For Week 6, please turn in the answers to the following questions:
- Why do we say money has time value?
- Why is it important for business managers to be familiar with time value of money concepts?
- Define Present Value.
- Define Future Value.
- What are present value and future value interest factors? (as in PVIF and FVIF)
- (calculating future value) You buy a 6 year, 8% CD for $1,000. Interest is compounded annually. How much is it worth at maturity?
- (calculating present value) What’s the present value of $1,000 to be received in 8 years? (Your required rate of return is 7% a year.)
- (calculating the rate of return) A friend promises to pay you $600 two years from now if you loan him $500 today. What interest rate is your friend offering you?
- (calculating the future value of an annuity) If you invest $100 a year for 20 years at 7% annual interest, how much will you have at the end of the 20th year
- (calculating the present value of an annuity) How much would you be willing to pay today for an investment that pays $800 a year at the end of the next 6 years? (Your required rate of return is 5% a year.)
the main topic for week 6 is Time Value of Money. This will be the most challenging financial concept in the entire course…however, learning the concepts will be a valuable tool to add to your toolbox of skills.
NOTE: I’ve put a helpful memo on how to do all kinds of TVM applications using Excel, in Announcements. I have Windows 7 2010 so if you have a different version my commands may not work the same for you.
If you instead choose to do it long hand, the hard way, get lots of paper, and I will pray for you.
TVM has many applications, such as: calculating your mortgage and car payments, figuring out how much you have to save up for retirement planning, how a firm decides to invest in project A vs B, how to answer the main question when you win the lottery, etc., etc.
So try these all…don’t wait till Sunday to try them; I’ll try and check each day to give you quick feedback to help you on the homework.
- . You and your friend both want to save up to buy a $1000 computer, 3 years from now. You have a track record of earning 10% on your investments, your friend has a track record of earning 5% on her investments.
WHO has to start out with the bigger amount of money, today? WHY?
- . Whats the FUTURE value or FV of putting $1 in a savings account today, and leaving in there for 2 years, if the bank is paying 10%? If its only paying 5%?
- . What the PRESENT value or PV of receiving $1.21 two years from now, if you have a track record of earning 10% on your money
- . NOW, the one everyone is waiting for:
You have just won the lottery
You are asked whether you want the $10,000,000 lump sum or a 20 year, $700,000/yr annuity
IGNORING taxes, how old you are, how sick you are, the likelihood of Tsunamis, whether the State Lottery will be bankrupt in 5 years, whether you want to leave $ to your kids…..
On what basis do you make your decision?? [remember, you are in a finance class]
Using Excel for TVM calculations REV2:
There are 4 methods to do TVM calculations:
- the longhand method of multiplying exponential formulas
- using any of the 4 TVM tables
- using excel
- using a financial calculator
In my opinion method 1 is too difficult. #2 takes too long; #3 I cannot help anyone with as every different calculator has its own 100 page instruction book
The easiest way is learning to use excel.
- To use excel, hit the “Fx” toolbar, and choose “financial” functions from the pulldown menu
To do any kind of present value problem, go to the PV function
To do any kind of FV problem, go to the FV function
Whichever function you choose will open a window into which you will type in data
Guidelines to follow:
- The “rate” means the decimal format of the discount or interest rate PER PERIOD to use; if its 5%, type in .05….if its 12% type in .12.
If instead of annual compounding, for example if problem dealt with semiannual compounding, and annual rate was 10%, you would type in .05.
- “Periods” means the number of compounding periods. If problem is 10 years, compounded annually, type in 10; if its 10 years compounded semi-annually, type in 20
- means what the future sum would be.
- “Payment” field would only be filled in if its an annuity [a stream of equal periodic payments like a car loan or mortgage], in which case you would type in the size of the periodic payment. Otherwise, leave it blank.
- Generally money paid in [like to a bank], should have a negative sign, and your answer will come out positive then
- For determining the PV of some future some, use the PV function, type in your discount rate as a decimal, type in the number of periods, and type in the future value. If its an annuity, type in the $ amount of the periodic payment in the “payment” field.
