Financial accounting tools for business decision making 9 KIeso ppt app g

Nature of InterestPayment for the use of money Difference between amount borrowed or invested principal and amount repaid or collected Elements involved in financing transaction • Pri

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Financial Accounting: Tools for Business

Decision Making

Ninth Edition

Kimmel ● Weygandt ● Kieso

Appendix G

Time Value of Money

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Prepared by COBY HARMON University of California, Santa Barbara

Westmont College

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Chapter Outline

Learning Objectives

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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Learning Objective 1

Compute Interest and Future Values

LO1

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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

• Principal (p): Amount borrowed or invested

• Interest Rate (i): An annual percentage

• Time (n): Number of years or portion of a year

that the principal is borrowed or 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.

Interest = Principal p x Rate i x Time n

= $1,200

LO1

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Compound Interest (2 of 2)

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.

LO1

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Compound Interest (2 of 2)

Bank TwoSimple Interest

Calculation InterestSimple Year-End BalanceAccumulated

Interest Calculation CompoundInterest Year-End BalanceAccumulated

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Future Value of a Single Amount (1 of 5)

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

LO1

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Illustration: The future value of a $1,000 investment earning

9% for three years is $1,295.03.

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Another method to compute the future value of a single

amount involves a compound interest table.

Table 1 Future Value of 1

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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

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

Present Value Factor Future Value

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Future Value of an Annuity (1 of 5)

Illustration: Assume you invest $2,000 at the end of each year

for three years at 5% interest compounded annually.

$2,000 $2,000 $2,000

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Invested

at End

of Year

Number of Compounding Periods Invested x Amount

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

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$2,500 x 4.37462 = $10,936.55

Payment Factor Future Value

Table 2 Future Value of an Annuity of 1

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Compute Present Values

LO2

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Present Value

Present value is the value now of a given amount to

be paid or received in the future, assuming

compound interest

Present value variables

a Dollar amount to be received (future amount)

b Length of time until amount is received (number of

periods)

c Interest rate (the discount rate)

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Present Value of a Single Amount (1 of 9)

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

p = principal (or present value)

i = interest rate for one period

n = number of periods

LO2

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Illustration: The computation of $1,000 discounted at 10% for

one year is as follows.

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$1,000 x 90909 = $909.09

Future Value Factor Present Value

Table 3 Present Value of 1

PV of a Single Amount (3 of 9)

LO2

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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

PV of a Single Amount (5 of 9)

LO2

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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?

What table do we use?

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$10,000 x 79383 = $7,938.30

What factor do we use?

LO2

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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.

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$5,000 x 70843 = $3,542.15

LO2

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Present Value of an Annuity (1 of 6)

The value now of a series of future receipts or

payments, discounted assuming compound interest Necessary to know the

a Discount rate

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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.

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$1,000 x 2.48685 = $2,486.85

Receipts Factor Present Value

Table 4 Present Value of an Annuity of 1

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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?

$6,000 $6,000 $6,000 $6,000

LO2

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$6,000 x 3.60478 = $21,628.68

Payments Factor Present Value

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$500 x 5.07569 = $2,537.85

Receipts Factor Present Value

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.

LO2

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Present Value Long-Term Note or Bond (1 of 7)

Determine the present value of 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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Present value of the principal

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$5,000 x 7.72173 = $38,609.00

Interest Payment Factor Present Value

Present value of the interest

LO2

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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

LO2

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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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Compute the Present Value in Capital Budgeting Situations

LO3

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Capital Budgeting Situations (1 of 5)

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

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?

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The cash flows that must be discounted to present value by

Nagel-Siebert are as follows.

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

b Net cash flow from operating the rig: $40,000 for 5 years (at the end of each year)

c Cash received from sale of rig at the end of 5 years: $35,000

LO3

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Time diagrams for latter two cash flows are as follows:

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

Net Operating Cash Flows

$40,000

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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

LO3

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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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Use a Financial Calculator to Solve Time Value of Money Problems

LO4

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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.

Inputs: 5 11 ? 0 84,253

Answer: -50,000

LO4

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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%.

Inputs: 5 12 ? 6,000 0

Answer: -21,628.66

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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.

Inputs: 15 7 20,000 0 ?

LO4

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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.

Inputs: 8 9 0 8,000 ?

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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.

Inputs: 7 ? -54,000 7,800 11,000

Answer: 4.52%

LO4

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Useful Applications – Auto Loan

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.

Inputs: 36 9.5 6,000 ? 0

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Useful Applications – Mortgage Loan

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?

Inputs: 180 8.4 ? -700 0

Answer: 71,509.81

LO4

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