Concept explainers
a.
To calculate: Present value of cash flow stream at 5% discounting rate.
Present value of cash flow:
It is also called as discounted value. It defines that amount of money that invested at a given rate of interest will increases the amount of future cash flow at that particular time in future.
a.
Explanation of Solution
Calculation of present value of cash flow stream at 5% discounting rate
Year | Discounting Rate | Cash Flows | Present value of cash flows | ||
Stream A | Stream B |
Stream A (B×C) |
Stream B (B×D) | ||
A | B | C | D | E | F |
0 | 1.000000 | 0 | 0 | 0 | 0 |
1 | 0.952381 | 150 | 250 | 142.8572 | 238.0953 |
2 | 0.907029 | 450 | 450 | 408.1631 | 408.1631 |
3 | 0.863838 | 450 | 450 | 388.7271 | 388.7271 |
4 | 0.822702 | 450 | 450 | 370.2159 | 370.2159 |
5 | 0.783526 | 250 | 150 | 195.8815 | 117.5289 |
Present value for Stream A and Stream B | 1505.845 | 1522.73 |
Table (1)
Working Note to calculate discounting rate
Formula to calculate discounting rate for year 1
Formula to calculate discounting rate for year 2
Formula to calculate discounting rate for year 3
Formula to calculate discounting rate for year 4
Formula to calculate discounting rate for year 5
Present value for Stream A and Stream B is $1,505.84 and $1,522.73, respectively.
b.
To calculate: Present value of cash flow stream at 0% discounting rate.
Present value of cash flow:
It is also called as discounted value. It defines that amount of money that invested at a given rate of interest will increases the amount of future cash flow at that particular time in future.
b.
Explanation of Solution
Calculation of present value of cash flow stream at 0% discounting rate
Year | Discounting Rate | Cash Flows | Present value of cash flows | ||
Stream A | Stream B |
Stream A
|
Stream B
| ||
A | B | C | D | E | F |
0 | 1.000000 | 0 | 0 | 0 | 0 |
1 | 1.000000 | 150 | 250 | 150 | 250 |
2 | 1.000000 | 450 | 450 | 450 | 450 |
3 | 1.000000 | 450 | 450 |
450 |
450 |
4 | 1.000000 | 450 | 450 | 450 | 450 |
5 | 1.000000 | 250 | 150 | 250 | 150 |
Present value for Stream A and Stream B | 1,750 | 1,750 |
Table (2)
Working Note to calculate discounting rate
Formula to calculate discounting rate for year 1
Formula to calculate discounting rate for year 2
Formula to calculate discounting rate for year 3
Formula to calculate discounting rate for year 4
Formula to calculate discounting rate for year 5
Present value for Stream A and Stream B is $1,750 and $1,750 respectively.
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