Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
P5-15. Personal finance: Time value and discount rates
LG 2; Intermediate
a. (1) N 10, I 6%, FV $1,000,000 (2) N 10, I 9%, FV $1,000,000
(3) N 10, I 12%, FV $1,000,000
b. (1) N 15, I 6%, FV $1,000,000 (2) N 15, I 9%, FV $1,000,000
(3) N 15, I 12%, FV $1,000,000
c. As the discount rate increases, the present value decreases. This decrease is due to the higher
P5-16. Personal finance: Time value comparisons of single amounts
LG 2; Intermediate
a. AN 3, I 11%, FV $28,500 BN 9, I 11%, FV $54,000
CN 20, I 11%, FV $160,000
b. Alternatives A and B are both worth greater than $20,000 in term of the present value.
c. The best alternative is B because the present value of B is greater than either A or C and is also greater
P5-17. Personal finance: Cash flow investment decision
LG 2; Intermediate
AN 5, I 10%, FV $30,000 BN 20, I 10%, FV $3,000
CN 10, I 10%, FV $10,000 DN 40, I 10%, FV $15,000
Purchase Do Not Purchase
A B
P5-18. Calculating deposit needed
LG 2; Challenge
Step 1: Determination of future value of initial investment
© 2015 Pearson Education, Inc.
Chapter 5 Time Value of Money 76
Step 2: Determination of future value of second investment
Step 3: Calculation of initial investment
P5-19. Future value of an annuity
LG 3; Intermediate
a. Future value of an ordinary annuity vs. annuity due
(1) Ordinary Annuity (2) Annuity Due
AN 10, I 8%, PMT $2,500 $36,216.41 1.08 $39,113.72
BN 6, I 12%, PMT $500 $4,057.59 1.12 $4,544.51
b. The annuity due results in a greater future value in each case. By depositing the payment at the
P5-20. Present value of an annuity
LG 3; Intermediate
a. Present value of an ordinary annuity vs. annuity due
(1) Ordinary Annuity (2) Annuity Due
AN 3, I 7%, PMT $12,000 $31,491.79 1.07 $33,696.22
b. The annuity due results in a greater present value in each case. By depositing the payment at the
© 2015 Pearson Education, Inc.
Chapter 5 Time Value of Money 77
P5-21. Personal finance: Time value—annuities
LG 3; Challenge
a. Annuity C (Ordinary) Annuity D (Due)
(1) N 10, I 10%, PMT $2,500 N 10, I 10%, PMT $2,200
Annuity Due Adjustment
$35,062.33 1.1 $38,568.57
(2) N 10, I 20%, PMT $2,500 N 10, I 20%, PMT $2,200
Annuity Due Adjustment
$57,109.10 1.2 $68,530.92
b. (1) At the end of year 10, at a rate of 10%, Annuity C has a greater value ($39,843.56 vs.
c. Annuity C (Ordinary) Annuity D (Due)
(1) N 10, I 10%, PMT $2,500 N 10, I 10%, PMT $2,200
(2) N 10, I 20%, PMT $2,500 N 10, I 20%, PMT $2,200
d. (1) At the beginning of the 10 years, at a rate of 10%, Annuity C has a greater value ($15,361.42 vs.
(2) At the beginning of the 10 years, at a rate of 20%, Annuity D has a greater value ($11,068.13 vs.
e. Annuity C, with an annual payment of $2,500 made at the end of the year, has a higher present value at
P5-22. Personal finance: Retirement planning
LG 3; Challenge
a. N 40, I 10%, PMT $2,000 b. N 30, I 10%, PMT $2,000
c. By delaying the deposits by 10 years, the total opportunity cost is $556,197. This difference is due to
d. Annuity Due:
© 2015 Pearson Education, Inc.
