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EXERCISE 6.8 (10–15 minutes)
(a)
Present value of an ordinary annuity of 1
for 4 periods @ 8%
3.31213
EXERCISE 6.9 (5–10 minutes)
The rate of interest is determined by dividing the future value by the present
value and then finding the factor in the FVF table with n = 2 that approxi-
mates that number:
EXERCISE 6.10 (10–15 minutes)
(a) The number of interest periods is calculated by first dividing the future
value of $1,000,000 by $148,644, which is 6.72748—the value $1.00 would
accumulate to at 10% for the unknown number of interest periods. The
factor 6.72748 or its approximate is then located in the Future Value of
1 Table by reading down the 10% column to the 20-period line; thus, 20 is
the unknown number of years Chopra must wait to become a millionaire.
EXERCISE 6.11 (10–15 minutes)
(a) Total interest = Total payments—Amount owed today
€155,820 (10 X €15,582) – €100,000 = €55,820.
EXERCISE 6.12 (10–15 minutes)
Building A—PV = $610,000.
Building B—
Building C—
Rent X (PV of ordinary annuity of 25 periods at 12%) = PV
Cash purchase price
$650,000
PV of rental income
– 47,059
Net present value
$602,941
EXERCISE 6.13 (15–20 minutes)
Time diagram:
Messier, SA
PV = ? i = 5% (10% ÷ 2)
PV – OA = ? Principal
Formula for the interest payments:
PV – OA = R (PVF – OAn, i)
Formula for the principal:
PV = FV (PVFn, i)
EXERCISE 6.14 (15–20 minutes)
Time diagram:
i = 8%
R =
PV – OA = ? $200,000 $200,000 $200,000
Formula: PV – OA = R (PVF – OAn, i)
OR
Time diagram:
i = 8%
EXERCISE 6.14 (Continued)
(i) Present value of the expected annual pension payments at the end of
the 10th year:
PV – OA = R (PVF – OAn, i)
(ii) Present value of the expected annual pension payments at the begin-
ning of the current year:
EXERCISE 6.15 (15–20 minutes)
(a)
i = 6%
PV = $1,000,000 FV = $1,898,000
(b) By setting aside $300,000 now, Lee can gradually build the fund to an
amount to establish the foundation.
PV = $300,000 FV = ?
0 1 2 8 9
EXERCISE 6.16 (10–15 minutes)
Amount to be repaid on March 1, 2027.
Time diagram:
i = 6% per six months (12% ÷ 2 payments annually)
PV = $90,000 FV = ?
Amount of annual contribution to debt retirement fund.
Time diagram:
i = 10%
R R R R R FV – AD =
R = ? ? ? ? ? $288,643
EXERCISE 6.16 (Continued)
1.
Future value of ordinary annuity of 1 for 5 periods
at 10% ..............................................................................
6.10510
EXERCISE 6.17 (10–15 minutes)
Time diagram:
i = 11%
R R R
PV – OA = £421,087 ? ? ?
EXERCISE 6.18 (10–15 minutes)
Time diagram:
i = 8%
PV – OA = ? ¥400,000 ¥400,000 ¥400,000 ¥400,000 ¥400,000
0 1 2 13 14 15
n = 15
EXERCISE 6.19 (10–15 minutes)
Time diagram:
i = 8%
PV – AD = ?
R =
¥400,000 ¥400,000 ¥400,000 ¥400,000 ¥400,000
Formula:
Using Table 6-4 Using Table 6-5
PV – AD = R (PVF – OAn, i) PV – AD = R (PVF – ADn, i)
EXERCISE 6.20 (15–20 minutes)
Expected
Cash Flow Probability Cash
Estimate X Assessment = Flow
(a) £4,800 20% £ 960
(b) £5,400 30% £1,620
7,200 50% 3,600
8,400 20% 1,680
Total Expected
Value £6,900
EXERCISE 6.21 (10–15 minutes)
Estimated
Cash Probability Expected
Outflow X Assessment = Cash Flow
$200 10% $ 20
EXERCISE 6.22 (15–20 minutes)
(a) This exercise determines the present value of an ordinary annuity or
expected cash flows as a fair value estimate.
