Appendix B – Time Value of Money
Appendix B
Time Value of Money
QUICK STUDIES
Quick Study B-1 (10 minutes)
1. 2% n = 8 periods
Quick Study B-2 (10 minutes)
Quick Study B-3 (10 minutes)
Quick Study B-4 (10 minutes)
Quick Study B-5 (10 minutes)
AppB-1999
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Appendix B – Time Value of Money
Quick Study B-6 (10 minutes)
Quick Study B-7 (10 minutes)
EXERCISES
Exercise B-1 (15 minutes)
In Table B.1, where n = 6 and i = 10%, the p = 0.5645.
Exercise B-2 (15 minutes)
Amount borrowed = present value of $20,000 at 10% for 3 years
Exercise B-3 (10 minutes)
Exercise B-4 (10 minutes)
AppB-1999
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Appendix B – Time Value of Money
Exercise B-5 (15 minutes)
10 years x 4 quarters = 40 interest periods
Exercise B-6 (15 minutes)
Exercise B-7 (10 minutes)
Exercise B-8 (10 minutes)
Exercise B-9 (10 minutes)
Interest rate per period = 12% annual / 12 months per year = 1% per month
Using Table B.3, where n = 40 and i = 1%, the p = 32.8347. This means:
AppB-1999
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Appendix B – Time Value of Money
Exercise B-10 (25 minutes)
1.
First Annuity Future
Payment
Number of
Periods
Interest
Rate
Table B.1
Value
Amount
Borrowed
First payment…….. $5,000 1 6% 0.9434 $ 4,717
Second payment… 5,000 2 6 0.8900 4,450
Second Annuity
Future
Payment
Number of
Periods
Interest
Rate
Table B.1
Value
Amount
Borrowed
First payment…….. $7,500 1 6% 0.9434 $ 7,076
2.
First Annuity
Payment size……………………………….. $ 5,000
Number of payments……………………. 6
Second Annuity
Payment size……………………………….. $ 7,500
AppB-1999
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Appendix B – Time Value of Money
Exercise B-11 (30 minutes)
1. Present value of the annuity
Payment size……………………………….. $13,000
Number of payments……………………. 4
2. Present value of the annuity
Payment size……………………………….. $13,000
Number of payments……………………. 4
3. Present value of the annuity
Payment size……………………………….. $13,000
Number of payments……………………. 4
Exercise B-12 (15 minutes)
Exercise B-13 (15 minutes)
AppB-1999
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Appendix B – Time Value of Money
Exercise B-14 (10 minutes)
Exercise B-15 (10 minutes)
(investor must make 16 annual payments to achieve investment goal).
Exercise B-16 (15 minutes)
12% annual / 12 months per year = 1% per month
Exercise B-17 (15 minutes)
10 years x 4 quarters per year = 40 total quarters
AppB-1999
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Appendix B – Time Value of Money
Exercise B-18 (10 minutes)
a. p = present value of $60,000 at 9% for 4 years
b. p = present value of $15,000 at 8% for 2 years
c. There are at least two ways to solve this problem. (1) We can take the
$463 today, compute its future value, and then compare it to the future
value amount of $1,000. (2) We can discount the $1,000 back to the
present and compare it to the $463 today.
The same answer results: choose $463 today
f = future value of $463 at 9% for 10 years
p = present value of $1,000 at 9% for 10 years
d. f = future value of $90 at 5% for 8 years
e. f = future value of $158,500 at 10% for 8 years
AppB-1999
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Appendix B – Time Value of Money
Exercise B-18 (concluded)
f. There are two aspects to this problem: a present value of a lump sum
part and a present value of an annuity part.
Part 1: p = present value of $10,000 at 6% for 10 years
Part 2: p = present value of $400 annuity at 6% for 10 years
The answer is the sum of the present values from parts 1 and 2:
g. p = present value of $500,000 at 6% for 20 years
Instructor note: It can be useful to extend this problem and assume a 30% tax rate. In this
case the annuity after-tax declines to $350,000. Accordingly, the present value of the
after-tax amount is $4,014,465. Again, nothing near the $10 million winnings advertised.
AppB-1999
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Appendix B – Time Value of Money
Exercise B-19 (20 minutes)
a. (1) Present Value of a single amount.
(2) Multiply $10,000 by p from Table B.1.
OR
(1) Future Value of a single amount.
b. (1) Future Value of an Annuity.
OR
(1) Present Value of an Annuity.
c. (1) Future Value of an Annuity.
d. (1) Present Value of an Annuity.
AppB-1999
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.