What is the present value of the following cash flow stream?
Year 01 to year 10: $300
Year 11 to year 20: $200
From year 21 and onwards: S100
Assume a 10% discount rate.
There are two parts of this question:
Then we sum up the two PVs
Now we find the PV of the perpetuity and the CFs from years 1-20
We should know that the perpetuity is at time 20 and not time 21
So the PV is :
Year | CF | Discount Factor | Discounted CF | ||
0 | $ - | 1/(1+0.1)^0= | 1 | 1*0= | - |
1 | $ 300.00 | 1/(1+0.1)^1= | 0.909090909 | 0.909090909090909*300= | 272.73 |
2 | $ 300.00 | 1/(1+0.1)^2= | 0.826446281 | 0.826446280991735*300= | 247.93 |
3 | $ 300.00 | 1/(1+0.1)^3= | 0.751314801 | 0.751314800901578*300= | 225.39 |
4 | $ 300.00 | 1/(1+0.1)^4= | 0.683013455 | 0.683013455365071*300= | 204.90 |
5 | $ 300.00 | 1/(1+0.1)^5= | 0.620921323 | 0.620921323059155*300= | 186.28 |
6 | $ 300.00 | 1/(1+0.1)^6= | 0.56447393 | 0.564473930053777*300= | 169.34 |
7 | $ 300.00 | 1/(1+0.1)^7= | 0.513158118 | 0.513158118230706*300= | 153.95 |
8 | $ 300.00 | 1/(1+0.1)^8= | 0.46650738 | 0.466507380209733*300= | 139.95 |
9 | $ 300.00 | 1/(1+0.1)^9= | 0.424097618 | 0.424097618372485*300= | 127.23 |
10 | $ 300.00 | 1/(1+0.1)^10= | 0.385543289 | 0.385543289429531*300= | 115.66 |
11 | $ 200.00 | 1/(1+0.1)^11= | 0.350493899 | 0.350493899481392*200= | 70.10 |
12 | $ 200.00 | 1/(1+0.1)^12= | 0.318630818 | 0.318630817710357*200= | 63.73 |
13 | $ 200.00 | 1/(1+0.1)^13= | 0.28966438 | 0.289664379736688*200= | 57.93 |
14 | $ 200.00 | 1/(1+0.1)^14= | 0.263331254 | 0.26333125430608*200= | 52.67 |
15 | $ 200.00 | 1/(1+0.1)^15= | 0.239392049 | 0.239392049369163*200= | 47.88 |
16 | $ 200.00 | 1/(1+0.1)^16= | 0.217629136 | 0.217629135790149*200= | 43.53 |
17 | $ 200.00 | 1/(1+0.1)^17= | 0.197844669 | 0.197844668900135*200= | 39.57 |
18 | $ 200.00 | 1/(1+0.1)^18= | 0.17985879 | 0.179858789909214*200= | 35.97 |
19 | $ 200.00 | 1/(1+0.1)^19= | 0.163507991 | 0.163507990826558*200= | 32.70 |
20 | $ 200.00 | 1/(1+0.1)^20= | 0.148643628 | 0.148643628024143*200= | 29.73 |
20 | $ 1,000.00 | 1/(1+0.1)^20= | 0.148643628 | 0.148643628024143*1000= | 148.64 |
NPV = Sum of all Discounted CF | 2,465.81 |
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