Chapter Thirteen

1. Chapter Thirteen Capital Budgeting and Other Time Value of Money Applications Richard E. McDermott, Ph.D.

2. CapitalBudgetingEvaluationProcess Many companies follow a carefully prescribed process in capital budgeting. At least once a year: 1) Proposals for projects are requested from each department. 2) The proposals are screened by a capital budgeting committee, which submits its finding to officers of the company. 3) Officers select projects and submit a list of projects to the board of directors.

3. Capital Budgeting Evaluation Process The capital budgeting decision depends on a variety of considerations: 1) The availability of funds. 2) Relationships among proposed projects. 3) The company’s basic decision-making approach. 4) The risk associated with a particular project.

4. Cash Payback Formula • The cash payback technique identifies the time period required to recover the cost of the capital investment from the annual cash inflow produced by the investment. • The formula for computing the cash payback period is:

5. Estimated Annual Net Income from Capital Expenditure Assume that Reno Co. is considering an investment of $130,000 in new equipment. The new equipment is expected to last 5 years. It will have zero salvage value at the end of its useful life. The straight-line method of depreciation is used for accounting purposes. The expected annual revenues and costs of the new product that will be produced from the investment are: Sales $200,000 Less: Costs and expenses $132,000 Depreciation expense ($130,000/5) 26,000 Selling and administrative expenses 22,000 180,000 Income before income taxes 20,000 Income tax expense 7,000 Net income $ 13,000

6. Annual (or net) cash inflow is approximated by taking net income and adding back depreciation expense. Depreciation expense is added back because depreciation on the capital expenditure does not involve an annual outflow of cash. Computation of Annual Cash Inflow Cash income per year equals net income plus depreciation expense.

7. Computation of Annual Cash Inflow

8. Computation of Annual Cash Inflow

9. Cash Payback Period The cash payback period in this example is therefore 3.33 years, computed as follows: $130,000 ÷ $39,000 = 3.33 years When the payback technique is used to decide among acceptable alternative projects, the shorter the payback period, the more attractive the investment. This is true for two reasons: 1) The earlier the investment is recovered, the sooner the cash funds can be used for other purposes, and 2) the risk of loss from obsolescence and changed economic conditions is less in a shorter payback period.

10. A $100,000 investment with a zero scrap value has an 8-year life. Compute the payback period if straight-line depreciation is used and net income is determined to be $20,000. Review Question • 8.00 years. • 3.08 years. • 5.00 years. • 13.33 years.

11. A $100,000 investment with a zero scrap value has an 8-year life. Compute the payback period if straight-line depreciation is used and net income is determined to be $20,000. Review Question • 8.00 years. • 3.08 years. • 5.00 years. • 13.33 years. Calculation of answer: First calculate depreciation: $100/000/8 years = $12,500 Add dep’n to income to get net cash flow: $20,000 + $12,500 = $32,500 Divide investment by yearly cash flow to get payback period: $100,000/$32,500 = 3.08 years.

12. Time Value of Money • Many cost of capital evaluation techniques involve time value money of calculations. • Let’s utilize Excel in learning how to analyze various investments or returns involving incoming or outgoing streams of money.

13. A Little Theory . . . Assume we invest a lump sum of $100 in time period zero. Money The interest rate is 10% per year. $300 $200 $100 Time 0 1 2 3

14. A Little Theory . . . We let it grow for three years. Money In one year it is worth $100 x 1.10 = $110 In two years it is worth $110 x 1.1 = $121 In three years it is worth $121 x 1.10 = $133.10 $133.10 $130 $120 $100 Time 0 1 2 3

15. A Little Theory . . . These figures can be calculated using Excel. Money Again we are talking about lump sums! The future value of $100 for three periods at 10% is $133.10. $133.10 $130 $120 $100 The present value of $133.10 for three periods is $100. This represents the future value and present value of a lump sum. Time 0 1 2 3

16. Practice Problem – Future Value of a Lump Sum • Let’s use Excel to work this problem. • This is future value of a lump sum problem. • We deposit a lump sum of $100, today, make no additional payments, and leave the money in the bank for three periods at 10% per period interest.

