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Agenda – 4/17/2013

• Discuss interest and the time value of money• Explore the Excel time value of money functions• Examine the accounting measures of profitability• Course Evaluations

Some Excel financial functions

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Function DescriptionCUMIPMT** Cumulative Interest Payments

CUMPRINC Cumulative Principal Payments

FV Future Value

IPMT** Interest Payment

IRR Internal Rate of Return

NPER Number of periods

NPV Net Present Value

PMT** Payment

PPMT** Principal Payment

PV Present Value

RATE Interest Rate

SLN Straight Line Depreciation

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Excel Functions are Excel Functions

To use them, you must understand the

TIME VALUE OF MONEY

Understanding time value of money

• Money will increase in value over time if the money is invested and can make more money.

• If you have $1,000 today, it will be worth more tomorrow if you invest that $1,000 and it earns additional money (interest or some other return on that investment).

• If you have $1,000 today, it will NOT be worth more tomorrow if you put it in an envelope and hide it in a drawer. Then the time value of money does not apply as an increase. It will most likely decrease in value because of inflation. Of course, you won’t lose the whole $1,000 either…

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Introduction to Interest Calculations

• When you borrow money you pay interest

• When you loan money, you receive interest

• When you make a payment part of the payment is applied to interest Part of the payment is applied to principal

Types of Interest

• Simple interest Interest is paid only on the principal Many certificates of deposit work this way

• Compound interest Interest is added to the principal each period Interest is calculated on the principal plus any

accrued interest Compounding can occur on different periods

• Annually, quarterly, monthly, daily

Difference between simple and compound interest

• Assume that you have $1,000 to invest. $1,000 is the present value (PV) of your money.

• You can invest it and receive “simple” interest or you can earn “compound” interest.

• The money that you have at the end of the time you have invested it is called the “future value” (FV) of your money.

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Future value of money

• Simple interest is always calculated on the initial $1,000. 5% interest on $1,000 is $50. Always $50.

• When interest is paid on not only the principal amount invested, but also on any previous interest earned, this is called compound interest.

FV = Principal + (Principal x Interest)

= 1000 + (1000 x .05)

= 1000 (1 + i)

= PV (1 + i)

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Simple vs. compound interest comparison

Year Simple Interest Compound Interest0 $1,000 $1,000

1 $1,050 $1,050

2 $1,100 $1,102.50

3 $1,150 $1,157.62

4 $1,200 $1,215.61

5 $1,250 $1,276.28

10 $1,500 $1,628.89

20 $2,000 $2,653.30

30 $2,500 $4,321.94

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$1,000 Invested at 5% return

How much money would you have if you invested $1000 for 5 years at an

interest rate of 5% a year?

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How much money would you have if you invested $1000 each year for 5 years at an interest rate of 5% a year?

Time Value of Money Functions

• We are just solving the same equation for a different variable RATE determines the interest rate NPER determines the number of periods PMT determines the payment PV determines the present value of a

transaction FV determines the future value of a

transaction

The RATE Function

• Determines the interest rate per period based on The number of periods The payment The present value The future value The type

The NPER Function

• Determines the number of periods based on The interest rate The payment The present value The future value The type

Future Value Function

Argument Descriptionrate Interest rate per compounding period

nper Number of compounding periods

Pmt Payment made each compounding period

Pv Present value of current amount

type Designates when payments or deposits are made

Type 0 – end of period. Default. Type 1 – beginning of period

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FV(rate, nper, pmt, pv, type)

If you receive $5000 5 years from now, and the “going”

interest rate is 5%, how much is that money worth

today?

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Present Value Function

Argument Descriptionrate Interest rate per compounding period

nper Number of compounding periods

pmt Payment made each period

fv Future value of the amount received today

type Designates when payments are madeType 0 – end of period. Default. Type 1 – beginning of period

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PV(rate, nper, pmt, fv, type)

What about if you borrow money?

• If you borrow money, the lender wants to earn “compound” money on his/her/its investment.

• If you borrow $1000 at 10%, then you won’t pay back just $1,100 (unless you pay it back at once during the initial time period).

• You will pay it back “compounded”. Interest will be calculated each period on your remaining balance.

