iven 2 (two-period) Jobs with the following cost and flows. Job A: will cost $50
ID: 2424345 • Letter: I
Question
iven 2 (two-period) Jobs with the following cost and flows.
Job A: will cost $50,000 in year 1 and will yield $84,000 in year 2
Job B: will cost $80,000 in year 1 and will yield $120,000 in year 2
Dwight and James are looking at these 2 jobs and will make choices. Job B looks more attractive by using simple arithmetic in a static world; but since these will occur in different periods, we know that the best way to evaluate each one is by getting the net present value of each job using each individual's discount rates. James is a patient and hard-working individual while Dwight is a happy-go-lucky come what may surfer type.
a. Given 2 discount rates of 30% and 8% and knowing Dwight and James' personalities, assign the discount rate appropriate to each individual. (2 points)
b. Solve for the NPVs of each Job for each individual. (Show your solution). (6 points)
c. Based on the NPVs, which Job will Dwight pick and which Job will James pick? (2 points)
d. Solve for the IRR (show your solution). What does this number (IRR) mean for Dwight or James when they are trying to choose between Jobs A or B? (5 points)
Explanation / Answer
a.
Assign the discount rate appropriate to each individual:
Discount rates must be assigning to each individual based on their personalities. As Mr. J is a patient and hard working 30% discount rate is highly suitable to him because he has more risk to work on job as he is a patient.
In contrast, Mr. D is happy man and no issues either and therefore less risky discount factor 8% is exactly suitable to him.
Solve for the NPVs of each Job for each individual:
Assumption: It is assumed that cash flows are beginning at the year ending.
Calculating NPV for Mr. D is as follows:
Year
Cash flows
from Job A
Discount
factor 8%
Discounted
cash flows
Cash flows
from Job B
Discount
factor 8%
Discounted
cash flows
1
$ (50,000)
0.9259
$ (46,295.00)
$(80,000)
0.9259
$ (74,072)
2
$ 84,000
0.8573
$ 72,013.20
$120,000
0.8573
$ 102,876
NPV
$ 25,718.20
NPV
$ 28,804
Calculating NPV for Mr. J is as follows:
Year
Cash flows
from Job A
Discount
factor 30%
Discounted
cash flows
Cash flows
from Job B
Discount
factor 30%
Discounted
cash flows
1
$ (50,000)
0.7692
$ (38,460.00)
$ (80,000)
0.7692
$ (61,536)
2
$ 84,000
0.5917
$ 49,702.80
$120,000
0.5917
$ 71,004
NPV
$ 11,242.80
NPV
$ 9,468
c.
Based on the above calculations, Mr. J would select Job A because it has higher NPV compare to Job B with 30% discount rate. In contrast, Mr. D would opt for Job B because it has higher NPV compare to Job A with 8% discount rate.
d.
Calculation of IRR:
IRR (Internal Rate of Return) for Mr. J for Job A based on his selection
Year
Cash flows
from Job A
Discount
factor 70%
Discounted
cash flows
1
$ (50,000)
0.5882
$ (29,410.00)
2
$ 84,000
0.346
$ 29,064.00
NPV
$ (346.00)
IRR for Job A = 30% + ($49,702.80 - $ 38,460) × 40%
($49,702.80 - $29,410)
=30% + (0.55403) × 40%
= 52.16%
IRR (Internal Rate of Return) for Mr. D for Job B based on his selection
Year
Cash flows
from Job B
Discount
factor 50%
Discounted
cash flows
1
$(80,000)
0.6667
$ (53,336)
2
$120,000
0.4444
$ 53,328
NPV
$ (8)
IRR for Job B = 8% + ($102,876 - $ 74,072) × 42%
($102,876 - $53,336)
=8% + (0.58143) × 42%
= 32.42%
IRR is the rate at which NPV would be '0' which means at that rate it is indifferent to accept or reject the Job.
Year
Cash flows
from Job A
Discount
factor 8%
Discounted
cash flows
Cash flows
from Job B
Discount
factor 8%
Discounted
cash flows
1
$ (50,000)
0.9259
$ (46,295.00)
$(80,000)
0.9259
$ (74,072)
2
$ 84,000
0.8573
$ 72,013.20
$120,000
0.8573
$ 102,876
NPV
$ 25,718.20
NPV
$ 28,804
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