the concept of present value
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The Concept of Present Value. Appendix 13A. Learning Objective 7. (Appendix 13A) Understand present value concepts and the use of present value tables. The Mathematics of Interest. - PowerPoint PPT PresentationTRANSCRIPT
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PowerPoint Authors:Susan Coomer Galbreath, Ph.D., CPACharles W. Caldwell, D.B.A., CMAJon A. Booker, Ph.D., CPA, CIACynthia J. Rooney, Ph.D., CPA
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
The Concept of Present ValueAppendix 13A
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Learning Objective 7
(Appendix 13A)
Understand present value concepts and the
use of present value tables.
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The Mathematics of Interest
A dollar received today is worth more
than a dollar received a year from now
because you can put it in the bank today
and have more than a dollar a year from
now.
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The Mathematics of Interest – An Example
Assume a bank pays 8% interest on a $100 deposit made today. How much
will the $100 be worth in one year?
FFnn = P(1 + r) = P(1 + r)nn
F = the balance at the end of the period n.P = the amount invested now.r = the rate of interest per period.n = the number of periods.
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The Mathematics of Interest – An Example
FFnn = P(1 + r) = P(1 + r)nn
FF11 = $100(1 + .08) = $100(1 + .08)11
FF11 = $108.00 = $108.00
Assume a bank pays 8% interest on a $100 deposit made today. How much
will the $100 be worth in one year?
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Compound Interest – An Example
FFnn = P(1 + r) = P(1 + r)nn
What if the $108 was left in the bank for a second year? How much would the original $100 be worth at the end
of the second year?
F = the balance at the end of the period n.P = the amount invested now.r = the rate of interest per period.n = the number of periods.
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Compound Interest – An Example
FF22 = $100(1 + .08) = $100(1 + .08)22
FF22 = $116.64 = $116.64
The interest that is paid in the second year on the interest earned in the first year is known as compound interest.
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Computation of Present Value
Present Value
Future Value
An investment can be viewed in two ways—its future value or its present
value.
Let’s look at a situation where the future value is known and the present
value is the unknown.
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Present Value – An Example
If a bond will pay $100 in two years, what is the present value of the $100 if an investor can earn
a return of 12% on investments?
(1 + r)(1 + r)nnP =P =FFnn
F = the balance at the end of the period n.P = the amount invested now.r = the rate of interest per period.n = the number of periods.
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Present Value – An Example
(1 + .12)(1 + .12)22P =P =$100$100
P =P = $79.72$79.72
This process is called discounting. We have discounted the $100 to its present value of $79.72. The interest rate used to find the present value is called the discount rate.
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Present Value – An Example
Let’s verify that if we put $79.72 in the bank today at 12% interest that it would
grow to $100 at the end of two years.
Year 1 Year 2Beginning balance 79.72$ 89.29$ Interest @ 12% 9.57 10.71 Ending balance 89.29$ 100.00$
Year 1 Year 2Beginning balance 79.72$ 89.29$ Interest @ 12% 9.57 10.71 Ending balance 89.29$ 100.00$
If $79.72 is put in the bank today and earns If $79.72 is put in the bank today and earns 12%, it will be worth $100 in two years.12%, it will be worth $100 in two years.
If $79.72 is put in the bank today and earns If $79.72 is put in the bank today and earns 12%, it will be worth $100 in two years.12%, it will be worth $100 in two years.
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RatePeriods 10% 12% 14%
1 0.909 0.893 0.877 2 0.826 0.797 0.769 3 0.751 0.712 0.675 4 0.683 0.636 0.592 5 0.621 0.567 0.519
RatePeriods 10% 12% 14%
1 0.909 0.893 0.877 2 0.826 0.797 0.769 3 0.751 0.712 0.675 4 0.683 0.636 0.592 5 0.621 0.567 0.519
Present Value – An Example
$100 × 0.797 = $79.72 present value
Present value factor of $1 for 2 periods at 12%.Present value factor of $1 for 2 periods at 12%.Present value factor of $1 for 2 periods at 12%.Present value factor of $1 for 2 periods at 12%.
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Quick Check
How much would you have to put in the bank today to have $100 at the end of five years if the interest rate is 10%?a. $62.10b. $56.70c. $90.90d. $51.90
How much would you have to put in the bank today to have $100 at the end of five years if the interest rate is 10%?a. $62.10b. $56.70c. $90.90d. $51.90
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How much would you have to put in the bank today to have $100 at the end of five years if the interest rate is 10%?a. $62.10b. $56.70c. $90.90d. $51.90
How much would you have to put in the bank today to have $100 at the end of five years if the interest rate is 10%?a. $62.10b. $56.70c. $90.90d. $51.90
Quick Check
$100 $100 0.621 = $62.10 0.621 = $62.10$100 $100 0.621 = $62.10 0.621 = $62.10
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Present Value of a Series of Cash Flows
11 22 33 44 55 66
$100$100 $100$100 $100$100 $100$100 $100$100 $100$100
An investment that involves a series of identical cash flows at the end of each year is
called an annuity.
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Present Value of a Series of Cash Flows – An Example
Lacey Inc. purchased a tract of land on which a $60,000 payment will be due each year for
the next five years. What is the present value of this stream of cash payments when the
discount rate is 12%?
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Present Value of a Series of Cash Flows – An Example
We could solve the problem like this . . .
Periods 10% 12% 14%1 0.909 0.893 0.877 2 1.736 1.690 1.647 3 2.487 2.402 2.322 4 3.170 3.037 2.914 5 3.791 3.605 3.433
Present Value of an Annuity of $1
$60,000 × 3.605 = $216,300
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Quick Check
If the interest rate is 14%, how much would you have to put in the bank today so as to be able to withdraw $100 at the end of each of the next five years?a. $34.33b. $500.00c. $343.30d. $360.50
If the interest rate is 14%, how much would you have to put in the bank today so as to be able to withdraw $100 at the end of each of the next five years?a. $34.33b. $500.00c. $343.30d. $360.50
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If the interest rate is 14%, how much would you have to put in the bank today so as to be able to withdraw $100 at the end of each of the next five years?a. $34.33b. $500.00c. $343.30d. $360.50
If the interest rate is 14%, how much would you have to put in the bank today so as to be able to withdraw $100 at the end of each of the next five years?a. $34.33b. $500.00c. $343.30d. $360.50
Quick Check
$100 $100 3.433 = $343.30 3.433 = $343.30$100 $100 3.433 = $343.30 3.433 = $343.30
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End of Appendix 13A