Opportunity cost of capital – rate of return expected to be received from alternate investments forgone. NPV – Present value of cash flows less the cost of acquiring the asset acquire assets with positive NPV, positive NPV = good project Rate of Return = profit/cost or investment (good investments have higher rate of return than opportunity cost) Higher discount rate ( lower discount factor (lower NPV

Investment Decision Rules:

1. accept if positive NPV

2. accept w rate of return > opp cost or hurdle rule

PV = C1* [1/(1+r)] = Discount factor * cash flow (calc: usually -PV ) Discount factor (DCF) = 1/(1+r) or PV/FV ** will be < 1 ** NPV = C1 + C1* [1/(1+r)]

If PV of $1 received n years from today at an interest rate of r=.270 then what is the future value of $1 invested today at an interest rate of r% for n years? FV = 1/(.270) = 3.71

retire in 30 yrs, wants to accumulate 1 mill before. I =12%, how much should he put into fun each year? (n=30, FV=1mill, I=12%, PV=0, PMT=?) = 4143.66

retire in 30 yrs., wants to accum 1 mill before. I=12%/yr. pmt monthly with monthly cmpd interest. (n=20*12=360; r=12%/12=1%monthly; FV=1mill; PV=0; PMT=?) =286.13

Chapter 3

FV = PV (1+r)t ; PV = FV * DCF

Perpetuity – a stream of cash flows with fixed payments each year lasting forever. PV = C/r r = C/PV Growing Perpetuity – a perpetuity with a constant growth rate (g)

** r must be greater than g **

Annuity – a stream of cash flows with a definite end

Ordinary annuity – payments at the end of the year

Annuity due – payments at the beginning of the year

PV of annuity due = PV of an ordinary annuity * (1+ r) Simple interest – interest earned only on principal (same amt every period) Compound interest – earn interest on principal and interest already earned. Compounding – “m” times per year (1 + r/m)m

As “m” approaches infinity it is continuous compounding. Formula for continuous compounding = Poert

Nominal interest rates & cash flows – measure what happens in ordinary dollar units. Real rates and cash flows – measures what happens in units of purchasing power. 1+rnominal = (1+rreal)(1+inflation rate) ** (rreal = reffective) rnominal = rreal + inflation rate

initial deposit = $100, 10% interest cmpd quarterly for 3 yrs, accum total? EAR= (1+.1/4)4 – 1 = 0.1038; 100(1.1038)3=134.49

▪ Investment @ 12% nominal rate cmpd monthly, annual rate? EAR= ((1.01)12-1=.12681 or 12% [12 NOM, 12 P, EFF%]

|PV of a perpetuity |= C/r c: periodic cash pymt, r: rate of return | |PV of a growing perpetuity |= C1/(r-g) g: growth rate | |PV of an annuity |= C[(1/r) – (1/r(1+r)t )] | | |= C/r [ 1- e rt ] continuous cmpd | |PV of growing annuity |= [PMT0 /r-g] – [PMTt/r-g * (1/1+r)]t | |Annuity factor |= [(1/r) – (1/r(1+r)t )] |

Chapter 4 (STOCKS)

Price of a stock - PV = Payment/r (preferred stock, perpetuity) DIV1 = DIV0 (1+r) DIV1 – Dividend expected to be paid next year. r – rate of return Po = (DIV1 + P1 ) / (1 + r) ; Po: current price of share

Po = DIV1 / (1 + r) + DIV2 / (1 + r)2 + DIV3 / (1 + r)3

r = (DIV1/ P0 ) + g

Stock when the dividend grows at a constant rate (growing perp): Common stock valuation : P0 = DIV1 /(r-g) ** r>g **

Plowback ratio –fraction of earnings reinvested in the business plowback ratio + payout ratio = 1.00 (100%)

Payout ratio = DIV1 / EPS1 ; PO = EPS / r

Dividend growth rate = g = ROE * plowback ratio

g = (1- DIV/EPS) (EPS/ Book Equity per Share)

Dividend yield = DIV1 / P0

Growth stocks – low earnings price ratio, most return to investors in the form of capital gains. where PVGO is large relative to EPS. a) Zero growth – all earnings...