THE ANALYSIS IS MOST SENSITIVE TO CHANGES IN INITIAL INVESTMENT SINCE
THIS LINE HAS THE STEEPEST (LARGEST ABSOLUTE VALUE) SLOPE. THE
ANALYSIS IS LEAST SENSITIVE TO CHANGES SALVAGE VALUE SINCE THIS
LINE HAS THE FLATEST (SMALLEST ABSOLUTE VALUE) SLOPE.
PERCENT CHANGE IN PARAMETER
PROBLEM 11.30
THE EQUATIONS BELOW CAN BE USED TO DETERMINE THE AW
FOR EACH OF THE REQUESTED SENSITIVITIES. THE VARIABLE “DELTA”
IS USED TO EXPRESS THE PROPORTION CHANGE IN THE PARAMETER
OF INTEREST.
INITIAL INVESTMENT
AW = -$80,000(A|P 12%,7)(1+DELTA) + $15,000 + $2,500(A|F 12%,7)
ANNUAL REVENUE
AW = -$80,000(A|P 12%,7) + $15,000(1+DELTA) + $2,500(A|F 12%,7)
-0.4 $4,730.04 -$8,281.80 -$2,380.92
-0.3 $2,977.08 -$6,781.80 -$2,356.14
-0.2 $1,224.12 -$5,281.80 -$2,331.36
-0.1 -$528.84 -$3,781.80 -$2,306.58
0 -$2,281.80 -$2,281.80 -$2,281.80
0.1 -$4,034.76 -$781.80 -$2,257.02
0.2 -$5,787.72 $718.20 -$2,232.24
0.3 -$7,540.68 $2,218.20 -$2,207.46
0.4 -$9,293.64 $3,718.20 -$2,182.68
0.5 -$11,046.60 $5,218.20 -$2,157.90
NOTE: FOR VALIDATION, STUDENTS SHOULD NOTICE THAT THE
DELTA=0 ROW SHOWS THE SAME VALUE FOR EACH SENSITIVITY COLUMN.
SENSITIVITY GRAPH
NOTE: ALTHOUGH ANALYSIS OF THIS GRAPH IS NOT REQUESTED IN THE
PROBLEM STATEMENT, IT CAN BE SEEN THAT THIS PROJECT IS NOT
ATTRACTIVE UNLESS AN ENHANCEMENT OF REVENUE OR A REDUCTION
IN INITIAL COST IS ACHIEVED. NO CHANGE IN THE SALVAGE VALUE
(WITHIN THE RANGE +/- 50%) WILL LEAD TO THE PROJECT BECOMING
ATTRACTIVE.
-$15,000
PERCENT CHANGE IN PARAMETER
PROBLEM 11.31
PESSIMISTIC MOST LIKELY OPTIMISTIC
CONSTRUCTION COST FOR BUILDING = $7,500,000 $5,000,000 $4,000,000
SALVAGE VALUE FOR BUILDING = $1,500,000 $1,000,000 $800,000
INITIAL FURNISHINGS COST = $3,000,000 $1,875,000 $1,000,000
FURNISHINGS LIFE = 5 5 5
ANNUAL O&M COST = $200,000 $125,000 $75,000
AVERAGE DAILY REVENUE PER OCCUPIED ROOM = $35 $55 $75
PLANNING HORIZON = 15 15 15
MARR = 12% 12% 12%
Pessimistic: 7,500,000(A|P 12%,15)+3,000,000(A|P 12%,5)
+200,000-7,500,000(20%)(A|F 12%,15)=365(35)(X)
X=163.8units occupied daily, or 44.8% occupancy
Optimistic: 4,000,000(A|P 12%,15)+1,000,000(A|P 12%,5)
+75,000-4,000,000(20%)(A|F 12%,15)=365(75)(X)
X=33.5 units occupied daily, or 9.2% occupancy
PROBLEM 11.32
THE EQUATIONS BELOW CAN BE USED TO DETERMINE THE AW
FOR EACH OF THE REQUESTED SENSITIVITIES. THE VARIABLE “DELTA”
IS USED TO EXPRESS THE PROPORTION CHANGE IN THE PARAMETER
OF INTEREST
INITIAL INVESTMENT
AW = -$800,000(A|P 20%,10)(1+DELTA) + $330,000 + $130,000(A|F 20%,10)
ANNUAL REVENUE
AW = -$800,000(A|P 20%,10) + $330,000(1+DELTA) + $130,000(A|F 20%,10)
0.00 $144,191.60 $144,191.60 $144,191.60
0.05 $134,650.80 $160,691.60 $144,441.98
0.10 $125,110.00 $177,191.60 $144,692.36
0.15 $115,569.20 $193,691.60 $144,942.74
0.20 $106,028.40 $210,191.60 $145,193.12
NOTE: FOR VALIDATION, STUDENTS SHOULD NOTICE THAT THE
DELTA=0 ROW SHOWS THE SAME VALUE FOR EACH SENSITIVITY COLUMN.
