Financial accounting 9th kieso kimmel appendix g

[4] Identify the variables fundamental to solving present value problems.. [4] Identify the variables fundamental to solving present value problems.. [4] Identify the variables fundam

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Accounting in Action

Learning Objectives

After studying this chapter, you should be able to:

[1] Distinguish between simple and compound interest.

[2] Solve for future value of a single amount

[3] Solve for future value of an annuity

[4] Identify the variables fundamental to solving present value problems

[5] Solve for present value of a single amount

[6] Solve for present value of an annuity

[7] Compute the present value of notes and bonds

[8] Compute the present values in capital budgeting situations

[9] Use a financial calculator to solve time value of money problems

Appendix

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Would you rather receive $1,000 today or in a year from now?

Basic Time Value Concepts

Time Value of Money

Today! “Interest Factor”

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 Payment for the use of money

 Difference between amount borrowed or invested

( principal ) and amount repaid or collected.

Elements involved in financing transaction:

1. Principal (p): Amount borrowed or invested.

2. Interest Rate (i): An annual percentage

3. Time (n): Number of years or portion of a year that

the principal is borrowed or invested.

Nature of Interest

LO 1

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 Interest computed on the principal only

Illustration G-1

Interest computations

Simple Interest

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 Computes interest on

► the principal and

► any interest earned that has not been paid or

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Illustration: Assume that you deposit $1,000 in Bank Two, where it

will earn simple interest of 9% per year, and you deposit another

$1,000 in Citizens Bank, where it will earn compound interest of 9%

per year compounded annually Also assume that in both cases you

will not withdraw any interest until three years from the date of deposit.

Nature of Interest - Compound Interest

Year 1 $1,000.00 x 9% $ 90.00 $ 1,090.00 Year 2 $1,090.00 x 9% $ 98.10 $ 1,188.10 Year 3 $1,188.10 x 9% $106.93 $ 1,295.03

Illustration G-2 Simple versus compound interest

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[1] Distinguish between simple and compound interest

[2] Solve for future value of a single amount.

Appendix

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Future value of a single amount is the value at a future

date of a given amount invested, assuming compound

interest.

Future Value Concepts

FV = future value of a single amount

p = principal (or present value; the value today)

i = interest rate for one period

n = number of periods

Formula for future value

Future Value of a Single Amount

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Illustration: If you want a 9% rate of return, you would

compute the future value of a $1,000 investment for three

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What table do we use?

Alternate Method

Illustration: If you want a 9% rate of return, you would

compute the future value of a $1,000 investment for three

years as follows:

Time diagram

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What factor do we use?

$1,000

x 1.29503 = $1,295.03

LO 2

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[3] Solve for future value of an annuity.

Appendix

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Future value of an annuity is the sum of all the payments

(receipts) plus the accumulated compound interest on

them

Necessary to know the

1 interest rate,

2 number of payments (receipts), and

3 amount of the periodic payments (receipts).

Future Value Concepts

Future Value of an Annuity

LO 3

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Illustration: Assume that you invest $2,000 at the end of each year for three years at 5% interest compounded annually.

Time diagram for a three-year annuity

Future Value of an Annuity

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When the periodic payments (receipts) are the same in each

period, the future value can be computed by using a future

value of an annuity of 1 table.

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[4] Identify the variables fundamental to solving present value problems.

Appendix

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The present value is the value now of a given amount to

be paid or received in the future, assuming compound

interest

Present value variables:

1 Dollar amount to be received (future amount).

2 Length of time until amount is received (number of

periods).

3 Interest rate (the discount rate).

Present Value Concepts

Present Value Variables

LO 4

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[5] Solve for present value of a single amount.

Appendix

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Present Value = Future Value ÷ (1 + i )n

Formula for present value

p = principal (or present value)

i = interest rate for one period

n = number of periods

Present Value of a Single Amount

LO 5

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Illustration: If you want a 10% rate of return, you would

compute the present value of $1,000 for one year as

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Illustration: If you want a 10% rate of return, you can also

compute the present value of $1,000 for one year by using

a present value table.

LO 5

Finding present value if discounted for one period

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$1,000 x .90909 = $909.09

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Finding present value if discounted for two period

Illustration: If the single amount of $1,000 is to be received in

two years and discounted at 10% [PV = $1,000 ÷ (1 + 102], its

present value is $826.45 [($1,000 ÷ 1.21).

LO 5

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$1,000 x .82645 = $826.45

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$10,000 x .79383 = $7,938.30

Illustration: Suppose you have a winning lottery ticket and the state gives you the option of taking $10,000 three years from now or taking the present value of $10,000 now The state uses an 8% rate in discounting How much will you receive if you accept your winnings now?