- For determining the Future value of some present sum, use the FV function and enter info as above whether its one present sum, or its an annuity stream
- If instead of a simple end of period annuity problem, its an “annuity due” problem [payment on the first day of the period vs., the last day, like an ordinary annuity], type “1” into the “type” field
- Determining the effective annual rate: EAR
Go to financial section of Fx toolbar, using pull down window to get “effective”. Type in the nominal or stated ANNUAL percentage rate[APR], as a decimal[12% would be .12] and type in the number of compounding periods per year[if monthly compounding type in 12; if weekly compounding type in 52]. The answer should ALWAYS be >ANNUAL rate you typed in, unless its annual compounding in which case APR=EAR
- Loan payment: to determine the size of the equal periodic loan payment, use the “payment” function, PMT. Type in the loan interest rate per period, as a decimal; if its an annual 12%, then its 1% per month, for example. Type the value of the money to be borrowed, in PV; type in the number of loan periodic payments. If you want the monthly loan payment, make sure the interest rate is expressed as “per period”
- For bond YTM problems
Use the “rate” function; type in number of periods, any periodic payment, what you are paying out [with a negative sign], what you get back as FV
- Valuing a bond:
Time value of money principles can be used to answer the question. “what is the appropriate market price, or value of a certain bond, which has a coupon or interest rate R, a face value of F, and has Y years left to maturity.”
As we go through this you’ll better understand why financial newscasters will frequently say “rising interest rates” cause a fall in bond prices, and lowering interest rates causes an increase in bond pricing-not trivial events when we’re talking about billions of dollars in bonds traded everyday.
The value of a bond is made up of two pieces-the PV of its face value upon maturity and the present value of the stream of coupon or interest payments over its remaining time to maturity.
To determine the PV of a bond you need to determine the PV of each of these components.
The present value of the face value is simply the maturity value ($1000 most of the time) discounted by the number of periods remaining at the appropriate discount rate. Always remember, your investment track record or discount rate may be higher or lower than the other party in the transaction of buying and selling a bond.
The present value of the stream of remaining coupon payments can be determined through a series of individual PV calculations or one annuity calculation
Maturity=30 years, but 5 years have passed already since the bond was initially issued and purchased so there’s 25 years left
Coupon rate=10% so annual interest payment is $1000 x .1=$100
Your personal investment track record of earnings, [or your discount rate]=6%
What’s the bonds appropriate price, or market value or… “PV?
You COULD do this in two pieces….
- PV of the face value
I=.06, n=25, PMT=0, FV=1000 equals $233
- PV of the annuity stream of interest payments=
I=.06, n=25, PMT=10% x 1000=100; FV=0 equals 1278.30
Total PV of these two pieces=$233+$1278.30=$1511
OR, using excel do it in one step
I=.06 n=25, PMT=100, FV=1000
As this is greater than the par or face value, its termed selling or valued or priced…. “at a premium”.
Why would it sell as a premium?
Compare your personal discount rate of 6%, with the coupon interest rate of 10%. You could do much better than usual by buying my bond at 10% interest; in fact its so good a deal that you’re going to be willing to pay me a “premium” to buy it.
Guess what would happen if your discount rate was HIGHER than the bonds coupon rate….yes, its PV would be <$1000, and it would be selling or valued at a “discount”. Why does this make sense?
You’d have to have a very good reasons to buy something, giving you a worse return,( lets say 5%) than your own track record of returns(6%). To convince you to buy it, I’ll have to put it on “sale” by selling it at a discount!
Ok…summarizing using excel to calculate a bonds value
go to the normal present value function in excel[PV]
- in the rate field type in the appropriate discount rate, marketplace interest rates, ytm, expected return…..in decimal format[this is NOT the same as the bonds coupon or interest rate, other than by coincidence]
- in the number of periods type in the number of periods of compounding
- in the “payment field” type in the $ value of the interest annuity. Its the stated coupon or interest rate x the bonds face value
- in the FV field type in the face value which is almost always 1000
Remember, that if bond pays interest more frequently, such as semi-annually, you have to make 3 adjustments to your calculations; yields on similar bonds, or discount rate or YTM rate/2, # of periods x 2, coupon payment/2
For IRR capital budgeting problems:
Enter into a series of excel worksheet cells, the outflow, or initial investment[with a negative], and inflows, in the proper order
Go to IRR function and it will ask for the range of cell containing the cash stream you wish to determine IRR for.
For example if in year0,1,2,3 you have cash flows of -10,000[you invest 10,000 on day 1], and then in years 1,2,3 cash inflows or benefits of 5000,6000,10,000. You would enter -10,000 in cell A1, 5000 in A2, 6000 in A3, and 10,000 in A4[all without commas].
Type in A1:A4 and it will tell you the IRR
Ignore the “guess” field
For capital budgeting NPV problems
NPV=PVinflows[or financial benefits]-PV outflow[or the initial investment]
Use excels NPV function
Type in sequentially the year 1,2,3, etc cash inflows or benefits you get each year.
Type in the appropriate discount rate as a decimal
It will give you the PV of the inflows
This will NOT give you the NPV of the project, it will only give you the PV of all the inflows; you STILL have to subtract the investment, or PV of the outflow