$0
$50,000
$100,000
$150,000
$200,000
$250,000
-30% -20% -10% 0% 10% 20% 30%
ANNUAL WORTH
SENSITIVITY GRAPH
INIT INV
ANN REV
SALVAGE
THE ANALYSIS IS MOST SENSITIVE TO CHANGES IN ANNUAL REVENUE SINCE
THIS LINE HAS THE STEEPEST (LARGEST ABSOLUTE VALUE) SLOPE. THE
ANALYSIS IS LEAST SENSITIVE TO CHANGES SALVAGE VALUE SINCE THIS
LINE HAS THE FLATEST (SMALLEST ABSOLUTE VALUE) SLOPE.
PERCENT CHANGE IN PARAMETER
PROBLEM 11.33
FIRST COST = $3,000,000
SALVAGE VALUE = $600,000
O&M COST SAVINGS = $1,500,000
PLANNING HORIZON = $10
MARR = 10%
EOY NCF NCF NCF NCF NCF NCF NCF
0 -$3,000,000 -$4,000,000 -$5,000,000 -$6,000,000 -$7,000,000 -$8,000,000 -$9,000,000
1 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000
2 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000
3 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000
4 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000
5 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000
6 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000
7 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000
8 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000
9 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000
10 $2,100,000 $2,100,000 $2,100,000 $2,100,000 $2,100,000 $2,100,000 $2,100,000
PW = $6,448,177 $5,448,177 $4,448,177 $3,448,177 $2,448,177 $1,448,177 $448,177
EOY NCF NCF NCF NCF NCF NCF NCF
0 -$3,000,000 -$3,000,000 -$3,000,000 -$3,000,000 -$3,000,000 -$3,000,000 -$3,000,000
1 $1,500,000 $1,300,000 $1,100,000 $900,000 $700,000 $500,000 $300,000
2 $1,500,000 $1,300,000 $1,100,000 $900,000 $700,000 $500,000 $300,000
3 $1,500,000 $1,300,000 $1,100,000 $900,000 $700,000 $500,000 $300,000
4 $1,500,000 $1,300,000 $1,100,000 $900,000 $700,000 $500,000 $300,000
5 $1,500,000 $1,300,000 $1,100,000 $900,000 $700,000 $500,000 $300,000
6 $1,500,000 $1,300,000 $1,100,000 $900,000 $700,000 $500,000 $300,000
7 $1,500,000 $1,300,000 $1,100,000 $900,000 $700,000 $500,000 $300,000
8 $1,500,000 $1,300,000 $1,100,000 $900,000 $700,000 $500,000 $300,000
9 $1,500,000 $1,300,000 $1,100,000 $900,000 $700,000 $500,000 $300,000
10 $2,100,000 $1,900,000 $1,700,000 $1,500,000 $1,300,000 $1,100,000 $900,000
PW = $6,448,177 $5,219,263 $3,990,350 $2,761,436 $1,532,523 $303,610 -$925,304
RANGE CONSIDERED
[$3 MILLION, 9 MILLION]
[$0.3 MILLION, 1.5 MILLION]
PROBLEM 11.34
THE ANALYSIS BELOW IS BASED ON A PW MEASURE OF WORTH. OTHER
MEASURES COULD BE USED SINCE THE PROBLEM STATEMENT DOES
NOT SPECIFY THE MEASURE TO BE USED.