LO 5

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Illustration: Determine the amount you must deposit today in your SUPER savings account, paying 9% interest, in order to accumulate $5,000 for a

down payment 4 years from now on a new car

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[6] Solve for present value of an annuity.

Appendix

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The value now of a series of future receipts or payments,

discounted assuming compound interest.

Necessary to know the:

1 Discount rate,

2 Number of payments (receipts).

3 Amount of the periodic payments or receipts.

Present Value of an Annuity

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Illustration: Assume that you will receive $1,000 cash annually for three years at a time when the discount rate is 10%

Calculate the present value in this situation.

Time diagram for a three-year annuity

LO 6

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$1,000 x 2.48685 = $2,484.85

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Illustration: Kildare Company has just signed a capitalizable lease

contract for equipment that requires rental payments of $6,000 each, to

be paid at the end of each of the next 5 years The appropriate discount rate is 12% What is the amount used to capitalize the leased

equipment?

$6,000 x 3.60478 = $21,628.68 Present Value of an Annuity

LO 6

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Illustration: Assume that the investor received $500

semiannually for three years instead of $1,000 annually when the

discount rate was 10% Calculate the present value of this annuity.

$500 x 5.07569 = $2,537.85 Present Value of an Annuity

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[7] Compute the present value of notes and bonds.

Appendix

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Two Cash Flows :

 Periodic interest payments (annuity)

 Principal paid at maturity (single sum).

Present Value of a Long-term Note or Bond

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Illustration: Assume a bond issue of 10%, five-year bonds with

a face value of $100,000 with interest payable semiannually on January 1 and July 1 Calculate the present value of the

principal and interest payments.

LO 7

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Illustration: Assume a bond issue of 10%, five-year bonds with a face value of $100,000 with interest payable semiannually on

January 1 and July 1

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Illustration: Now assume that the investor’s required rate of return

is 12%, not 10% The future amounts are again $100,000 and

$5,000, respectively, but now a discount rate of 6% (12% ÷ 2) must

be used Calculate the present value of the principal and interest

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Illustration: Now assume that the investor’s required rate of

return is 8% The future amounts are again $100,000 and $5,000,

respectively, but now a discount rate of 4% (8% ÷ 2) must be used

Calculate the present value of the principal and interest

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[8] Compute the present values in capital budgeting situations.

Appendix

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Illustration: Nagel-Siebert Trucking Company, a cross-country freight

carrier in Montgomery, Illinois, is considering adding another truck to its

fleet because of a purchasing opportunity Navistar Inc., Nagel-Siebert’s

primary supplier of overland rigs, is overstocked and offers to sell its

biggest rig for $154,000 cash payable upon delivery Nagel-Siebert knows that the rig will produce a net cash flow per year of $40,000 for five years

(received at the end of each year), at which time it will be sold for an

estimated salvage value of $35,000 Nagel-Siebert’s discount rate in

evaluating capital expenditures is 10% Should Nagel-Siebert commit to

the purchase of this rig?

Computing the Present Values in a Capital

Budgeting Decision

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Present Value in a Capital Budgeting Decision

The cash flows that must be discounted to present value by

Nagel-Siebert are as follows.

 Cash payable on delivery (today): $154,000.

 Net cash flow from operating the rig: $40,000 for 5 years

(at the end of each year).

 Cash received from sale of rig at the end of 5 years:

$35,000.

The time diagrams for the latter two cash flows are shown in

Illustration G-22 which follows.

LO 8

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The time diagrams for the latter two cash are as follows:

Time diagrams for Siebert Trucking Company

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The computation of these present values are as follows:

Present value computations at 10%

The decision to invest should be accepted

LO 8

Advance slide in presentation mode to reveal answer.

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Assume Nagle-Siegert uses a discount rate of 15%, not 10%.

The decision to invest should be rejected

Present value computations at 15%

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[9] Use a financial calculator to solve time value of money problems.

Appendix

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Using Financial Calculators

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Present Value of a Single Sum

Assume that you want to know the present value of $84,253

to be received in five years, discounted at 11% compounded

annually.

LO 9

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Calculator solution for present value of an annuity

Assume that you are asked to determine the present value of

rental receipts of $6,000 each to be received at the end of

each of the next five years, when discounted at 12%.

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Useful Applications – Auto Loan

The loan has a 9.5% nominal annual interest rate,

compounded monthly The price of the car is $6,000, and you

want to determine the monthly payments, assuming that the

payments start one month after the purchase.

LO 9

Calculator solution for auto loan payments

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