Question

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.

Answer 1

There are two parts of this question:

1. Find the PV of the CFs for years 1-20
2. Find the PV value of the perpetuity for years 21 onward

Then we sum up the two PVs

100 Perpetuity = = 1000

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