Investment A |
||||
Year |
cost |
Cash flow |
working |
cost yet to be recovered |
0 |
16000 |
0 |
- |
|
1 |
1,850 |
16000-1850 |
14,150 |
|
2 |
1,925 |
14150-1925 |
12,225 |
|
3 |
2,567 |
12225-2567 |
9,658 |
|
4 |
3,850 |
9658-3850 |
5,808 |
|
5 |
3,850 |
5808-3850 |
1,958 |
|
6 |
5,133 |
1958-5133 |
-3,175 |
|
7 |
5,775 |
|||
8 |
5,850 |
as we can see that the cost to be recovered turns negative in the 6th year |
that means that the cost is recovered between 5th and 6th year |
Now, Payback period = years before full recovery + (Unrecovered investment at start of the year/Cash flow during the year) |
Payback period =5 + (1958/5133) |
Payback period =5.38 years or 5 years 4.5 months |
So payback period of Investment A is 5 years aprox.
investment B |
||||
Year |
cost |
Cash flow |
working |
cost yet to be recovered |
0 |
9500 |
0 |
- |
|
1 |
3,200 |
9500-3200 |
6,300 |
|
2 |
3,200 |
6300-3200 |
3,100 |
|
3 |
3,200 |
3100-3200 |
-100 |
|
4 |
3,000 |
|||
5 |
3,000 |
as we can see that the cost to be recovered turns negative in the 3rd year |
that means that the cost is recovered between 2nd and 3rd year |
Now, Payback period = years before full recovery + (Unrecovered investment at start of the year/Cash flow during the year) |
Payback period =2 + (3100/3200) |
Payback period =2.97 years or 2 years 11.6 months or 3 years approx. |
So payback period of Investment b is 3 years
We will choose investment B , as it takes less time to payback the cost and so is more profitable.
Investment |
years |
Average |
|||||||
A |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
|
after tax benefit |
1,850 |
1,925 |
2,567 |
3,850 |
3,850 |
5,133 |
5,775 |
5,850 |
|
value of A |
|||||||||
1st Jan |
- |
1,850 |
3,775 |
6,342 |
10,192 |
14,042 |
19,175 |
24,950 |
|
31st Dec |
1,850 |
1,925 |
2,567 |
3,850 |
3,850 |
5,133 |
5,775 |
5,850 |
|
Average |
1850 |
1887.5 |
2114 |
2548 |
2,808.40 |
3,195.83 |
3,564.29 |
3850 |
|
Average annual rate of return for A |
26% |
Here , 1st jan balance is last years closing balance
Closing balance is the after tax benefit of that years
Average is the opening balance + closing balance / number of years
For example. For the 2nd year
Opening balance = 1850
Closing = 1925
Average = 1850+1925/2
Average annual rate of return = average annual net earning / initial cost *100
Here annual avg earning= 3850
Initial cost = investment –salvage value
= 16000-1000
AARR= 3850/(16000-1000) *100
= 25.67 or 26%
Similarly for investment B
investment |
years |
Average |
|||||||
B |
1 |
2 |
3 |
4 |
5 |
||||
after tax benefit |
3200 |
3200 |
3200 |
3000 |
3000 |
||||
value of B |
|||||||||
1st Jan |
- |
3,200 |
6,400 |
9,600 |
12,600 |
||||
31st Dec |
3,200 |
3,200 |
3,200 |
3,000 |
3,000 |
||||
Average |
3200 |
3200 |
3200 |
3150 |
3,120.00 |
||||
Average annual rate of return for B |
35% |
Year (n) |
Cash Flow |
working : factor= 1/(1+r)^n |
present value factor = 1/(1+r)^n |
after tax present value = Cash flow * discount value |
1 |
1,850 |
1/ (1+0.08)^1 |
0.93 |
$ 1,712.96 |
2 |
1,925 |
1/ (1+0.08)^2 |
0.86 |
$ 1,650.38 |
3 |
2,567 |
1/ (1+0.08)^3 |
0.79 |
$ 2,037.77 |
4 |
3,850 |
1/ (1+0.08)^4 |
0.74 |
$ 2,829.86 |
5 |
3,850 |
1/ (1+0.08)^5 |
0.68 |
$ 2,620.25 |
6 |
5,133 |
1/ (1+0.08)^6 |
0.63 |
$ 3,234.66 |
7 |
5,775 |
1/ (1+0.08)^7 |
0.58 |
$ 3,369.66 |
8 |
5,850 |
1/ (1+0.08)^8 |
0.54 |
$ 3,160.57 |
Total |
$ 20,616.11 |
|||
Less : initial investment |
$ 16,000.00 |
|||
Net present value |
$ 4,616.11 |
|||
benefit cost ratio |
= 20616/16000= 1.29 |
Investment B
Year (n) |
Cash Flow |
working : factor= 1/(1+r)^n |
present value factor = 1/(1+r)^n |
after tax present value = Cash flow * discount value |
1 |
3,200 |
1/ (1+0.08)^1 |
0.93 |
$ 2,962.96 |
2 |
3,200 |
1/ (1+0.08)^2 |
0.86 |
$ 2,743.48 |
3 |
3,200 |
1/ (1+0.08)^3 |
0.79 |
$ 2,540.26 |
4 |
3,000 |
1/ (1+0.08)^4 |
0.74 |
$ 2,205.09 |
5 |
3,000 |
1/ (1+0.08)^5 |
0.68 |
$ 2,041.75 |
Total |
$ 12,493.55 |
|||
Less : initial investment |
$ 9,500.00 |
|||
Net present value |
$ 2,993.55 |
|||
benefit cost ratio |
1.32 |
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