Chapter 5 Time Value of Money 78
P5-23. Personal finance: Value of a retirement annuity
LG 3; Intermediate
P5-24. Personal finance: Funding your retirement
LG 2, 3; Challenge
a. N 30, I 11%, PMT $20,000 b. N 20, I 9%, FV $173.875.85
c. Both values would be lower. In other words, a smaller sum would be needed in 20 years for
d. N 30, I 10%, PMT $20,000 b. N 20, I 10%, FV $188,538.29
P5-25. Personal finance: Value of an annuity vs. a single amount
LG 2, 3; Intermediate
a. N 25, I 5%, PMT $40,000
b. N 25, I 7%, PMT $40,000
c. View this problem as an investment of $500,000 to get a 25-year annuity of $40,000. The discount
P5-26. Perpetuities
LG 3; Basic
Case Equation Value
A $20,000 0.08 $250,000
B$100,000 0.10 $1,00,000
© 2015 Pearson Education, Inc.
Chapter 5 Time Value of Money 79
P5-27. Personal finance: Creating an endowment
LG 3; Intermediate
a. 6% interest rate
b. 9% percent interest rate
($600 3) 0.09 $20,000
P5-28. Value of a mixed stream
LG 4; Challenge
a.
Cash Flow
Stream Year
Number of Years
to Compound Cash flow
Interest
Rate Future Value
A1 2 $ 900 $ 1,128.96
B1 4 $30,000 $ 47,205.58
C1 3 $ 1,200 $1,685.91
b. If payments are made at the beginning of each period the present value of each of the end-of-period
P5-29. Personal finance: Value of a single amount vs. a mixed stream
LG 4; Intermediate
Lump-Sum Deposit
Mixed Stream of Payments
© 2015 Pearson Education, Inc.
Chapter 5 Time Value of Money 80
Beginning of
Year
Number of Years
to Compound Cash Flow Interest Rate Future Value
1 5 $ 2,000 7% $ 2,805.10
Gina should select the stream of payments over the front-end lump sum payment. Her future wealth will
be higher by $1,596.51.
P5-30. Value of mixed streams
LG 4; Basic
Project A
CF1 $2,000, CF2 $3,000, CF3 $4,000, CF4 $6,000, CF5 $8,000
P5-31. Present value—Mixed streams
LG 4; Intermediate
a. Stream A
b. Cash flow stream A, with a present value of $109,856, is higher than cash flow stream B’s present
P5-32. Value of a mixed stream
LG 1, 4; Intermediate
a.
© 2015 Pearson Education, Inc.
Chapter 5 Time Value of Money 81
b. CF1 $30,000, CF2 $25,000, CF3 $15,000, F3 7, CF4 $10,000
c. Harte should accept the series of payments offer. The present value of that mixed stream of payments
P5-33. Personal finance: Funding budget shortfalls
LG 4; Intermediate
a. CF1 $5,000, CF2 $4,000, CF3 $6,000, CF4 $10,000, CF5 $3,000
b. An increase in the earnings rate would reduce the amount calculated in part a. The higher rate would
P5-34. Relationship between future value and present value-mixed stream
LG 4; Intermediate
a. CF1 $800, CF2 $900, CF3 $1,000, CF4 $1,500, CF5 $2,000
b. The maximum you should pay is $5,243.17.
c. A higher 7% discount rate will cause the present value of the cash flow stream to be lower than
P5-35. Relationship between future value and present value
LG 4; Intermediate
Step 1: Calculation of present value of known cash flows
Year CFtPV @ 4%
1 $10,000 $9,615.38
Step 2: Identify difference between total amount and sum in Step 1.
Step 3: Calculate the amount needed in 3 years that is worth the Step 2 value today
© 2015 Pearson Education, Inc.
Chapter 5 Time Value of Money 82
P5-36. Changing compounding frequency
LG 5; Intermediate
a. Compounding frequency
(1) Annual Semiannual
(2) Annual Semiannual
(3) AnnualSemiannual
b. Effective interest rate: ieff (1 r/m)m – 1
(1) Annual Semiannual
Quarterly
(2) Annual Semiannual
Quarterly
© 2015 Pearson Education, Inc.
Chapter 5 Time Value of Money 83
ieff 0.170 17%
(3) Annual Semiannual
P5-37. Compounding frequency, time value, and effective annual rates
LG 5; Intermediate
a. Compounding frequency:
b. Effective interest rate: ieff (1 r%/m)m – 1
c. The effective rates of interest rise relative to the stated nominal rate with increasing compounding
frequency.
P5-38. Continuous compounding: FVcont. PVex (e 2.7183)
LG 5; Intermediate
© 2015 Pearson Education, Inc.
