Key Concept Questions: Chapter 7 Project Seed Capital Rate of Return (%) Net Cas
ID: 2726666 • Letter: K
Question
Key Concept Questions: Chapter 7
Project
Seed Capital
Rate of Return (%)
Net Cash Flow Year 1
Net Cash Flow Year 2
Net Cash Flow Year 3
Net Cash Flow Year 4
Net Cash Flow Year 5
Other Net Cash Flow
Payback Period
NPV
A
$1,000
5%
$200
$300
$400
$500
$0
$0
B
$250,000
8%
$2,000
$25,000
$25,000
$1,000,000
$148,000
$200,000 per year for 5 years
C
$8,000,000
17%
$0
$0
$0
$1,000,000
$5,000,000
$6,000,000 for 3 years
D
$50,000
25%
$0
$1,000
$29,000
$35,0000
$70,000
$0
E
$120 million
6%
$0
$0
$20 million
$80 million
$40 million
$20 million in Year 6, $5 million in Year 7
Project
Seed Capital
Rate of Return (%)
Net Cash Flow Year 1
Net Cash Flow Year 2
Net Cash Flow Year 3
Net Cash Flow Year 4
Net Cash Flow Year 5
Other Net Cash Flow
Payback Period
NPV
A
$1,000
5%
$200
$300
$400
$500
$0
$0
B
$250,000
8%
$2,000
$25,000
$25,000
$1,000,000
$148,000
$200,000 per year for 5 years
C
$8,000,000
17%
$0
$0
$0
$1,000,000
$5,000,000
$6,000,000 for 3 years
D
$50,000
25%
$0
$1,000
$29,000
$35,0000
$70,000
$0
E
$120 million
6%
$0
$0
$20 million
$80 million
$40 million
$20 million in Year 6, $5 million in Year 7
Explanation / Answer
the payback period is when the cumulative cash inflows are equal to investment
net present value is when the difference between present value of cash inflows with present value of cash outflows
the assumptions of project A
The initial investment is $1.000
The cost of capital is 5%
The term of project is 4 years
The calculation of cash flows and NPV is given below
Project A
year
intial investment
Cash inflows
other cash inflows
annual cash inflow
pV factor @5%
cash inflow at present value
1000
1
200.00
0
200
0.952381
190
2
300.00
0
300
0.842815
253
3
400.00
0
400
0.802681
321
4
500.00
0
500
0.764458
382
1,147
Present value of cash inflows for 4 years
1,147
present value of total cash inflow
1,147
less
present value of cash outflow
1000
Net NPV
147
When cash inflows are uneven, we need to calculate the cumulative net cash flow for each period and then use the following formula for payback period:
Payback Period = A +
B
C
In the above formula,
A is the last period with a negative cumulative cash flow;
B is the absolute value of cumulative cash flow at the end of the period A;
C is the total cash flow during the period after A
year
cash flow
cumulative cash inflow
0
(1,000)
(1,000)
1
200.00
(800.00)
2
300.00
(500.00)
3
400.00
(100.00)
4
500.00
400.00
Payback period = 3 + (-100/500)
= 3+(100/500)
=3+.20
=3.20 years
The assumptions of project B
The initial investment is $250,000
The cost of capital is 8%
The term of project is 5 years
The calculation of cash flows and NPV is given below
Project B
year
intial investment
Cash inflows
other cash inflows
annual cash inflow
pV factor @8%
cash inflow at present value
250,000
1
$2,000
200000
202,000
0.925926
187,037
2
$25,000
200000
225,000
0.857339
192,901
3
$25,000
200000
225,000
0.793832
178,612
4
$1,000,000
200000
1,200,000
0.73503
882,036
5
$148,000
200000
348,000
0.680583
236,843
1,677,429
Present value of cash inflows for 5 years
1,677,429
present value of total cash inflow
1,677,429
less
present value of cash outflow
250,000
Net NPV
1,427,429
year
cash flow
cumulative cash inflow
0
(250,000)
(250,000)
1
202,000
(48,000.00)
2
225,000.00
177,000.00
Payback period = 1 + (-48000/225000)
= 1+(48000/225000)
=1+0.21
= 1.21 years
The assumptions of project C
The initial investment is $ $8,000,000
The cost of capital is 17%
The term of project is 5 years
The calculation of cash flows and NPV is given below
year
intial investment
Cash inflows
other cash inflows
annual cash inflow
pV factor @17%
cash inflow at present value
8,000,000
1
$0
6000000
6,000,000
0.854701
5,128,205
2
$0
6000000
6,000,000
0.730514
4,383,081
3
$0
6000000
6,000,000
0.624371
3,746,223
4
$1,000,000
1,000,000
0.53365
533,650
5
$5,000,000
5,000,000
0.456111
2,280,556
16,071,716
Present value of cash inflows for 5 years
16,071,716
present value of total cash inflow
16,071,716
less
present value of cash outflow
8,000,000
Net NPV
8,071,716
year
cash flow
cumulative cash inflow
0
(8,000,000)
(8,000,000)
1
6,000,000
(2,000,000)
2
6,000,000
4,000,000
Payback period = 1 + (-2000000/6000000)
= 1+(2000000/6000000)
=1+0.33
= 1.33 years
The assumptions of project D
The initial investment is $ $50,000
The cost of capital is 25%
The term of project is 5 years
The calculation of cash flows and NPV is given below
year
intial investment
Cash inflows
other cash inflows
annual cash inflow
pV factor @25%
cash inflow at present value
50,000
1
$0
-
0.8
-
2
$1,000
1,000
0.64
640
3
$29,000
29,000
0.512
14,848
4
$350,000
350,000
0.4096
143,360
5
$70,000
70,000
0.32768
22,938
181,786
Present value of cash inflows for 5 years
181,786
present value of total cash inflow
181,786
less
present value of cash outflow
50,000
Net NPV
131,786
year
cash flow
cumulative cash inflow
0
(50,000)
(50,000)
1
-
(50,000)
2
1,000
(49,000)
3
29,000.00
(20,000)
4
350,000.00
Payback period = 3 + (-20000/350000)
= 3+(20000/350000)
=3+0.057
= 3.06 years
Project A
year
intial investment
Cash inflows
other cash inflows
annual cash inflow
pV factor @5%
cash inflow at present value
1000
1
200.00
0
200
0.952381
190
2
300.00
0
300
0.842815
253
3
400.00
0
400
0.802681
321
4
500.00
0
500
0.764458
382
1,147
Present value of cash inflows for 4 years
1,147
present value of total cash inflow
1,147
less
present value of cash outflow
1000
Net NPV
147
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