $1,100/(1+ r) Solve for r = IRR r = ($1100 $1000)/$1000 = 0.10 Decision rule: invest in this project if there are no other investments that earn more than 10%

18 Internal rate of return Good points Popular approach with lenders and investors Simple seems like a breakeven rate Weak points Assumes investors can always reinvest at the IRR Multiple rates of return if cash flows change from + to more than once over the investment s time horizon

19 Internal rate of return analysis A more complete model NPV = 0 = -INV + P 1 /(1+i) + P 2 /(1=i) 2 + P 3 /(1+i) (P N + V N )/(1+i) N Solve for i = IRR (using a financial calculator or a spreadsheet)

20 Internal rate of return analysis Solving for the IRR for investments A, B and C we obtain the following results: IRR-A 12.01% IRR-B 13.82% IRR-C 17.57% Ranking by IRR: C>B>A

21 Comparing NPV and IRR

22 Bob s rule Stick with NPV as an analytical method Requires you to specify a discount rate (or rates) that is a good thing. Relatively unambiguous You can always calculate the IRR anyway, since the underlying model is the same

23 Plans for Tuesday, March 9 Meet in the computer lab in Heady Hall Learn to use Excel to model capital budgeting or investment problems Hands on session More to come after break! I ll send an on Monday to remind you!

Session 2, Monday, April 3 rd (11:30-12:30)

Session 2, Monday, April 3 rd (11:30-12:30) Capital Budgeting Continued and the Cost of Capital v2.0 2014 Association for Financial Professionals. All rights reserved. Session 3-1 Chapters Covered Internal