a PESSIMISTIC ESTIMATES
PW = -$10,500,000 + ($1,500,000 – $350,000)(P|A 20%,15)
PW = -$10,500,000 + ($1,500,000 – $350,000)(4.67547)
PW = -$5,123,209.50
USING PESSIMISTIC ESTIMATES, THE MOTEL IS NOT ATTRACTIVE.
b MOST LIKELY ESTIMATES
PW = -$8,875,000 + ($2,500,000 – $175,000)(P|A 20%,15)
PW = -$8,875,000 + ($2,500,000 – $175,000)(4.67547)
PW = $1,995,467.75
USING MOST LIKELY ESTIMATES, THE MOTEL IS ATTRACTIVE.
c OPTIMISTIC ESTIMATES
PW = -$6,000,000 + ($3,500,000 – $150,000)(P|A 20%,15)
PW = -$6,000,000 + ($3,500,000 – $150,000)(4.67547)
PW = $9,662,824.50
USING OPTIMISTIC ESTIMATES, THE MOTEL IS ATTRACTIVE.
d EXPECTED VALUE ESTIMATES
INITIAL COST = ($10,500,000 + (4)($8,875,000) + $6,000,000) / 6 = $8,666,667
OPERATING COST = ($350,000 + (4)($175,000) + $150,000) / 6 = $200,000
REVENUE = ($1,500,000 + (4)($2,500,000) + $3,500,000) / 6 = $2,500,000
PW = -$8,666,667 + ($2,500,000 – $200,000)(P|A 20%,15)
PW = -$8,666,667+ ($2,500,000 – $200,000)(4.67547)
PW = $2,086,914.00
PROBLEM 11.35
a THERE WILL BE TWENTY-SEVEN AW VALUES. THE TABLE BELOW LISTS
THE PARAMETER COMBINATION FOR EACH AW
NUMBER INITIAL INVESTMENT
RECEIPTS
LIFE SALVAGE MARR
1$15,000.00 $1,750.00 8$250.00 15.00%
2$15,000.00 $1,750.00 8$500.00 15.00%
3$15,000.00 $1,750.00 8$750.00 15.00%
13 $15,000.00 $2,500.00 10 $250.00 15.00%
14 $15,000.00 $2,500.00 10 $500.00 15.00%
15 $15,000.00 $2,500.00 10 $750.00 15.00%
16 $15,000.00 $2,500.00 12 $250.00 15.00%
17 $15,000.00 $2,500.00 12 $500.00 15.00%
18 $15,000.00 $2,500.00 12 $750.00 15.00%
b THE SOLUTIONS BELOW USE EXCEL’S PMT FUNCTION TO CALCULATE THE AW FOR EACH
COMBINATION.
AW = RECEIPTS-PMT(MARR,LIFE,-INVESMENT,SALVAGE)
NUMBER INITIAL INVESTMENT
RECEIPTS
LIFE SALVAGE MARR AW
1$15,000.00 $1,750.00 8$250.00 15.00% -$1,574.54
2$15,000.00 $1,750.00 8$500.00 15.00% -$1,556.33
12 $15,000.00 $2,500.00 8$750.00 15.00% -$788.11
13 $15,000.00 $2,500.00 10 $250.00 15.00% -$476.47
14 $15,000.00 $2,500.00 10 $500.00 15.00% -$464.15
15 $15,000.00 $2,500.00 10 $750.00 15.00% -$451.84
16 $15,000.00 $2,500.00 12 $250.00 15.00% -$258.59
17 $15,000.00 $2,500.00 12 $500.00 15.00% -$249.97
23 $15,000.00 $3,250.00 10 $500.00 15.00% $285.85
24 $15,000.00 $3,250.00 10 $750.00 15.00% $298.16
25 $15,000.00 $3,250.00 12 $250.00 15.00% $491.41
26 $15,000.00 $3,250.00 12 $500.00 15.00% $500.03
27 $15,000.00 $3,250.00 12 $750.00 15.00% $508.65
PROBLEM 11.36
THERE WILL BE TWENTY-SEVEN PW VALUES. THE TABLE BELOW LISTS
THE PARAMETER COMBINATION FOR EACH AW
NUMBER INITIAL COST OPERATING REVENUE
1 -$10,500,000.00 -$350,000.00 $1,500,000.00
2 -$10,500,000.00 -$350,000.00 $2,500,000.00
3 -$10,500,000.00 -$350,000.00 $3,500,000.00
4 -$10,500,000.00 -$175,000.00 $1,500,000.00
