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371 ActSc 7.7 and 7.8 Practice Problems
1. What is the profitability index for the following cash flows, if the relevant discount rate is 15%?
Year 0
Year 1
Year 2
Year 3
$-10,000
$6,500
$4,000
$2,500
A)
1
B)
1.03
C)
1.3
D)
1.05
E)
1.11
Solution: PV of cash flows after the initial investment is: 10,320.54. The PI is this value divided
by the absolute value of the original investment This is 10320.54/10000=1.03
2. The Ziggy Trim and Cut Company can purchase equipment on sale for $4,300. The asset has a
three-year life, will produce a cashflow of $1,200 in the first and second year, and $3,000 in the
third year. The interest rate is 12%. Calculate the project's discounted payback and Profitability
Index assuming end of year cash flows. Should the project be taken?
Solution:
CF0=-4300
CF1=1200
CF2=1200
CF3=3000
Step 1: Calculate the NPV using the calculator = -136.60
Because NPV is less than zero, discounted payback cannot be calculated.
Step 2: to calculate the PI, first calculate the NPV without including the initial cashflow (i.e. 4300). This is: 4163.40. Then, divide this value by the absolute value of the initial investment
(i.e. 4300). PI=0.97. Because PI is less than 1, we should reject the project.
Therefore, under both methods we should reject the project. Both methods indicate that your
cost of capital is not being covered.
3. The Walker Landscaping Company can purchase a piece of equipment for $3,600. The asset has
a two-year life, will produce a cashflow of $600 in the first year and $4200 in the second year.
The interest rate is 15%. Calculate the project's discounted payback and Profitability Index
assuming steady cashflows. Should the project be taken? If the accounting rate of return was
positive, how would this affect your decision?
Answer:
CF0=-3600
CF1=600
CF2=4200
Step 1: Calculate the NPV: 97.54
NPV is positive, so we can calculate the projects payback.
600
600/1.15
521.74
4200
4200/1.15^2
3175.80
Given discounted the initial investment was -3600: after 1 year, payback is 3078.26. The proportion of the
second year cash inflow that goes towards payback is: 3078.26/3175.80=0.97. Therefore, the
projects discounted payback is 1.97 years.
Step 2: Calculate PI using PV of Cashflows without initial investment: 3697.54. Divide this value
by the absolute value of the original investment: 3697.54/3600=1.03. Since it is greater than 1,
we should accept this project.
Both measures indicate acceptance. A positive accounting rate of return would be consistent
with this decision. Reliance on AAR should not be the key, as DPP and PI indicate earning a rate
greater than cost of capital.
4. An investment project has the cashflow stream of -250, 75, 125, 100, and 50. The cost of capital is
12%. What is the discount payback period?
-250
75
75/1.12
66.96
125
125/1.12^2
99.65
100
100/1.12^3
71.18
50
50/1.12^4
31.78
The sum of the PVs first three cash inflows is 237.79. Therefore, 250-237.79=12.21 of the
fourth cash flow needs to be applied. This is the ratio: 12.21/31.78=0.38. Therefore, the answer
is 3.38 years.
5. Halloween Co. wish to buy a new sewing machine to being costume manufacturing for next year
in order to increase productivity. The initial net cash outlay is 15,600. The cashflows associated
with the acquisition of the new sewing machine are as follows:
Year Cash Flow from Operation
1
6,610
2
5,650
3
4,690
4
4,630
5
3,670
Assuming the required rate of return is 10%
4. What is the Net Present Value for this project? 4,043.31
Since this value is positive, you
should accept this investment.
5. What is the Profitability Index? The PV of cash flows after the initial investment is: 19,643.31.
Then, divide this by the initial investment: 1.26. Since this value is greater than 1, you should
accept the project.

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