TM 661Chapter 5Solutions 1

Chapter 51

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 NCF-1 SV-1 NCF-2 SV-20 -60,000 60,000 -100,000 100,0001 35,000 30,000 30,000 60,0002 35,000 10,000 30,000 40,0003 35,000 0 30,000 25,0004 30,000 15,0005 30,000 10,000

a. Least Common Multiple b. Shortest Lifet NCF-1 NCF-2 t NCF-1 NCF-20 -60,000 -100,000 0 -60,000 -100,0001 35,000 30,000 1 35,000 30,0002 35,000 30,000 2 35,000 30,0003 -25,000 30,000 3 35,000 55,0004 35,000 30,0005 35,000 -60,000 c. Longest Life6 -25,000 30,000 t NCF-1 NCF-27 35,000 30,000 0 -60,000 -100,0008 35,000 30,000 1 35,000 30,0009 -25,000 30,000 2 35,000 30,00010 35,000 -60,000 3 -25,000 30,00011 35,000 30,000 4 35,000 30,00012 -25,000 30,000 5 45,000 40,00013 35,000 30,00014 35,000 30,000 d. 4-Year15 35,000 40,000 t NCF-1 NCF-2

0 -60,000 -100,000d. 2-Year 1 35,000 30,000

t NCF-1 NCF-2 2 35,000 30,0000 -60,000 -100,000 3 -25,000 30,0001 35,000 30,000 4 65,000 45,0002 45,000 70,000

Soln:

Chapter 52


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 Acceptable Reason

A, B, C, D no exceeds budget

A, B, C no exceeds budget

A, B, D no exceeds budget

A, C, D yes

A, C no C contingent on D

A, B no exceeds budget

A, D yes

B, C, D yes

B, C no C is contingent on D

B, D yes

C, D no D is contingent on A or B

A no A is contingent on C or D

B yes

C no C is contingent on D

D no D is contingent on A or B

Chapter 53


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.

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

NPW = -12,000 + 3,325(3.6048)

= -14

Choose A

t NCF-A NCF-B0 -30,000 -42,0001 9,300 12,6252 9,300 12,6253 9,300 12,6254 9,300 12,6255 9,300 12,625

t NCF-A NCF-B NCF (B-A)0 -30,000 -42,000 -12,0001 9,300 12,625 3,3252 9,300 12,625 3,3253 9,300 12,625 3,3254 9,300 12,625 3,3255 9,300 12,625 3,325

Chapter 54


5-23) (Cont)

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

t NCF-A NCF-B0 -30,000 -42,0001 9,300 12,6252 9,300 12,6253 9,300 12,6254 9,300 12,6255 9,300 12,625

Chapter 55


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 56


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 Cost Refurbish Revenue NCF0 -5,000,000 -1,875,000 -6,875,0001 1,129,219 1,129,2192 1,129,219 1,129,2193 1,129,219 1,129,2194 1,129,219 1,129,2195 -1,875,000 1,129,219 -745,7816 1,129,219 1,129,2197 1,129,219 1,129,2198 1,129,219 1,129,2199 1,129,219 1,129,21910 -1,875,000 1,129,219 -745,78111 1,129,219 1,129,21912 1,129,219 1,129,21913 1,129,219 1,129,21914 1,129,219 1,129,21915 1,000,000 1,129,219 2,129,219

NPV = 66,198

TM 661Chapter 5Solutions 1

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