5 -$10,500,000.00 -$175,000.00 $2,500,000.00
6 -$10,500,000.00 -$175,000.00 $3,500,000.00
7 -$10,500,000.00 -$150,000.00 $1,500,000.00
8 -$10,500,000.00 -$150,000.00 $2,500,000.00
18 -$8,875,000.00 -$150,000.00 $3,500,000.00
19 -$6,000,000.00 -$350,000.00 $1,500,000.00
20 -$6,000,000.00 -$350,000.00 $2,500,000.00
21 -$6,000,000.00 -$350,000.00 $3,500,000.00
22 -$6,000,000.00 -$175,000.00 $1,500,000.00
23 -$6,000,000.00 -$175,000.00 $2,500,000.00
NUMBER INITIAL COST OPERATING REVENUE PW
1 -$10,500,000.00 -$350,000.00 $1,500,000.00 -$5,123,209.50
2 -$10,500,000.00 -$350,000.00 $2,500,000.00 -$447,739.50
3 -$10,500,000.00 -$350,000.00 $3,500,000.00 $4,227,730.50
4 -$10,500,000.00 -$175,000.00 $1,500,000.00 -$4,305,002.25
5 -$10,500,000.00 -$175,000.00 $2,500,000.00 $370,467.75
6 -$10,500,000.00 -$175,000.00 $3,500,000.00 $5,045,937.75
7 -$10,500,000.00 -$150,000.00 $1,500,000.00 -$4,188,115.50
14 -$8,875,000.00 -$175,000.00 $2,500,000.00 $1,995,467.75
15 -$8,875,000.00 -$175,000.00 $3,500,000.00 $6,670,937.75
16 -$8,875,000.00 -$150,000.00 $1,500,000.00 -$2,563,115.50
17 -$8,875,000.00 -$150,000.00 $2,500,000.00 $2,112,354.50
18 -$8,875,000.00 -$150,000.00 $3,500,000.00 $6,787,824.50
19 -$6,000,000.00 -$350,000.00 $1,500,000.00 -$623,209.50
20 -$6,000,000.00 -$350,000.00 $2,500,000.00 $4,052,260.50
21 -$6,000,000.00 -$350,000.00 $3,500,000.00 $8,727,730.50
22 -$6,000,000.00 -$175,000.00 $1,500,000.00 $194,997.75
23 -$6,000,000.00 -$175,000.00 $2,500,000.00 $4,870,467.75
24 -$6,000,000.00 -$175,000.00 $3,500,000.00 $9,545,937.75
25 -$6,000,000.00 -$150,000.00 $1,500,000.00 $311,884.50
26 -$6,000,000.00 -$150,000.00 $2,500,000.00 $4,987,354.50
27 -$6,000,000.00 -$150,000.00 $3,500,000.00 $9,662,824.50
PROBLEM 11.37
INITIAL INVESTME
$15,000
INVESTMENT TERM
3
INTEREST
RATE
PROB
4% 0.2
6% 0.4
8% 0.4
COMB 1 2 3 PROB FW PROD
34% 4% 8% 0.016 $17,521.92 $280.35
44% 6% 4% 0.016 $17,197.44 $275.16
64% 6% 8% 0.032 $17,858.88 $571.48
74% 8% 4% 0.016 $17,521.92 $280.35
84% 8% 6% 0.032 $17,858.88 $571.48
94% 8% 8% 0.032 $18,195.84 $582.27
10 6% 4% 4% 0.016 $17,197.44 $275.16
11 6% 4% 6% 0.032 $17,528.16 $560.90
22 8% 6% 4% 0.032 $17,858.88 $571.48
23 8% 6% 6% 0.064 $18,202.32 $1,164.95
24 8% 6% 8% 0.064 $18,545.76 $1,186.93
25 8% 8% 4% 0.032 $18,195.84 $582.27
26 8% 8% 6% 0.064 $18,545.76 $1,186.93
$17,859 19.2%
$17,865 6.4%
$18,196 9.6%
$18,202 19.2%
$18,546 19.2%
$18,896 6.4%
PROBLEM 11.38
INVESTMENT = $12,000 N p(N)
ANNUAL RECEIPTS = $4,500 10.10
MARR = 15% 20.15
30.20
PW=-12,000+4,500(P|A 15%,N) > 0 4 0.25
50.15
(P|A 15%,N) > 12,000/4,500 = 2.66666667 60.10
70.05
THEREFORE, N > 4
THE PROBABILITY THE INVESTMENT IS PROFITABLE IS THE PROBABILITY N > 4, OR 0.55.
