Answer::
given
Initial Investment P=$13500
Annual cash flow A=$3900
If discount rate r=0%
Discounted cashflow= A/(1+r)^n
where n= year in which cash flow occur
for year 1
Discounted cashflow D=3900/(1+0%)^1=$3900
Remaining value of Investment=P-D=13500-3900=$9600
Since after 1 year we have to only recover $9600 so this become our investment for second year.
r | 0% | |||
Year | Investment P | Cashflow | discounted cash flow D | Remaining value of Investment P-D |
1 | 13500 | 3900 | 3900 | 9600 |
2 | 9600 | 3900 | 3900 | 5700 |
3 | 5700 | 3900 | 3900 | 1800 |
4 | 1800 | 3900 | 3900 | -2100 |
5 | -2100 | 3900 | 3900 | -6000 |
6 | -6000 | 3900 | 3900 | -9900 |
Since payback period occur when Remaining value of Investment =0
so from above table we found that payback period will occur between 3 and 4 years
So payback period =3+(1800/3900)=3.46 years
If discount rate r=7%
Discounted cashflow= A/(1+r)^n
where n= year in which cash flow occur
for year 1
Discounted cashflow D=3900/(1+7%)^1=$3644.86
Remaining value of Investment=P-D=13500-3644.86=$9855.14
Since after 1 year we have to only recover $9844.15 so this become our investment for second year.
r | 7% | |||
Year | Investment P | Cashflow | discounted cash flow D | Remaining value of Investment P-D |
1 | 13500.00 | 3900.00 | 3644.86 | 9855.14 |
2 | 9855.14 | 3900.00 | 3406.41 | 6448.73 |
3 | 6448.73 | 3900.00 | 3183.56 | 3265.17 |
4 | 3265.17 | 3900.00 | 2975.29 | 289.88 |
5 | 289.88 | 3900.00 | 2780.65 | -2490.77 |
6 | -2490.77 | 3900.00 | 2598.73 | -5089.50 |
Since payback period occur when Remaining value of Investment =0
so from above table we found that payback period will occur between 4 and 5 years
So payback period =4+(289.88/2975.29)=4.097 years
If discount rate r=21%
Discounted cashflow= A/(1+r)^n
where n= year in which cash flow occur
for year 1
Discounted cashflow D=3900/(1+21%)^1=$3223.14
Remaining value of Investment=P-D=13500-3644.86=$10276.86
Since after 1 year we have to only recover $10276.86 so this become our investment for second year.
r | 21% | |||
Year | Investment P | Cashflow | discounted cash flow D | Remaining value of Investment P-D |
1 | 13500.00 | 3900.00 | 3223.14 | 10276.86 |
2 | 10276.86 | 3900.00 | 2663.75 | 7613.11 |
3 | 7613.11 | 3900.00 | 2201.45 | 5411.66 |
4 | 5411.66 | 3900.00 | 1819.38 | 3592.28 |
5 | 3592.28 | 3900.00 | 1503.62 | 2088.66 |
6 | 2088.66 | 3900.00 | 1242.66 | 846.00 |
Since payback period occur when Remaining value of Investment =0
So from above table we found that payback period will be more than 6 years
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