Answer:
a) scenario A NPV positive 28.68, scenario B NPV Negative 16.16, scenario C NPV positive 664.92, scenario D NPV positive 889.72 (b) The scenario with the highest positive NPV is the most profitable (c) The scenario B with the interest rate of 17% has Negative NPV of 16.16 produces less investment (d) The scenario C with the highest interest rate of 20% has the positive NPV of 664.92 he scenario D with the highest interest rate of 20% has the highest positive NPV of 889.72, produces more investment
Explanation:
Calculation of Discount Factor
Effective rate for scenario C and D
Using the formula (1 + m/1 + i)∧n - 1 Where i = rate of inflation, m = cost of capital, n = numbers of years
For C since interest rate = 20% = 20÷100 = 0.2, since rate of inflation = 2% = 2÷100 = 0.02
(1 + 0.2/1 + 0.02)∧n - 1
= 1.2 /1.02 -1
=1.1764 -1
=0.1764 ×100 = 17.64%
Discount Factor for C using the formula ( 1 + r)∧-n -1/ r since n = 3 ,r = 0.1764
= ( 1 + 0.2)∧-3 - 1/ 0.1764
= (1.2)∧-3 -1/0.1764
=0.5787 -1
= 0.4213÷ 0.1764
= 2.3883
For D Effective rate
( 1 + 0.2)∧n - 1/(1 + 0.05)
= 1.2/1.05 -1
=1.1428 -1
= 0.1428 × 100 = 14.28%
DF for D
= (1 + 0.2)∧-3 -1 / 0.1428
=0.5787 -1 = 0.4213
=0.4213÷0.1428
=2.9503
DF for year 1 and 2 for C and D
Using the formula ( 1 + r) ∧-n
( 1 + 0.2)∧-1 = ( 1.2)∧-1 = 0.83
(1 + 0.2)∧-2 = (1.2)∧-2 = 0.694
DF for scenario A For year 1 -3 using ( 1+ r)∧-n
= ( 1 + 0.14)∧-1 = (1.14)∧-1 = 0.8772
= (1+0.14)∧-2 = (1.14)∧-2 = 0.7695
=(1+0.14)∧-3 = (1.14)∧-3 = 0.6750
DF for scenario B using the same formula
=( 1 + 0.17)∧-1 =(1.17)∧-1 = 0.8547
=(1+0.17)∧-2 = (1.17)∧-2 = 0.7305
=(1 + 0.17)∧-3 = (1.17)∧-3 = 0.6244
Scenario A
Year. C.F. DF PV
$ $
0. 900 1 (900)
1 400 0.8772 350.88
2 400 0.7695 307.8
3 400 0.6750 270
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NPV positive 28.68
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Workings = C F × DF = PV
Scenario B
Year. CF DF PV
$ $
0 900 1 (900)
1. 400 0.8547 341.88
2 400 0.7305 292.2
3. 400 0.6244 249.76
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NPV Negative 16.16
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Scenario C
Year CF DF PV
$ $
0 900 1 (900)
1 400 0.83 332
2 400 0.694 277.6
1-3 400 2.3883. 955.32
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NPV positive 664.92
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Scenario D
Year CF DF PV
$ $
0 900 1 (900)
1 400 0.83 332
2. 400 0.694 277.6
1-3 400 2.9503 1,180.12
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NPV positive 889.72
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