Question

Using the tables in Exhibits 26-3 and 26-4, determine the present value of the following cash flows, discounted at an annual rate of 15 percent. (Round "PV factors" to 3 decimal places. Do not round intermediate calculations and round your final answers to the nearest whole dollar amount.)

a. $8,500 to be received 20 years from today.

b. $13,000 to be received annually for 10 years.

c. $6,700 to be received annually for five years, with an additional $12,000 salvage value expected at the end of the fifth year.

d. $31,000 to be received annually for the first three years, followed by $20,000 received annually for the next two years (total of five years in which cash is received).

Answer 1

• All working forms part of the answer
• Working: PV factor table at 15%

Year	PV factor at 15%
1	0.870
2	0.756
3	0.658
4	0.572
5	0.497
6	0.432
7	0.376
8	0.327
9	0.284
10	0.247
11	0.215
12	0.187
13	0.163
14	0.141
15	0.123
16	0.107
17	0.093
18	0.081
19	0.070
20	0.061

• Requirement ‘a’

$ 8500 to be received in Year 20

PV = 8500 x PV factor of Year 20
= 8500 x 0.061
= $ 518.5 or $ 519

• Requirement ‘b’

Sum total of PV factor from Year 1 to Year 10 = 5.019

PV of $ 13,000 to be received annually for 10 years = 13000 x 5.019

= $ 65,247

• Requirement ‘c’

Sum total of PV factor from Year 1 to year 5 = 3.353

PV of 6700 to be received annually for 5 years = 6700 x 3.353 = $ 22,465

PV of $ 12000 received at the end of 5 year = 12000 x PV factor of 5^th year = 12000 x 0.497 = $ 5,964

Total PV = 22465 + 5964 = $ 28,429

• Requirement ‘d’

PV factor at 15%	Amount received	Present Value
[A]	[B]	[A x B]
Year 1 0.87	$              3,000.00	$           2,610.00
Year 2 0.756	$              3,000.00	$           2,268.00
Year 3 0.658	$              3,000.00	$           1,974.00
Year 4 0.572	$              2,000.00	$           1,144.00
Year 5 0.497	$              2,000.00	$               994.00
Total PV of the sums		$           8,990.00

Total PV = $ 8990