COMMERCE 2FA3 Chapter Notes - Chapter 5-7: Investment, Net Present Value, Price–Earnings Ratio
27 Apr 2018
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Chapter 5:
FV and Compounding
- Future Value (FV) refers to the amt. of money to which an inv. Would grow over some
length of time at some given int. rate
Investing for a Single Pd.
- Invest $100 in a savings act. That pays 10% int/ yr.
- In one yr., you would have $110
o Principal = 100
o Interest = 10
o 100(1+10%)= 110
Investing for > than 1 pd.
- Invest $100 in a savings act., that pays 10%/ yr
o What will you have in 2 yrs?
▪ 110(0.1)=11 110+11=121
• 100=Principal
• 10= interest in first yr.
• 10= interest in second yr.
• 1= interest earned on second yr. on int. paid in first yr.
▪ =100(1+0.1)^2
- Compounding: leaving your $$ and any accum. Interest in an inv. For more than 1 pd.,
reinvesting the $$
o Earning interest on interest compound interest
o Simple Interest: Int. is not reinvested, int. is earned each pd. Only on the org.
principal
-
- FV= PV (1+r)^N
o Future Value Interest factor (FVIF)= (1+r)^N
PV and Discounting
- Present Value (PV) refers to the amt. needed at the current moment
Single-pd. Case
- How much do we invest today at 10% int. rate to get $1 in 1 yr?
o FV=$1, PV=?
o PV= FV/ (1+r)
- Instead of compd., we discount it back to the present
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PV for Multiple Pds.
- You need $1000 in 2 yrs., you earn 7%, how much do you have to invest now to get $1K?
o PV= 1000/ (1.07)^2 = 873.44
o Disc. Factor: 1/(1+r)^n; Calc. disc. Rt.
▪ Also called Present Value Interest Factor (PVIF)
Chapter 6
- Future and Present Values of Multiple CF
- FV w/ Multiple CF
o Suppose you deposit $100 td. Paying 8%. In 1 yr, you deposit another $100. How
much at the end of second yr?
▪ Make a timeline
▪ Have $100 deposited in each yr
▪ x .=… + x.
o Two ways to calc. FV for Multiple CF
▪ Compd. The accum. Balance forward one yr. at a time
▪ Calc. the FV of each CF first an then add them up
- PV w/ Multiple CF
o Two ways to determine the PV of a series of future CF
▪ Disc. Back one pd. At a time
▪ Calc. the PV individually and add them up
o Suppose you need $1000 in one yr, and $2000 more in two yrs. If you can earn
9% on your money, how much do yoy have to put up td. To exactly cover these
at. i the future? What’s the PV of the two CF at %?
▪ 2000/(1.09)^2= 1683.36
▪ 1000/ (1.09)^1= 917.43
▪ = 2600.79
- Valuing Lvl. CF: Annuities and Perpetuities
o Annuity: A series of constant or lvl. CF that occur at the end of each pd. For some
fxd. # of pds.; known as ordinary annuity
- PV for Annuity CF
o Suppose we were examining an asset that promised to pay $500 at the end of
each of the next three years. The cash flows from this asset are in the form of a
three-year, $500 annuity. If we wanted to earn 10 percent on our money, how
much would we offer for this annuity?
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o For this q, you can use the old formula, BUT
▪ If the # of CF was a lrg. Amt., you use the perpetuity formula (eg. 25 yrs.
For 300 pmt.)
o
▪ Anything in the brackets is known as PVIFA
o
- FV for Annuities
- For example, suppose you plan to contribute $2,000 every year into a Registered
Retirement Savings Plan (RRSP) paying 8 percent. If you retire in 30 years, how much will
you have?
o
o The formula FOR FVIFA
o
- For Ord. Annuities, CF occurs at the end of each pd.
o Eg. The first loan pmt. Happens one month after you get the loan
- For Annuity Due: pmt. Is received immediately
o Eg. For a lease, you pay at the beginning of the mth.
o When CF occurs at the start of each pd.
o If you have 5 pmt. Of $400, on the timeline it would be portrayed
o
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Document Summary
Future value (fv) refers to the amt. of money to which an inv. Would grow over some length of time at some given int. rate. In one yr. , you would have : principal = 100. Compounding: leaving your 7492 and any accum. For more than 1 pd. , reinvesting the $: earning interest on interest compound interest, simple interest: int. is not reinvested, int. is earned each pd. Fv= pv (1+r)^n: future value interest factor (fvif)= (1+r)^n. Present value (pv) refers to the amt. needed at the current moment. How much do we invest today at 10% int. rate to get in 1 yr: fv=, pv=, pv= fv/ (1+r) Instead of compd. , we discount it back to the present. You need in 2 yrs. , you earn 7%, how much do you have to invest now to get k: pv= 1000/ (1. 07)^2 = 873. 44, disc. Rt: also called present value interest factor (pvif) Future and present values of multiple cf.
