TM 661
Chapter 5
Solutions 1
5.4) Consider the net cash flows and salvage values for each of alternatives 1 and 2 having
lives 3 and 5 years respectively.
t
0
1
2
3
4
5
NCF-1
-60,000
35,000
35,000
35,000
SV-1
60,000
30,000
10,000
0
NCF-2
-100,000
30,000
30,000
30,000
30,000
30,000
SV-2
100,000
60,000
40,000
25,000
15,000
10,000
Soln:
a. Least Common Multiple
t
NCF-1
NCF-2
0
-60,000
-100,000
1
35,000
30,000
2
35,000
30,000
3
-25,000
30,000
4
35,000
30,000
5
35,000
-60,000
6
-25,000
30,000
7
35,000
30,000
8
35,000
30,000
9
-25,000
30,000
10
35,000
-60,000
11
35,000
30,000
12
-25,000
30,000
13
35,000
30,000
14
35,000
30,000
15
35,000
40,000
d. 2-Year
t
0
1
2
NCF-1
-60,000
35,000
45,000
NCF-2
-100,000
30,000
70,000
b. Shortest Life
t
NCF-1
0
-60,000
1
35,000
2
35,000
3
35,000
NCF-2
-100,000
30,000
30,000
55,000
c. Longest Life
t
NCF-1
0
-60,000
1
35,000
2
35,000
3
-25,000
4
35,000
5
45,000
NCF-2
-100,000
30,000
30,000
30,000
30,000
40,000
d. 4-Year
t
0
1
2
3
4
NCF-2
-100,000
30,000
30,000
30,000
45,000
Chapter 5
1
NCF-1
-60,000
35,000
35,000
-25,000
65,000
TM 661
Chapter 5
Solutions 2
5-10) A firm has available 4 proposals A, B, C, D. Proposal is contingent on acceptance of
either proposal C or proposal D. In addition, proposal C is contingent on proposal D,
while proposal D s contingent on either proposal A or proposal B. The firm has a
budget limitation of $500,000. The cash flows are as follows:
Initial Costs
A = 250,000
B = 350,000
C = 50,000
D = 38,000
Soln: Note we did not need to include the entire cash flow since only the initial costs
affect the initial budget of $500,000.
Alternative
A, B, C, D
A, B, C
A, B, D
A, C, D
A, C
A, B
A, D
B, C, D
B, C
B, D
C, D
A
B
C
D
Acceptable
no
no
no
yes
no
no
yes
yes
no
yes
no
no
yes
no
no
Reason
exceeds budget
exceeds budget
exceeds budget
C contingent on D
exceeds budget
C is contingent on D
D is contingent on A or B
A is contingent on C or D
C is contingent on D
D is contingent on A or B
Chapter 5
2
TM 661
Chapter 5
Solutions 3
5-23) Two mutually exclusive proposals, each with a life of 5 years, are under consideration.
MARR is 12%. Each proposal has the following cash flow profile.
t
0
1
2
3
4
5
NCF-A
-30,000
9,300
9,300
9,300
9,300
9,300
NCF-B
-42,000
12,625
12,625
12,625
12,625
12,625
Soln:
a. Net Present Worth
A
NPW = -30,000 + 9,300 (P/A, 12, 5)
= -30,000 + 9,300 (3.6048)
= $ 3,525
B
NPW = -42,000 + 12,625 (3.6048)
= $3,511
Choose A
b. Incremental Method
t
0
1
2
3
4
5
NCF-A
-30,000
9,300
9,300
9,300
9,300
9,300
NCF-B
-42,000
12,625
12,625
12,625
12,625
12,625
NCF (B-A)
-12,000
3,325
3,325
3,325
3,325
3,325
Chapter 5
3
NPW = -12,000 + 3,325(3.6048)
= -14
Choose A
TM 661
Chapter 5
5-23) (Cont)
t
0
1
2
3
4
5
NCF-A
-30,000
9,300
9,300
9,300
9,300
9,300
NCF-B
-42,000
12,625
12,625
12,625
12,625
12,625
Soln:
c. Equivalent Annual Worth
A
EUAW = -30,000 (A/P, 12, 5) + 9,300
= -30,000 (0.2774) + 9,300
= $ 978
B
EUAW = -42,000 (0.2774) + 12,625
= $ 974
Choose A
Chapter 5
4
Solutions 3
TM 661
Chapter 5
Solutions 5
5-36) An aluminum extrusion plant manufactures a particular product at a variable cost of
$0.04 per unit, including material costs. The fixed costs associated with
manufacturing the product equal $30,000 per year. Determine the break-even value
for annual sales if the selling price per unit is a) $0.40, b) $0.30, and c) $0.20.
Soln:
Let S = selling price
Profit = SX - 30,000 - .04X
= (S - .04)X -30,000
Since profit = 0 at breakeven
X = 30,000 / (S - .04)
a.
X = 30,000 / (.4 - .04)
= 83,333
b.
X = 30,000 / (.3 - .04)
= 115,384
c.
X = 30,000 / (.2 - .04)
= 187,500
Chapter 5
5
TM 661
Chapter 5
Solutions 6
5-37) Owners of a nationwide motel chain are considering locating a new motel in Snyder,
Arkansas. The complete cost of building a 150-unit motel is $5 million. The firm
estimates that the furnishings will cost $1,875,000 initially and every 5 years
thereafter. Annual operating and maintenance cost for the facility is estimated to be
$125,000. The average rate for a unit is anticipated to be $55 per day. A 15 year
planning horizon is used by the firm in evaluating new ventures of this type. Salvage
value is estimated at $1 million. Determine the breakeven if the daily occupancy is
estimated to be 10%.
Soln: I set up a spreadsheet showing revenues and costs. Revenues were based on an
occupancy rate in cell C3. Net present worth is computed at 10%. I then just altered
cell C3 until I got a NPV relatively close to 0. I compute an occupancy rate of 37.5%.
Revenue = 150 units x % occupancy x $55 / unit x 365 days / yr.
Occupancy rate =
0.375
MARR =
0.1
t
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Cost
Refurbish
-5,000,000 -1,875,000
-1,875,000
-1,875,000
1,000,000
Revenue
1,129,219
1,129,219
1,129,219
1,129,219
1,129,219
1,129,219
1,129,219
1,129,219
1,129,219
1,129,219
1,129,219
1,129,219
1,129,219
1,129,219
1,129,219
NPV =
NCF
-6,875,000
1,129,219
1,129,219
1,129,219
1,129,219
-745,781
1,129,219
1,129,219
1,129,219
1,129,219
-745,781
1,129,219
1,129,219
1,129,219
1,129,219
2,129,219
66,198
Chapter 5
6