340aclass13 - University of Missouri–St. Louis



340aclass13

October 3, 2002

For next time:

Reading: Start on Chapter 7

Bring Amortization schedule page to class - on web today

Supplemental 2 on the web by this weekend! It is due Oct 29 (3 weeks from next Tues.!)

Today:

Go over exam 1

Present value and Future value concepts

Note: Drop date is October 8. Come see me if you scored below 140 on the exam.

Through the first exam, we were focussing on the basic tools and language used to prepare the financial reports. This chapter kind of stands alone – it is not based on GAAP or FASB guidelines, it is instead a fundamental business education concept, one that you probably covered or will cover in finance.

The Time Value of Money – what does this mean? This is a very basic concept about money and human beings and what makes us happy – we tend to prefer to have money NOW rather than patiently waiting to have money in the FUTURE. Would you rather have $1000 today or would you prefer that I send it to you in 2 years? I know what I would like – I would like to hold on to my money for 2 more years. You would probably like to have the money NOW.

How do we make up for having to wait for money? How do we adjust our happiness so that we are just as happy if we have to wait to get our money? We expect to be paid – INTEREST – (interest is sometimes called the cost of using someone else’s money). How much interest? Well that depends upon how much it takes to adjust our happiness. (Everyone has a price).

Interest can be SIMPLE or COMPOUND.

SIMPLE interest: Principal is multiplied by the interest rate only once.

Ex. Simple interest on a loan : Principal = $1000, Interest rate = 10%

Simple interest = $1000 * 10%

COMPOUND interest: Principal is multiplied by the interest rate and the resulting interest is added to the principal – THEN the next time the interest rate is multiplied by the new bigger amount and on and on.

Ex. Let’s make a deal – I have the absolute coolest new Jaguar XK8 convertible (list price $75,550) and am looking for someone to sell it to. And the payment plan is super easy:

You pay me 1¢ today and then double the amount you pay me each day. How many days do you have to keep paying me? (take guesses)

Think,pair,share

3 weeks? What you pay: $20,971.50

4 weeks? What you pay: $2,684,354.55

6 months? What you pay: $1.532495 * 1052

23 days What you pay: $83,886.07

How does this happen? COMPOUND INTEREST! What was the rate of interest in this example? (100%) How often was it compounded? (daily)

This is an extreme example but it makes the point. Money grows over time because of the effects of interest. Now let’s look at some terminology and some more down to earth examples of the concepts.

Draw a time line:

Present value: This is the value today, right now. A $1000 winning ticket today is worth $1000 (you wouldn’t accept any less or pay any more than $1000 for the right to receive $1000 today)

Future value: This is the value at some point out in the future. How much would you expect to receive if your $1000 winning ticket today would not be paid out to you until the end of 10 years? You would expect more than $1000 (just think what you could have done with $1000 over the 10 year period) – you have to be compensated for waiting that long.

Let’s look at some simple examples of these concepts:

1. Suppose you put $1000 in a savings account that pays 8% annual interest, compounded annually. At the end of 5 year, how much will you have in the account (if you make no other deposits and no withdrawls)?

This question is asking you to find the FUTURE VALUE of your initial investment, the $1000. Now let’s look at the time line to see what happens to your $1000 over time (this seems like a basic step, but it will make problems a lot easier to do!)

Time-0- $1000 Yr 1 int Yr 2 int Yr 3 int Yr 4 int Yr 5 int

You could do this one step at a time but that would take a long time (and this is a simple problem!) OR

There is a formula for figuring this out: FV = PV(1+int)n or $1000(1+.08)5 = $1000*(1.4693) = $1,469.30 OR

You can also use a table to figure this out: Look at page 244 of the text : Find n, i. The table gives you a factor (1.46933 – look familiar?) that you multiply by the PV.

2. Suppose that you want to save for your tuition in the MBA program that you will start 3 years from today. To pay your tuition, you must have $10,000 on the day that the program starts (3 years from today). How much should you put into your 7% money market account today to have $10,000 in 3 years?

This question is asking you to find the PRESENT VALUE of some amount you need or want to have in the future. Draw a time line to make sure you understand the cash flows.

