Question

Exercise 24-2

Doug’s Custom Construction Company is considering three new projects, each requiring an equipment investment of $25,080. Each project will last for 3 years and produce the following net annual cash flows.

Year AA BB CC
1 $7,980 $11,400 $14,820
2 10,260 11,400 13,680
3 13,680 11,400 12,540
Total $31,920 $34,200 $41,040

The equipment’s salvage value is zero, and Doug uses straight-line depreciation. Doug will not accept any project with a cash payback period over 2 years. Doug’s required rate of return is 12%. Click here to view PV table.

(a)

Compute each project’s payback period. (Round answers to 2 decimal places, e.g. 15.25.)

AA
years
BB
years
CC
years

Which is the most desirable project?

The most desirable project based on payback period is

Project AA
Project BB
Project CC

Which is the least desirable project?

The least desirable project based on payback period is

Project BB
Project AA
Project CC

(b)

Compute the net present value of each project. (Enter negative amounts using either a negative sign preceding the number e.g. -45 or parentheses e.g. (45). Round final answers to the nearest whole dollar, e.g. 5,275. For calculation purposes, use 5 decimal places as displayed in the factor table provided.)

AA
BB
CC

Which is the most desirable project based on net present value?

The most desirable project based on net present value is

Project AA
Project BB
Project CC
.

Which is the least desirable project based on net present value?

The least desirable project based on net present value is

Project CC
Project BB
Project AA
.

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Answer 1

a)

AA:

Cumulative cash flow for year 0 = -25,080

Cumulative cash flow for year 1 = -25,080 + 7,980 = -17,100

Cumulative cash flow for year 2 = -17,100 + 10,260 = -6,840

Cumulative cash flow for year 3 = -6,840 + 13,680 = 6,840

6840 / 13,680 = 0.5

Payback period = 2 + 0.5 = 2.5 years

BB:

Cumulative cash flow for year 0 = -25,080

Cumulative cash flow for year 1 = -25,080 + 11,400 = -13,680

Cumulative cash flow for year 2 = -13,680 + 11,400 = -2,280

Cumulative cash flow for year 3 =  -2,280 + 11,400 = 9,120

2280 / 11400 = 0.2

Payback period for BB = 2.2 years

CC:

Cumulative cash flow for year 0 = -25,080

Cumulative cash flow for year 1 = -25,080 + 14,820= -10,260

Cumulative cash flow for year 2 = -10,260 + 13,680 = 3,420

10,260 / 13,680 = 0.75

Payback period for CC = 1.75

Project CC is most desirable as it has the lowest payback period.

Project AA is least desirable as it has the highest payback period.

b)

AA:

NPV = Present value of cash inflows - present value of cash outflows

Present value of cash inflows = 7,980 / ( 1 + 0.12) + 10,260 / ( 1 + 0.12)² + 13,680 / ( 1 + 0.12)³

Present value of cash inflows = 7,125 + 8,179.21 + 9,737.15

Present value of cash inflows = 25,041.36

NPV = 25,041.36 - 25,080 = -39

BB:

Present value of cash inflows = 11,400 / ( 1 + 0.12) + 11,400 / ( 1 + 0.12)² + 11,400 / ( 1 + 0.12)³

Present value of cash inflows = 10,178.57 + 9,088.01 + 8,114.29

Present value of cash inflows = 27,380.87

NPV = 27,380.87 - 25,080 = $2,301

CC:

Present value of cash inflows = 14,820 / ( 1 + 0.12) + 13,680 / ( 1 + 0.12)² + 12,540 / ( 1 + 0.12)³

Present value of cash inflows = 13,232.14 + 10,905.61 + 8,925.72

Present value of cash inflows = 33,063.47

NPV = 33,063.47 - 25,080 = $7,984

Project CC is the most desirable as it has the highest NPV

Project AA is least desirable as it has a negative NPV