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Amortization table $1,000 loan, pay $100 year, 5% year interest

Year Amount Owed Amount Plus Interest

Payment

1 $1,000.00 $1,050.00 $100.002 $950.00 $997.50 $100.003 $897.50 $942.38 $100.004 $842.38 $884.49 $100.005 $784.49 $823.72 $100.006 $723.72 $759.90 $100.007 $659.90 $692.90 $100.008 $592.90 $622.54 $100.009 $522.54 $548.67 $100.00

10 $448.67 $471.11 $100.0011 $371.11 $389.66 $100.0012 $289.66 $304.14 $100.0013 $204.14 $214.35 $100.0014 $114.35 $120.07 $100.0015 $20.07 $21.07 $21.07

Total Paid $1,421.07

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What would that same amortization table (also called a schedule) look like if the interest

was compounded AFTER you paid, rather than BEFORE you

paid?

(this is a type 1 on Excel financial functions)

Amortization table $1,000 loan, pay $100 year, 5% year interest

Year Amount Owed Payment Amount Plus Interest

1 $1,000.00 $100.00 $945.002 $945.00 $100.00 $887.253 $887.25 $100.00 $826.614 $826.61 $100.00 $762.945 $762.94 $100.00 $696.096 $696.09 $100.00 $625.897 $625.89 $100.00 $552.198 $552.19 $100.00 $474.809 $474.80 $100.00 $393.54

10 $393.54 $100.00 $308.2211 $308.22 $100.00 $218.6312 $218.63 $100.00 $124.5513 $124.55 $100.00 $25.7814 $25.78 $25.78 $0.00

Total Paid $1,325.78

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Types of financial questions asked

• How much will it cost each month to pay off a loan if I want to borrow $150,000 at 4% interest each year for 30 years? (PMT function)

• Assume that you need to have exactly $40,000 saved 10 years from now. How much must you deposit each year in an account that pays 2% interest, compounded annually, so that you reach your goal of $40,000? (PMT function)

• If you invest $2,000 today and accumulate $2,676.45 after exactly five years, what rate of annual compound interest did you earn? (INTRATE function)

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Payment function

Argument Descriptionrate Interest rate per compounding period

nper Number of compounding periods

pv Present value

fv Future value, residual left over after the loan is completed. Could be a balloon payment. Can be omitted if = 0.

type Designates when payments are madeType 0 – end of period. Default. Type 1 – beginning of period

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PMT(rate, nper, pv, fv, type)

The PMT Function (Example)

The IPMT Function (Introduction)

• Use IPMT to calculate the interest applicable to a particular period Use the initial balance for the present value

no matter the period• Use PPMT to calculate the principal applicable to a

particular period

• The arguments to both functions are the same

Interest Payment

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Argument Description

rate Interest rate per compounding period

per Period for which interest should be calculated.

nper Number of compounding periods

pv Present value

fv Future value, residual left over after the loan is completed. Could be a balloon payment. Can be omitted if = 0.

type Designates when payments are madeType 0 – end of period. Default. Type 1 – beginning of period

IPMT(rate, per, nper, pv, fv, type)

Principal Payment

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Argument Description

rate Interest rate per compounding period

per Period for which principal payment should be calculated.

nper Number of compounding periods

pv Present value

fv Future value, residual left over after the loan is completed. Could be a balloon payment. Can be omitted if = 0.

type Designates when payments are madeType 0 – end of period. Default. Type 1 – beginning of period

PPMT(rate, per, nper, pv, fv, type)

The CUMIPMT Function (Introduction)

• CUMIPMT calculates the cumulative interest between two periods

• CUMPRINC calculates the cumulative principal between two periods

• The arguments to both functions are the same

• Functions require the analysis tool pack add-in

Cumulative Interest Payments

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Argument Description

rate Interest rate per compounding period

nper Number of compounding periods

pv Initial loan amount (Present value).

Start_period Starting period. Begins at 1 and increments by 1.

End_period Ending period. Begins at 1 and increments by 1

type Designates when payments are madeType 0 – end of period. Default. Type 1 – beginning of period

CUMIPMT(rate, nper, pv, start_period, end_period, type)

Financial questions

• If you borrow $1,000 for 5 years and pay 4% yearly interest compounded monthly, how much interest will you pay? First do the calculation. Second, what Excel formula would you use

to do the calculation for you? Third, what Excel formula would calculate

the payment?• If you invest $1,000 and receive 3% yearly interest

compounded quarterly, how much will you have at the end of 10 years?

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