17. Excel Worksheet Select Formulas Select Financial

18. Excel Worksheet Select FV for “future value”

19. Excel Worksheet This box will appear on your screen.

20. Excel Worksheet Notice that we put nothing in the Pmt box since the $100 is the only deposit.

21. Excel Worksheet Hit “Ok.” The future value of $100 for 3 periods at 10% per period is $133.10.

22. Another Method • One can also type financial commands into Excell. • The command for future value is =fv • Enter “=fv(“ and you get the following on your screen • FV(rate,nper,pmt,[pv],[type]) • Entering the values • =fv(.10,3,0,100,0) • The answer given is ($133.10)

24. Future Value of Lump Sum Problem • Assume you are 25 years of age and inherit $25,000 from your grandfather. • You decide to save this money for retirement at age 65. • You deposit it in a certificate of deposit earning 4% per year. • How much will you have at retirement? • Answer: $120,025.52

25. Present Value of Future Lump Sum • Let’s say you want to leave $1,000,000 to your great-grandson 100 years from now. You can invest your money at 10% per year (compounded monthly). • What lump sum must you invest today to accrue that amount. • =pv(rate,nper,pmt,[fv],[type]) • =pv(.10/12,1200,0,1000000,0) • The answer is $47.32!

26. Present Value of Future Lump Sum • What if you compound the interest yearly instead of monthly, does it make a difference? • Let’s see. • This time let’s use the menu approach to solving the Excel problem.

27. Calculation • From the Excel screen select formulas, then financial just as we did before.

28. Now Let’s Calculate Present Value • This time select PV from the drop down menu.

29. This Box Will Appear

30. Present Value of a Future Lump Sum Hit OK. The amount you must deposit today is $72.57.. Compunding monthly instead of yearly obviously makes a difference.

31. A Little More Theory . . . • A lump sum is one sum of money invested at some point in time. • We can also have annuities. • An annuity is a series of payments of the same amount received or paid at equal periods of time. • $100 invested for 3 periods is an annuity.

32. To Illustrate . . . The first year we make a payment of $100. That amount grows with interest until we make a second payment which in turn grows with interest until we make a third payment. Money New Axis $331 At the end of three years we have $331 from the annuity. $300 $200 $100 The future value of 3 payments of $100 at 10% interest per period is $331. Again, we could calculate this using Excel. Time 0 1 2 3

33. Calculation of Future Value of an Annuity Problem Select Formulas Select Financial

34. We are still going to use the FV function However we are going to fill the pop up box in differently. Now we will insert $100 in the Pmt box.

35. The Answer is $331.00 The same amount shown on the earlier chart!

36. What does this mean? If you deposit three yearly payments of $100 each, at the end of three years you will have $331.00 in savings.

37. Practice Problem • An individual saves $500 a month for thirty years at 8% interest a year. • How much will he have in savings at the end of thirty years?

38. Things to Be Aware of • Make sure you pay attention to the fact that the money is deposited in savings monthly. • The pop-up box, interest, periods, and payments must all be consistent. • The interest rate will not be .08 but .08/12 months = .006667. • The number of periods will be 30 years x 12 months = 360.

39. Calculation • From the menu at the top of the screen, select Formulas and then Financial just as we have before. • Select FV as before, and fill the box that appears in as shown on the following screen:

40. Pop-up Box

41. The Answer is: At the end of thirty years, you will have $745,785.11 in the bank! Again, this problem is a future value of an annuity problem. The annuity is $500 per month.

42. Now Let’s do a Present Value of an Annuity • Your daughter is going away to college. • Living expenses and tuition and books will cost $33,000 for six years (she wants to get a graduate degree) • You can invest money at 7% a year. • How much must you deposit today so that she can draw out $33,000 a year six years earning a 7% return on money in the bank?

43. Present Value of An Annuity • Select Formulas and Financial from the Excel menu as before. • Select PV as before (remember PV and FV can be used for both lump sums and annuities). • You will get the following pop-up box.

44. Present Value of an Annuity Hit ok. The answer is $157,296.81!

45. PV and FV Functions • With the PV and FV functions, we can combine and annuity and a lump sum calculation. • For example, assume you have $25,000 to deposit in the bank today at 6%. • Then for the next ten years you will deposit $5,000 a year at 6%. • How much will you have (what will the future value be) at the end of ten years?

46. Future Value of a Lump Sum and Annuity • Select Formulas, and Financial as before. • Select FV to get the following box.

47. The answer is . . . • $70,339.57

48. Discounting Cash Flows that Are Not Equal • Earlier we said that an annuity was a series of equal payments, equally spaced. • What if we are to receive payments that are unequal in amount but equally spaced? • How do we find the present value?

49. Discounting Cash Flows that Are Not Equal • Why do we care? • Because this is one way of valuing a business!

50. Why We Care • Most business valuations are done by discounting projected cash flows. • Also, stocks, bonds, and businesses are valued by taking the present value of future cash flows. • Let’s do some examples.