Accounting principles, 13th edition appxg

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Chapter Outline

Learning Objectives

LO 1 Compute interest and future values.

LO 2 Compute present values.

LO 3 Compute the present value in capital budgeting situations.

LO 4 Use a financial calculator to solve time value of money problems.

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Interest and Future Values

Nature of Interest

Payment for the use of money

Difference between amount borrowed or invested ( principal ) and amount repaid or

collected

Elements involved in financing transaction:

invested.

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Simple Interest

Interest computed on principal only

Illustration: Assume you borrow $5,000 for 2 years at a simple interest rate of 12% annually Calculate the

annual interest cost.

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Compound Interest

Computes interest on

Most business situations use compound interest

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Illustration: Assume 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 cash until three years from the date of deposit.

Compute the interest to be received and the accumulated year-end balances for Citizens Bank.

LO 1

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Bank TwoSimple Interest

Calculation

Simple Interest

Accumulated Year-End Balance

Interest Calculation

CompoundInterest

Accumulated Year-End Balance

Simple versus compound interest

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Future Value of a Single Amount

Value at a future date of a given amount invested, assuming compound interest.

FV = p × (1 + i)n

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

LO 1

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Illustration: The future value of a $1,000 investment earning 9% for three years is $1,295.03.

ILLUSTRATION G.4

Time diagram

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Another method to compute the future value of a single amount involves a compound interest table.

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Illustration: John and Mary Rich invested $20,000 in a savings account paying 6% interest at the time their

son, Mike, was born The money is to be used by Mike for his college education On his 18th birthday, Mike

withdraws the money from his savings account How much did Mike withdraw from his account?

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

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$20,000 x 2.85434 = $57,086.80

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Future Value of an Annuity

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

Time diagram for a three-year annuity

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Invested

at End

of Year

Number of Compounding Periods

Amount Invested x

Future Value of 1 Factor at 5% =

Future Value

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When 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.

Table 2 Future Value of an Annuity of 1

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Illustration: John and Char Lewis’s daughter, Debra, has just started high school They decide to start a

college fund for her and will invest $2,500 in a savings account at the end of each year she is in high school (4 payments total) The account will earn 6% interest compounded annually How much will be in the

college fund at the time Debra graduates from high school?

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$2,500 x 4.37462 = $10,936.55

Table 2 Future Value of an Annuity of 1

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Present Values

Present Value Variables

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).

LO 2

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Present Value of a Single Amount

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

p = principal (or present value)

i = interest rate for one period

n = number of periods

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Illustration: The computation of $1,000 discounted at 10% for one year is as follows.

Finding present value if discounted for one period

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$1,000 x 90909 = $909.09

Table 3 Present Value of 1

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Illustration: If the single amount of $1,000 is to be received in two years and discounted at 10% [PV =

$1,000 ÷ (1 + 10)2], its present value is $826.45 [($1,000 ÷ 1.21).

1

What table do we use?

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$1,000 x 82645 = $826.45

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Illustration: Suppose you have a winning lottery ticket and the state gives you the option of taking $10,000

3 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 2

What table do we use?

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$10,000 x 79383 = $7,938.30

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Illustration: Determine the amount you must deposit today in a savings account, paying 9% interest, in

order to accumulate $5,000 for a down payment 4 years from now on a new car.

LO 2

Present

Value (?)

0 Today

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$5,000 x 70843 = $3,542.15

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Present Value of an Annuity

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

LO 2

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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.

Present

Value (?)

0 Today

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$1,000 x 2.48685 = $2,486.85

What factor do we use?

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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 present value of the rental payments—that is, the amount used to capitalize the leased equipment?

Present

Value (?)

0 Today

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$6,000 x 3.60478 = $21,628.68

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$500 x 5.07569 = $2,537.85

Table 4 Present Value of an Annuity of 1

Illustration: Assume 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.

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LO 2

Present Value Long-Term Note or Bond

Two Cash Flows:

a Periodic interest payments (annuity)

b Principal paid at maturity (single sum)

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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.