PROBLEM 11.39
INVESTMENT = $12,000 N p(N) MARR p(MARR)
ANNUAL RECEIPTS = $4,500 1 0.10 10% 0.2
MARR = 15% 2 0.15 12% 0.6
3 0.20 15% 0.2
PW=-12,000+4,500(P|A MARR%,N) > 0 4 0.25
5 0.15
(P|A MARR%,N) > 12,000/4,500 = 2.66666667 6 0.10
7 0.05
THEREFORE, THE COMBINATION OF N AND MARR MUST > 2 2/3
THE PROBABILITY THE INVESTMENT IS PROFITABLE GIVEN MARR = 10% IS 0.55.
THE PROBABILITY THE INVESTMENT IS PROFITABLE GIVEN MARR = 12% IS 0.55.
THE PROBABILITY THE INVESTMENT IS PROFITABLE GIVEN MARR = 15% IS 0.55.
THEREFORE, THE PROBABILITY THE INVESTMENT IS PROFITABLE IS 0.55(0.2) + 0.55(0.6) + 0.55(0.2) = 0.55.
MARR = 10%
EOY CF Cum PW Profitable? Probability
0 -$12,000 -12,000
1 $4,500 -$7,909 No 0.10
2 $4,500 -$4,190 No 0.15
3 $4,500 -$809 No 0.20
4 $4,500 $2,264 Yes 0.25
5 $4,500 $5,059 Yes 0.15
6 $4,500 $7,599 Yes 0.10
7 $4,500 $9,908 Yes 0.05
Probability of being profitable = 0.25 + 0.15 + 0.10 + 0.05, or 0.55
0 -$12,000 -12,000
1 $4,500 -$7,982 No 0.10
4 $4,500 $1,668 Yes 0.25
5 $4,500 $4,221 Yes 0.15
6 $4,500 $6,501 Yes 0.10
7 $4,500 $8,537 Yes 0.05
Probability of being profitable = 0.25 + 0.15 + 0.10 + 0.05, or 0.55
PROBLEM 11.40
INVESTMENT = $12,000 N p(N) R p(R)
ANNUAL RECEIPTS = $4,500 1 0.10 $5,000 0.2
MARR = 15% 2 0.15 $4,500 0.6
3 0.20 $4,000 0.2
4 0.25
5 0.15
6 0.10
7 0.05
MARR = 15%
EOY CF Cum PW Profitable? Probability
0 -$12,000 -$12,000
1 $5,000 -$7,652 No 0.10
2 $5,000 -$3,871 No 0.15
3 $5,000 -$584 No 0.20
4 $5,000 $2,275 Yes 0.25
5 $5,000 $4,761 Yes 0.15
6 $5,000 $6,922 Yes 0.10
7 $5,000 $8,802 Yes 0.05
Probability of being profitable = 0.25 + 0.15 + 0.10 + 0.05, or 0.55
MARR = 15%
EOY CF Cum PW Profitable? Probability
0 -$12,000 -$12,000
1 $4,500 -$8,087 No 0.10
2 $4,500 -$4,684 No 0.15
3 $4,500 -$1,725 No 0.20
7 $4,500 $6,722 Yes 0.05
EOY CF Cum PW Profitable? Probability
0 -$12,000 -$12,000
1 $4,000 -$8,522 No 0.10
2 $4,000 -$5,497 No 0.15
3 $4,000 -$2,867 No 0.20
4 $4,000 -$580 No 0.25
Probability of being profitable = 0.15 + 0.10 + 0.05, or 0.30
PROBLEM 11.41
5-51. The combinations not yet considered are shown below.
