Here is a list of activity times for a project as well as crashing costs for its activities. Determine which activities should b
e crashed and the total cost of crashing if the goal is to shorten the project by three weeks as cheaply as possible. There are three paths (top, middle and bottom). Each path contains three sequential activities which must be performed in the order they are listed (e.g., A before B, B before C). Note that Activity C is contained on both the top and middle paths.
Path
Activity
Duration (weeks)
First Crash
Second Crash
Top
A
5
$8
$10
B
6
7
9
C
3
14
15
Middle
D
3
9
11
E
7
8
9
C
3
14
15
Bottom
F
5
10
15
G
5
11
13
H
5
12
14
Activity
Cost
First crash
$
Second crash
$
Third crash
$
Path
Activity
Duration (weeks)
First Crash
Second Crash
Top
A
5
$8
$10
B
6
7
9
C
3
14
15
Middle
D
3
9
11
E
7
8
9
C
3
14
15
Bottom
F
5
10
15
G
5
11
13
H
5
12
14
Activity
Cost
First crash
$
Second crash
$
Third crash
$
1 answer:
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Answer:
$106,595
Explanation:
Given:
Initial market rate = 9%
Dropped market interest rate, r = 7% per year
or
= 7% × [6 ÷ 12]
= 3.5% = 0.035
Remaining time, n = 9 years = 18 semi annual periods
Now,
Value of the bond at the retirement
= [ PVAF × Interest payment] + [ PVF × face value]
here,
Present value of annuity factor, PVAF =
or
PVAF =
or
PVAF = 13.189
And,
Interest payment = $100,000 × 8% × [6 ÷ 12 ] [since, 8% bonds]
= $4000
Present value factor =
= 0.538
par value = $100,000
= [13.189 × $40] + [0.538 × 100,000]
= 52,758.7316 + 53,836.114
= $106,595
Hence,
The correct answer is option $106,595