This chapter discusses net present value (NPV) analysis and time value of money concepts. It introduces formulas for calculating future value, present value, and NPV for single-period and multi-period cash flows. It also covers compounding periods, perpetuities, annuities, and growing cash flows. The key concepts of this chapter are NPV analysis, discounting future cash flows, and accounting for the time value of money.

1. CHAPTER 4 Net Present Value

12. Future Value and Compounding 0 1 2 3 4 5

20. EAR on a financial Calculator keys: display: description: 12 [gold] [P/YR] 12.00 Sets 12 P/YR. Hewlett Packard 10B 18 [gold] [NOM%] 18.00 Sets 18 APR. Texas Instruments BAII Plus keys: description: [2nd] [ICONV] Opens interest rate conversion menu [↓] [EFF=] [CPT] 19.56 [↓] [NOM=] 18 [ ENTER] Sets 18 APR. [↑] [C/Y=] 12 Sets 12 payments per year [gold] [EFF%] 19.56

31. What is the present value of a four-year annuity of $100 per year that makes its first payment two years from today if the discount rate is 9%? 0 1 2 3 4 5 $100 $100 $100 $100 $323.97 $297.22

34. PV of Growing Annuity You are evaluating an income property that is providing increasing rents. Net rent is received at the end of each year. The first year's rent is expected to be $8,500 and rent is expected to increase 7% each year. Each payment occur at the end of the year. What is the present value of the estimated income stream over the first 5 years if the discount rate is 12%? $34,706.26 0 1 2 3 4 5

38. We begin by substituting for PMT and for r becomes

39. We can now simplify terms:

40. We continue to simplify terms. Note that:

41. We continue to simplify terms. Finally, note that: (1 + r ) – (1 + g ) = r – g

44. PV of Growing Annuity: BAII Plus PMT I/Y FV PV N 19,417.48 = 6.80 = 0 – 265,121.57 40 PV A defined-benefit retirement plan offers to pay $20,000 per year for 40 years and increase the annual payment by three-percent each year. What is the present value at retirement if the discount rate is 10 percent per annum? 20,000 1.03 1.10 1.03 – 1 × 100

46. PV of a delayed growing annuity The first step is to draw a timeline. The second step is to decide on what we know and what it is we are trying to find. Year 0 1 2 3 Cash flow $1.50 $1.65 $1.82 4 $1.82×1.05 …

47. PV of a delayed growing annuity Year 0 1 2 3 Cash flow $1.50 $1.65 $1.82 dividend + P 3 PV of cash flow $32.81 = $1.82 + $38.22