MARR = 10%
EOY CF Cum PW Profitable? Probability
0 -$12,000 -$12,000
1$4,000 -$8,364 No 0.10
2$4,000 -$5,058 No 0.15
3$4,000 -$2,053 No 0.20
4$4,000 $679 Yes 0.25
7$4,000 $7,474 Yes 0.05
Probability of being profitable = 0.25 + 0.15 + 0.10 + 0.05, or 0.55
EOY CF Cum PW Profitable? Probability
0 -$12,000 -$12,000
1$4,000 -$8,429 No 0.10
2$4,000 -$5,240 No 0.15
3$4,000 -$2,393 No 0.20
4$4,000 $149 Yes 0.25
7$4,000 $6,255 Yes 0.05
Probability of being profitable = 0.25 + 0.15 + 0.10 + 0.05, or 0.55
1$5,000 -$7,455 No 0.10
2$5,000 -$3,322 No 0.15
3$5,000 $434 Yes 0.20
4$5,000 $3,849 Yes 0.25
6$5,000 $9,776 Yes 0.10
7$5,000 $12,342 Yes 0.05
Probability of being profitable = 0.20 + 0.25 + 0.15 + 0.10 + 0.05, or 0.75
MARR = 12%
1$5,000 -$7,536 No 0.10
2$5,000 -$3,550 No 0.15
3$5,000 $9 Yes 0.20
4$5,000 $3,187 Yes 0.25
12% $4,000 0.12 0.55 0.0660
12% $4,500 0.36 0.55 0.1980
12% $5,000 0.12 0.75 0.0900
15% $4,000 0.04 0.30 0.0120
15% $4,500 0.12 0.55 0.0660
15% $5,000 0.04 0.55 0.0220
Sum = 0.5720
The probability of the investment being profitable is 0.572
PROBLEM 11.42
Since all calculations are for PW, for an investment of $9,000 check on all PW values greater than
or equal to -$3,000 for an investment of $11,000, check on all PW values greater or equal to -$1,000.
The results are given below.
Investment = $9,000
MARR Receipts Probability Pr(Profitable) Product
10% $4,000 0.04 0.75 0.0300
10% $4,500 0.12 0.75 0.0900
10% $5,000 0.04 0.75 0.0300
12% $4,000 0.12 0.75 0.0900
12% $4,500 0.36 0.75 0.2700
12% $5,000 0.12 0.75 0.0900
15% $4,000 0.04 0.75 0.0300
15% $4,500 0.12 0.75 0.0900
15% $5,000 0.04 0.75 0.0300
Sum = 0.7500
Investment = $11,000
MARR Receipts Probability Pr(Profitable) Product
10% $4,000 0.04 0.55 0.0220
10% $4,500 0.12 0.75 0.0900
10% $5,000 0.04 0.75 0.0300
12% $4,000 0.12 0.55 0.0660
12% $4,500 0.36 0.55 0.1980
12% $5,000 0.12 0.75 0.0900
15% $4,000 0.04 0.55 0.0220
15% $4,500 0.12 0.55 0.0660
15% $5,000 0.04 0.75 0.0300
Sum = 0.6140
Since it is equally likely to be $9,000 or $11,000, the probability equals (0.750 + 0.614)/2, or 0.682
PROBLEM 11.43
Receipt PW=R-11000 P(PW)
$20,000 $9,000 0.16%
$19,500 $8,500 1.92%
$19,000 $8,000 9.28%
$18,500 $7,500 23.04%
$18,000 $7,000 31.20%
$17,500 $6,500 23.04%
$17,000 $6,000 9.28%
$16,500 $5,500 1.92%
$16,000 $5,000 0.16%