CF Winter 2014

Discounted Cash Flow Valuation ch 6

Multiple Cash Flows  FV you have:  bank account that earns 8% interest  $7,000 in bank now you:  deposit $4,000 at end of each of next 3 years How much at the end of 3 years?

Multiple Cash Flows  FV -7, , ? FV 0 +FV 1 +FV 2 +FV 3 PV 0 = -7, PV 1 = -4, PV 2 = -4, PV 3 = -4, t 0 = t 1 = t 2 = t 3 =

Multiple Cash Flows  FV -7, , FV PV 0 = -7, PV 1 = -4, PV 2 = -4, PV 3 = -4, t 0 = t 1 = t 2 = t 3 =

Multiple Cash Flows  FV you have:  mutual fund that earns 9% interest  invest $500 now  another $600 in 1 year How much at the end of 2 years? What if you leave it in for 5 years?

Multiple Cash Flows  FV PV FV How much at the end of 2 years? PV 1

Multiple Cash Flows  FV PV FV PV 1 How much at the end of 5 years? FV

Multiple Cash Flows  FV you have:  account the earns 8% interest  invest $100 at year 1  another $300 at year 3 How much at the end of 5 years?

Multiple Cash Flows  FV PV PV 1 r =.08 FV

Multiple Cash Flows  PV you are offered an investment that pays  $200 at year 1  another $400 at year 2  another $600 at year 3  another $800 at year 4 you can earn 12% on similar investments How much is this investment worth today?

Multiple Cash Flows  PV r =.12 $ FV 1 $ FV 2 $ FV 3 $ FV 4 PV 0

Multiple Cash Flows  PV You are considering an investment that pays  $1,000 at year 1  another $2,000 at year 2  another $3,000 at year 3 If you want to earn 10% on your money, how much should you be willing to pay?

Multiple Cash Flows  PV 0123 r =.10 $1, FV 1 $2, FV 2 $3, FV 3 PV 0

Multiple Cash Flows  PV  you’re CEO of small printing company  you want to make profits at least 10%.  your staff tell you if you buy a used printing machine for $5,000 it will make profits of:  $1,000 at the end of year 1  another $2,000 at the end of year 2  another $3,000 at the end of year 3  machine will be worthless after year 3 Should you buy the machine?

Multiple Cash Flows  PV 0123 r =.10 $1, FV 1 $2, FV 2 $3, FV 3 PV 0 $5,000?

Multiple Cash Flows  PV your staff have a new idea:  buy a machine for $100,000  will make $40,000 profit at the end of year 1 $75,000 profit at the end of year 2  after year 2 again, machine value = $0  this is a lot of money, so you want 15% return

Multiple Cash Flows  PV 012 r =.15 $40, FV 1 $75, FV 2 PV 0 $100,000?

Fri

Saving For Retirement you are offered opportunity to put some money away for retirement  you will receive 5 annual payments $25,000 each beginning in 40 years How much would you be willing to invest today if you desired an interest rate of 12%? simplify

Saving For Retirement  5 annual payments $25, each beginning in 40 years interest rate of 12% how much willing to invest? simplify chart

Saving for Retirement PV 0 25, FV 40 25, FV 41 25, FV 42 25, FV 43 25, FV 44 chart r =.12

Perpetuities & Annuities payments at regular intervals  Annuity a finite series  ordinary annuity »payment at end of each period  annuity due »payment at beginning of each period  Perpetuity an infinite series

Perpetuity  PV What?Co.  preferred stock $ dividend every year  interest rate of comparable investment 8.00% PV =present price=? c =dividend every period= r =interest=.0800

Perpetuity  PV What?Co.  wants to issue preferred stock  desired price $  dividend of ? Why?Co.  has a preferred stock  current price $40.00 dividend of $1.00 every quarter r = 2.50%/quarter c = $2.50/quarter

Growing Perpetuity  PV What?Co.  preferred stock $ dividend every year  dividend grows every year 6.00%  comparable interest 8.00%

Annuities Future Value annuity factor Present Value annuity factor

Annuity  PV FV 1 PV FV FV 3 r = 10% PV = $1,243.43

Annuity  PV Cadillac Escalade  loan payments $632.00/month  bank terms 1%/month 48 months  How much can you borrow? PV = $23,999.54

Annuity  PV Publishers Clearinghouse  $10 million prize  paid 30 equal annual installments $333, each  if PC can borrow money at 5% how much does it actually cost them? PV = $5,124,150.29

Annuity  c Finding the Payment  want to borrow $20,000  8% per year compounded monthly  4-year loan c = -$488.26

Annuity  t borrow  $2,  at 5.00% annual payments  $  How long before you pay off the loan? solving for t t = 3.00

Annuities  FV Saving for retirement  $2,000.00/year  7.50% interest rate  How much will you have in 40 years?

Growing Annuity  PV

$50,000-a-year job  increase by 5.00%/year  retire in 40 years  8.00% interest rate  What is the present value of this job?

EAR Effective Annual Rate  Which savings account is better? 15.0%  compounded daily 15.5%  compounded quarterly 16.00%  compounded annually m = # times interest compounded during the year

APR

CorpFi Applications Annuities  capital spending “rational” price lease or buy Printing machine  $1, profit/year for 10 years What should we pay?

CorpFi Applications Annuities  capital spending “rational” price lease or buy Printing machine  which is better buy for $6,000.00? lease for $800.00/year?

CorpFi Applications Growing Annuities  What should my company be worth? “rational” price Profit this year made  $16,000 growing at 3%/year  alternative: 7.5%/year

CorpFi Applications Annuities  “rational” price stock  common  preferred bonds