Question

Consider the following three cash flow series: End of Year Cash Flow Series A Cash Flow Series B Cash Flow Series C $2,420 $3,420 $2,820 $2,220 $1,620 $1,020 0 $1,000 1.5X 2.0X 2.5X 3.0X 3 2Y 2Y 2Y 4 Determine the values of X and Y so that all three cash flows are equivalent at an interest rate of 16% per year compounded yearly Carry all interim calculations to 5 decimal places and then round your final answer to the nearest dollar. The tolerance is ±5.

Answer 1

The first step is to find the PV of the Series B:
EOY	Cash flow	PVIF at 16%	PV at 16%
0	-2420	1	-2420.00
1	3420	0.86207	2948.28
2	2820	0.74316	2095.72
3	2220	0.64066	1422.26
4	1620	0.55229	894.71
5	1020	0.47611	485.64
			5426.60
To be equivalent, the PV of Series A should also be 5426.60
Hence, -1000*1+0.86207*x+1.5*0.74316*x+2*0.64066*x+2.5*0.55229*x+3.0*0.47611*x = 5426.60
Solving for x, we have
PVIF at 16%	Constant with x	Product
0.86207	1.00	0.86207
0.74316	1.50	1.11474
0.64066	2.00	1.28132
0.55229	2.50	1.38073
0.47611	3.00	1.42834
		6.06720
The above equality becomes
6.06720*x = 6426.60
So x = 6426.60/6.0672 =		$         1,059	(Answer)
CHECK:
EOY	Cash flow	PVIF at 16%	PV at 16%
0	-1000	1	-1000.00
1	1059	0.86207	912.93
2	1589	0.74316	1180.51
3	2118	0.64066	1356.91
4	2648	0.55229	1462.19
5	3177	0.47611	1512.61
			5425.16
Similarly, for Series C,
EOY	Constant with y	PVIF at 16%	Product
0	1	1	1.00
1	1	0.86207	0.86
2	1	0.74316	0.74
3	2	0.64066	1.28
4	2	0.55229	1.10
5	2	0.47611	0.95
			5.94
The equality becomes
5426.60 = 5.94*y
Y = 5426.60/5.94=	$                914	(Answer)
CHECK:
EOY	Cash flow	PVIF at 16%	PV at 16%
0	914	1	914.00
1	914	0.86207	787.93
2	914	0.74316	679.25
3	1828	0.64066	1171.12
4	1828	0.55229	1009.59
5	1825	0.47611	868.91
			5430.80