Cash flow Probability Expected
Estimate X Assessment = Cash Flow
$ 380,000 20% $ 76,000
TIME AND PURPOSE OF PROBLEMS
Problem 6.1 (Time 15–20 minutes)
Purpose—to present an opportunity for the student to determine how to use the present value tables in
Problem 6.2 (Time 15–20 minutes)
Purpose—to present an opportunity for the student to determine solutions to four present and future
Problem 6.3 (Time 20–30 minutes)
Purpose—to present the student with an opportunity to determine the present value of the costs of
competing contracts. The student is required to decide which contract to accept.
Problem 6.4 (Time 20–30 minutes)
Problem 6.5 (Time 20–25 minutes)
Purpose—to provide the student with an opportunity to determine which of four insurance options results
Problem 6.6 (Time 25–30 minutes)
Purpose—to present an opportunity for the student to determine the present value of a series of
Problem 6.7 (Time 30–35 minutes)
Purpose—to present the student an opportunity to use time value concepts in business situations.
Problem 6.8 (Time 20–30 minutes)
Purpose—to present the student with an opportunity to determine the present value of an ordinary
annuity and annuity due for three different cash payment situations. The student must then decide
which cash payment plan should be undertaken.
Time and Purpose of Problems (Continued)
Problem 6.9 (Time 30–35 minutes)
Problem 6.10 (Time 30–35 minutes)
Purpose—to present the student with the opportunity to assess whether a company should purchase or
lease. The computations for this problem are relatively complicated.
Problem 6.11 (Time 25–30 minutes)
Problem 6.12 (Time 20–25 minutes)
Problem 6.13 (Time 20–25 minutes)
Purpose—to present the student an opportunity to compute expected cash flows and then apply present
value techniques to determine a warranty liability.
Problem 6.14 (Time 20–25 minutes)
Problems 6.15 (Time 20–25 minutes)
SOLUTIONS TO PROBLEMS
PROBLEM 6.1
(a) Given no established value for the building, the fair market value of
the note would be estimated to value the building.
Time diagram:
i = 9%
PV = ? FV = ¥24,000,000
Formula: PV = FV (PVFn, i)
PROBLEM 6.1 (Continued)
(b) Time diagram:
i = 11%
Principal
¥100,000 x 300 = ¥30,000,000
Interest = ¥30,000,000 x 9% Interest
PV – OA = ? ¥2,700,000 ¥2,700,000 ¥2,700,000 ¥2,700,000
Present value of the principal
FV (PVF10, 11%) = ¥30,000,000 (.35218) ................
= ¥10,565,400
(c) Time diagram:
i = 8%
PV – OA = ? ¥400,000 ¥400,000 ¥400,000 ¥400,000 ¥400,000
PROBLEM 6.1 (Continued)
(d) Time diagram:
i = 12%
PV – OA = ?
¥2,000,000 ¥500,000 ¥500,000 ¥500,000 ¥500,000 ¥500,000 ¥500,000 ¥500,000 ¥500,000
(e) Time diagram:
i = 11%
PV – OA = ? ¥12,000,000 ¥12,000,000 ¥12,000,000 ¥12,000,000
0 1 2 8 9
n = 9
PROBLEM 6.2
(a) Time diagram:
i = 8% FV – OA = $90,000
R R R R R R R R
R = ? ? ? ? ? ? ? ?
(b) Time diagram:
i = 12%
FV – AD =
R R R R $500,000
R = ? ? ? ?
PROBLEM 6.2 (Continued)
1.
Future value of an ordinary annuity of 1 for
25 periods at 12% ..............................................
133.33387
(c) Time diagram:
i = 9%
PV = $20,000 FV = $47,347
0 1 2 3 n
Future value approach
Present value approach
FV = PV (FVFn, i)
PV = FV (PVFn, i)
PROBLEM 6.2 (Continued)
(d) Time diagram:
i = ?
PV = FV =
$19,553 $27,600
Future value approach
Present value approach
FV = PV (FVFn, i)
PV = FV (PVFn, i)
or
