An initial investment of $22,500 results in independent annual receipts of $6,25
ID: 2725192 • Letter: A
Question
An initial investment of $22,500 results in independent annual receipts of $6,250 until the end of the project life. The probability distribution for the project’s life is shown in the table below. MARR is 15%/year.
Life (Years)
Probability
A) Determine the probability that the present worth of the project is greater than 0.
B) Determine the probability that the present worth of the project is greater than $1,000
Life (Years)
Probability
4 0.10 5 0.25 6 0.45 7 0.15 8 0.05A) Determine the probability that the present worth of the project is greater than 0.
B) Determine the probability that the present worth of the project is greater than $1,000
Taxable Income (TI) Tax Rate (f) Income Tax (T) 0 < TI 50,000 .15 .15 (TI) 50,000 < TI 75,000 .25 7500 + 0.25 (TI - 50,000) 75,000 < TI 100,000 .34 13,750 + 0.34 (TI - 75,000) 100,000 < TI 335,000 .039(.34 +.05) 22,250 + 0.39 (TI - 100,000) 335,000 < TI 10,000,000 .34 113,900 + 0.34(TI - 335,000) 10,000,000 < TI 15,000,000 .35 3,400,000 + 0.35 (TI - 10,000,000) 15,000,000 < TI 18,333,333 .38(0.35+0.03) 5,150,000 + 0.38 (TI - 15,000,000) 18,333,333 < TI .35 .35 (TI)Explanation / Answer
The net present value is when the difference between present value of cash inflows with present value of cash outflows
The assumptions of project
The initial investment is $22,500
The cost of capital is 15%
The term of project is till 8 years
We will calculate NPV from 4 years to 8 years
The year NPV is greater than zero ,the corresponding probability will the answer
The calculation of cash flows and NPV is given below
year
intial investment
Cash inflows
annual cash inflow
pV factor @15%
cash inflow at present value
cumulative cash inflow at present value
NPV
a
b
c
d
e=c*d
f
G= f-a
22,500
1
$6,250
6,250
0.869565
5,435
5,435
2
$6,250
6,250
0.756144
4,726
10,161
3
$6,250
6,250
0.657516
4,109
14,270
4
$6,250
6,250
0.571753
3,573
17,844
(4,656.39)
5
$6,250
6,250
0.497177
3,107
20,951
(1,549)
6
$6,250
6,250
0.432328
2,702
23,653
1,153.02
7
$6,250
6,250
0.375937
2,350
26,003
8
$6,250
6,250
0.326902
2,043
28,046
We see that at year 6 the cumulative present value of cash inflows is greater than 0 hence the probability is 0.45
The assumptions of project
The initial investment is $22,500
The cost of capital is 15%
The term of project is till 8 years
The tax rate is .15 or 15% as the income per annum is not more than$50,000
We will calculate NPV from 4 years to 8 years
The year NPV is greater than $1000 ,the corresponding probability will the answer
The calculation of cash flows and NPV is given below
year
intial investment
Cash inflows
tax rate @.15
annual cash inflow
pV factor @15%
cash inflow at present value
cumulative cash inflow at present value
NPV
a
b
c
d=b-c
e
f=d*e
g
G= g-a
22,500
1
$6,250
$937.50
5,313
0.869565
4,620
4,620
2
$6,250
$937.50
5,313
0.756144
4,017
8,637
3
$6,250
$937.50
5,313
0.657516
3,493
12,130
4
$6,250
$937.50
5,313
0.571753
3,037
15,167
(7,332.93)
5
$6,250
$937.50
5,313
0.497177
2,641
17,808
(4,692)
6
$6,250
$937.50
5,313
0.432328
2,297
20,105
(2,394.94)
7
$6,250
$937.50
5,313
0.375937
1,997
22,102
(398)
8
$6,250
$937.50
5,313
0.326902
1,737
23,839
1,339
In year 8 the present value of cumulative cash inflow is $23,839 and the present value is $22,500, hence the NPV is $1,339 greater than $1000. The corresponding probability for year 8 is 0.05
year
intial investment
Cash inflows
annual cash inflow
pV factor @15%
cash inflow at present value
cumulative cash inflow at present value
NPV
a
b
c
d
e=c*d
f
G= f-a
22,500
1
$6,250
6,250
0.869565
5,435
5,435
2
$6,250
6,250
0.756144
4,726
10,161
3
$6,250
6,250
0.657516
4,109
14,270
4
$6,250
6,250
0.571753
3,573
17,844
(4,656.39)
5
$6,250
6,250
0.497177
3,107
20,951
(1,549)
6
$6,250
6,250
0.432328
2,702
23,653
1,153.02
7
$6,250
6,250
0.375937
2,350
26,003
8
$6,250
6,250
0.326902
2,043
28,046