Question

Find the present worth in year 0 for the cash flows shown using an interest rate of 5% per year. *solve it in Excel, show formula P = ? i=5% 3 4 5 6 7 8 9 10 11 A=$10,000 $8000+$10,000 $12,000+$10,000

Answer 1

Following is the table with the NPV calculated:

Year	CF	Discount Factor		Discounted CF
0	$                             -	1/(1+0.05)^0=	1	1*0=	$                             -
1	$                             -	1/(1+0.05)^1=	0.952380952	0.952380952380952*0=	$                             -
2	$             10,000.00	1/(1+0.05)^2=	0.907029478	0.90702947845805*10000=	$                9,070.29
3	$             10,000.00	1/(1+0.05)^3=	0.863837599	0.863837598531476*10000=	$                8,638.38
4	$             10,000.00	1/(1+0.05)^4=	0.822702475	0.822702474791882*10000=	$                8,227.02
5	$             22,000.00	1/(1+0.05)^5=	0.783526166	0.783526166468459*22000=	$             17,237.58
6	$             10,000.00	1/(1+0.05)^6=	0.746215397	0.746215396636628*10000=	$                7,462.15
7	$             10,000.00	1/(1+0.05)^7=	0.71068133	0.710681330130121*10000=	$                7,106.81
8	$             18,000.00	1/(1+0.05)^8=	0.676839362	0.676839362028687*18000=	$             12,183.11
9	$             10,000.00	1/(1+0.05)^9=	0.644608916	0.644608916217797*10000=	$                6,446.09
10	$             10,000.00	1/(1+0.05)^10=	0.613913254	0.613913253540759*10000=	$                6,139.13
11	$             10,000.00	1/(1+0.05)^11=	0.584679289	0.584679289086437*10000=	$                5,846.79
				NPV = Sum of all Discounted CF	$             88,357.36

Same can be calculated by solving the following equation:

FVS FV: PV = PVannuity + (1 + r) (1+r)"

PV = PMT X- * 1-(1+r) TX (1+r) FV5 T (1 + r) FV: + (1 + r)

1- (1 + 0.05)-10 PV = 10000 x 3 0.05 x 1.05 12000 8000 (1.05)5+ (1.05)8

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PV = 88357,36

Following is the screenshot of excel formula