Again, you could do this one step at a time – but who wants to do that? OR

There is a formula for figuring this out: PV = FV* 1/((1+int)n) = $10,000* 1/ (1+.07)3 = $10,000*(.8163) = $8,163 OR

You can use a table to figure this out: Look at page 245 of the text: Find n, i. The table gives you a factor (.8163) that you multiply by the FV.

Now let’s add a twist.

3. Assume the same as example 1 but this time the money market account compounds the annual 8% interest semi-annually . Draw the time line. How much will you have (before we start, do you think it will be more or less than $1,469.30?)

What interest rate do you use for the formula or the table? Does your account pay 8% every six months? (NO, it is an 8% annual rate) What happens every six months? The account computes 4% interest on the balance and adds this amount to your account. So when you use the formula or the table you should use 4%.

What n should you use (how many periods?) Your account grows every six months or 2 times each year. So you should multiply the number of years by 2 (2*5 years= 10 periods). Use 10 as the “n”.

Table factor: n=10, I=4 : 1.4802 ; 1.4802*1000 = $1,480.20

What if the interest was compounded quarterly? N=4*5=20, I=8/4 = 2% each quarter

Table factor: 1.48595

These examples have assumed that you only make one deposit (today). Often times, you are interested in finding either the present value of a series of payments or the future value of a series of payments. A series of payments is referred to as an ANNUITY if:

1. The payments occur at equal time intervals (every year for example).

2. Each payment is for the same amount.

If each payment is made at the end of the time interval, this is referred to as an ORDINARY ANNUITY.

If each payment is made at the beginning of the time interval, this is referred to as an ANNUITY DUE.

How do we figure the FV of an annuity? Draw a time line showing that the FV of a 5 year ordinary annuity is equivalent to the FV of a 5 year deposit + FV of a 4 year deposit + FV of a 3 year deposit + FV of a 2 year deposit + FV of a 1 year deposit.

Figuring out the FV of 5 different cash flow streams would take a long time. Luckily, we have tables to use (there are also formulas but you don’t need to memorize them). Look at page 246.

4. Suppose that you will make a $1000 deposit at the end of each of the next 5 years. If the deposit earns 8% compounded annually, what will the balance in the account be at the end of the 5 years?

Table on page 246: n=5, I=8%; factor = 5.8660 : FV = $1000 * 5.8660 = $5,866

Prove that each column in this table is an accumulated sum of the FV table on page 244. 5 different cash flows:

FV factor:

N=4,I=8%; factor = 1.36049 (end of yr 1 deposit)

N=3,I=8%; factor = 1.25971 (end of yr 2 deposit)

N=2,I=8%; factor = 1.1664 (end of yr 3 deposit)

N=1,I=8% ; factor = 1.08 (end of yr 4 deposit)

N=0,I=8% ; factor = 1 (end of yr 5 deposit – this one isn’t on the table, but think about it!!)

Sum up all the factors and you get 5.8666!

(1000*1.36049)+(1000*1.25971)+(1000*1.1664)+(1000*1.08)+(1000*1) = $5,866

What if the deposits are made at the beginning of each year? Then this is an ANNUITY DUE! Table on page 248: n=5, I=8%; factor = 6.33593 : FV = $1000*6.33593 = $6,339.59

If you did each year at a time, using the FV table on page 244:

N=5,I=8%; factor = 1.46933 (beginning of yr 1 deposit)

N=4,I=8%; factor = 1.36049 (beginning of yr 2 deposit)

N=3,I=8%; factor = 1.25971 (beginning of yr 3 deposit)

N=2,I=8%; factor = 1.1664 (beginning of yr 4 deposit)

N=1,I=8% ; factor = 1.08 (beginning of yr 5 deposit)

Sum up all the factors and you get 6.3359!

5. Now let’s combine some ideas> Suppose that someone is selling the right to receive cash flows : you pay them $X now and then for the next 10 years you will receive $100 at the end of each year PLUS $1000 at the end of the 10th year. If your happiness is worth an interest rate of say, 9%, how much would you be willing to pay them now for the future cash flows?

(we worked this out in class)

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download