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$100,000 x 61391 = $61,391.00

Present Value Principal

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$5,000 x 7.72173 = $38,609.00

Table 4 Present Value of an Annuity of 1

Present Value Interest

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LO 2

5% Contractual Rate— 5% Discount Rate

Present value of principal to be received at maturity

$100,000 × PV of 1 due in 10 periods at 5%

$100,000 × 61391 (Table 3) $ 61,391

Present value of interest to be received periodically

over the term of the bonds

$5,000 × PV of 1 due periodically for 10 periods at 5%

$5,000 × 7.72173 (Table 4) 38,609*

Present value of bonds $100,000

*Rounded

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Assume the investor’s required rate of return is 6%, not 5%.

$100,000 × 55839 (Table 3) $ 55,839

$5,000 × 7.36009 (Table 4) 36,800

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LO 2

Assume the investor’s required rate of return is 4%, not 5%.

$100,000 × 67556 (Table 3) $ 67,556

$5,000 × 8.11090 (Table 4) 40,555*

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Capital Budgeting Situations

Illustration: Nagel-Siebert Trucking Company, a cross-country freight carrier in Montgomery, Illinois, is

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 Siebert’s discount rate in evaluating capital expenditures is 10%

Nagel-Should Nagel-Siebert commit to the purchase of this rig?

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The cash flows that must be discounted to present value by Nagel-Siebert are as follows.

The time diagrams for the latter two cash flows are shown as follows.

LO 3

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Time diagrams for latter two cash flows are as follows:

PV (?)

0 Today

i = 10%

n = 5

4 3

Cash from Sale

$35,000

PV (?)

0 Today

$40,000 $40,000 $40,000

Net Operating Cash Flows

$40,000

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LO 3

Computation of these present values are as follows:

Present Values— 10% Discount Rate

Present value of net operating cash flows received

annually over 5 years

$40,000 × PV of 1 received annually for 5 years at 10%

$40,000 × 3.79079 $ 151,631.60

Present value of salvage value to be received in 5 years

$35,000 × PV of 1 received in 5 years at 10%

$35,000 × 62092 21,732.20

Present value of cash inflows 173,363.80

Present value of cash outflows (price due today at 10%)

$154,000 × PV of 1 due today

$154,000 × 1.00000 (154,000.00)

Net present value $ 19,363.80

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

Present Values— 15% Discount Rate

Present value of net operating cash flows received

annually over 5 years at 15%

$40,000 × 3.35216 $ 134,086.40

Present value of salvage value to be received in 5 years

at 15%

$35,000 × 49718 17,401.30

Present value of cash inflows 151,487.70

Present value of cash outflows (price due today at 15%)

$154,000 × 1.00000 (154,000.00)

Net present value $ (2,512.30)

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Using Financial Calculators

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Present Value of a Single Sum

Calculator solution for

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.

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LO 4

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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Future Value of a Single Sum

future value of a single sum

Assume you will invest $20,000 today into a fund and you intend to leave it there for 15 years The fund earns 7% interest Compute the future value at the end of year 15.

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LO 4

future value of an annuity

Assume you will invest $8,000 into a fund at the end of each of the next eight years The fund earns 9% interest Compute the future value of the fund at the end of the eighth year.

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Internal Rate of Return

Calculator solution for internal rate of return

A purchase of a piece of equipment with a seven-year life requires an initial investment of $54,000, has positive cash flows of $7,800 per year, and has an estimated salvage value of $11,000 Compute the internal rate of return.

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Useful Applications – Auto Loan

LO 4

Calculator solution for auto loan payments

You are financing the purchase of a car with a three-year loan The annual interest rate is 9.5%,

compounded monthly The price of the car is $6,000 Calculate the monthly payments, assuming payments start one month after purchase.

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Useful Applications – Mortgage Loan

Calculator solution for mortgage amount

You decide the maximum mortgage payment you can afford is $700 per month The annual interest rate is 8.4% What is the maximum purchase price you can afford if the mortgage requires you to make monthly payments over a 15 years?

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