Question

Suppose Appin coal mine values their coal extraction benefits as: Amount $18,000(YEAR 1) $23,000 (YEAR 2) $27,000 (YEAR 3) $30,000 (YEAR 4) $32,000 (YEAR 5) a. Find the net present value of their extraction benefit when the discount rate is 12%. b. Now suppose the discount rate changes to 2%, find the new net present value and explain what Appin coal mine will do as a result of this change and why.

Answer #1

(a)

NPV of benefit ($) = 18,000 x P/F(12%, 1) + 23,000 x P/F(12%, 2) + 27,000 x P/F(12%, 3) + 30,000 x P/F(12%, 4) + 32,000 x P/F(12%, 5)

= 18,000 x 0.8929** + 23,000 x 0.7972** + 27,000 x 0.7118** + 30,000 x 0.6355** + 32,000 x 0.5674**

= 16,072.2 + 18,335.6 + 19,218.6 + 19,065 + 18,156.8

= 90,848.2

(b)

NPV of benefit ($) = 18,000 x P/F(2%, 1) + 23,000 x P/F(2%, 2) + 27,000 x P/F(2%, 3) + 30,000 x P/F(2%, 4) + 32,000 x P/F(2%, 5)

= 18,000 x 0.9804** + 23,000 x 0.9612** + 27,000 x 0.9423** + 30,000 x 0.9238** + 32,000 x 0.9057**

= 17,647.2 + 22,107.6 + 25,442.1 + 27,714 + 28,982.4

= 121,893.3

Since NPV of benefit will be higher when discount rate is lowered, the coal mine will extract coal as long as NPV of costs of extraction is no more than $121,893.30.

**From P/F factor table

Suppose Appin coal mine values their coal extraction benefits
as:
Amount $18,000(YEAR 1)
$23,000(YEAR 2)
$27,000(YEAR 3)
$30,000 (YEAR 4)
$32,000 (YEAR 5)
a. Find the net present value of their extraction benefit when
the discount rate is 12%. b. Now suppose the discount rate changes
to 2%, find the new net present value and explain what Appin coal
mine will do as a result of this change and why.

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1
2
3
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Discount rate
12%
Project 1
Year 1
Year 2
Year 3
Year 4
Year 5
TOTAL
Costs
220,000
35,000
35,000
25,000
20,000
?
Discount factor
?
?
?
?
?
Discounted costs
?
?
?
?
?
?
Benefits
0
80,000
80,000
65,000
60,000
?
Discount factor
?
?
?
?
?
?
Discount benefits
?
?
?
?
?
?
Discounted benefits – Discounted costs (NPV)
?
?
?
?
?
?
ROI =
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Year
Costs
Benefits
0
$10,000
0
1
$1,000
$5,000
2
$1,000
$5,000
3
$2,000
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Rate
Net Benefit Year 1
Net Benefit
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New Benefit
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50,000
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100.000
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