Question

Consider the following two cash flow series of payments: Series A is a geometric series increasing at a rate of 4% per year. The initial cash payment at the end of year 1 is $1,000. The payments occur annually for 5 years. Series B is a uniform series with payments of value X occurring annually at the end of years 1 through 5. You must make the payments in either Series A or Series B. Click here to access the TVM Factor Table Calculator Your answer is incorrect. Try again. Determine the value of X for which these two series are equivalent if your TVOM is i = 6%. $ Carry all interim calculations to 5 decimal places and then round your final answer to the nearest dollar. The tolerance is ±5. Your answer is incorrect. Try again. If your TVOM is 8%, would you be indifferent between these two series of payments? Enter the PW for each series to support this choice. PW, Series A: $ PW, Series B: $ Carry all interim calculations to 5 decimal places and then round your final answer to the nearest dollar. The tolerance is ±5%. Your answer is incorrect. Try again. If your TVOM is 5%, would you be indifferent between these two series of payments? Enter the PW for each series to support this choice. PW, Series A: $ PW, Series B: $ Carry all interim calculations to 5 decimal places and then round your final answer to the nearest dollar. The tolerance is ±5.

Answer 1

	Series A
Year	Geometric Series		TVOM F at 6%		TVOM at 6%
	C/f (n+1)=C/f( n)*1.04
1	2	3	4	5	6=3*5
1	1000	1000	1/1.06^1=	0.94340	943.39623
2	1000*1.04=	1040	1/1.06^2=	0.89000	925.59630
3	1040*1.04=	1081.60000	1/1.06^3=	0.83962	908.13222
4	1081.6*1.04=	1124.86400	1/1.06^4=	0.79209	890.99765
5.00000	1124.864*1.04=	1169.85856	1/1.06^5=	0.74726	874.18637
	Total PW of the series			4.21236	4542.30876
PW of Series B should be EQUAL to PW of the payments under geometric Series A
Using P/A,i= 6%,n=5, 4.21236
4.21236*X=4542.30876
So, X=4542.30876/4.21236=
1078.3287
So,
the value of X for which these two series are equivalent if the TVOM is i = 6%=
1078

2…	Series A
Year	Geometric Series		TVOM F at 8%		TVOM at 8%
	C/f (n+1)=C/f( n)*1.04
1	2	3	4	5	6=3*5
1	1000	1000	1/1.08^1=	0.92593	925.92593
2	1000*1.04=	1040	1/1.08^2=	0.85734	891.63237
3	1040*1.04=	1081.60000	1/1.08^3=	0.79383	858.60895
4	1081.6*1.04=	1124.86400	1/1.08^4=	0.73503	826.80862
5	1124.864*1.04=	1169.85856	1/1.08^5=	0.68058	796.18608
	Total PW of the series			3.99271	4299.16195
	PW of Series A	4299
	PW of Series B	4304
	(1078*3.99271)=
	4304.14138
	YES--given the tolerance is ±5%

3..	Series A
Year	Geometric Series		TVOM F at 5%		TVOM at 5%
	C/f (n+1)=C/f( n)*1.04
1	2	3	4	5	6=3*5
1	1000	1000	1/1.05^1=	0.95238	952.38095
2	1000*1.04=	1040	1/1.05^2=	0.90703	943.31066
3	1040*1.04=	1081.60000	1/1.05^3=	0.86384	934.32675
4	1081.6*1.04=	1124.86400	1/1.05^4=	0.82270	925.42840
5	1124.864*1.04=	1169.85856	1/1.05^5=	0.78353	916.61479
	Total PW of the series			4.32948	4672.06155
	PW of Series A	4672
	PW of Series B	4667
	(1078*4.32948)=
	4667.17944
	YES--given the tolerance is ±5