Problem 3 Reconsider the series of cash flows from Problem 2 Cumulative Month Amount 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 CF (1,000s of $) $400 00 700 1200 600 300 1000 1200 400 300 1000 1200 400 300 1000 1200 400 300 1000 1200 400 300 1000 What uniform periodic payment would you need in order to produce the same NPV as you found in Problem 2 if the MARR yields 15 This is an ordinary annuity (or an annuity in arrears), with a monthly payment schedule Caution Remember to adjust the units for the MARR Also, watch the signs of your results A Use an appropriate equation from Peterson to compute the uniform monthly payment required to produce the same NPV B Then, separately, use Excel's PMT function to compute the same value C Finally, separately lay out that stream of 20 identical payments and use it to check your results by the same methods as in Problem 2 That is, use the CF stream of that ordinary annuity to compute the NPV Note The correct result is the same as Peterson's Annual Equivalent method (Well the same except that you have computed a Monthly Equivalent here) Now, what if we change this to an annuity due (or an annuity in advance) and we change the payment schedule to annual What series of uniform payments would we need to provide the same NPV, given that we have a MARR of 15 D Rearrange and use an appropriate equation from Peterson to compute the annual payments required to produce the same NPV E Separately, use Excel's PMT function to compute the same value F Use the CF stream of that annuity due to compute the NPV Problem 2 Consider the following series of cash flows Cumulative Month Amount 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 CF (1,000s of $) $400 00 700 1200 600 300 1000 1200 400 300 1000 1200 400 300 1000 1200 400 300 1000 1200 400 300 1000 What is the NPV if the MARR yields 15 Compute your solution by two (2) methods as follows Example Compute the PV month by month and sum those monthly results to find the NPV I've done this for you as an example A Read through the example provided in the Example tab Explicitly state that you reviewed the example and understand what is happening B Then, separately, use Excel's NPV function C Now recompute the NPV at a MARR of 65 I know that is awfully high, but see what happens Comment about the difference D Compute the FV at the end of month 20 at a MARR of 15 Note I do not know of an Excel function that performs this calculation Example n 20 months i A 15 per year MARR Annual This is an effective annual interest rate i M 1 171 per month MARR Monthly This is an effective monthly interest rate Month Cumulative 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Undiscounted CF $400 00 700 1200 600 300 1000 1200 400 300 1000 1200 400 300 1000 1200 400 300 1000 1200 400 300 1000 Discount (or PW) Factors 1 0 988421 0 976976 0 965663 0 954481 0 943429 0 932505 0 921707 0 911034 0 900485 0 890058 0 879752 0 869565 0 859496 0 849544 0 839707 0 829984 0 820373 0 810874 0 801484 0 792204 Discounted CFs 700 1186 105 586 1853 289 6989 954 481 1132 11 373 002 276 512 911 034 1080 582 356 0233 263 9256 869 5652 1031 4 339 818 251 912 829 9837 984 4477 324 3495 240 4453 792 204 NPV by summing DCFs $248 84 Example $248 84 Example Problem 3 Reconsider the series of cash flows from Problem 2 Cumulative Month Amount 9 10 11 12 3 141561718920 CF (1,000s of S) $400 00 700 1200 600 300 1000 1200 400 3001000 00 400300 1000 1200 300 1000 1200 400 1000 what uniform periodic payment would you need in order to produce the same NPV as you found in Problem 2 if the MARR yields 15 This is an ordinary annuity (or an annuity in arrears), with a monthly payment schedule Caution Remember to adjust the units for the MARR Also, watch the signs of your results A Use an appropriate equation from Peterson to compute the uniform monthly payment required to produce the same NPV B Then, separately, use Excel's PMT function to compute the same value C Finally, separately lay out that stream of 20 identical payments and use it to check your results by the same methods as in Problem 2 That is, use the CF stream of that ordinary annuity to compute the NPV Note The correct result is the same as Peterson's Annual Equivalent method (Well the same except that you have computed a Monthly Equivalent here) Now, what if we change this to an annuity due (or an annuity in advance) and we change the payment schedule to annual What series of uniform payments would we need to provide the same NPV, given that we have a MARR of 15 D Rearange and use an appropriate equation from Peterson to compute the annual payments required to produce the same NPV E Separately, use Excel's PMT function to compute the same value F Use the CF stream of that annuity due to compute the NPV Problem 2 Consider the following series of cash flows 10 12 16 18 CF (1,000s of $) S400 00 7001200 300 1000 1200 300 1000 200 300 1000 200300 1000 200 300 1000 he NPV if the MARR yields 15 Compute your solution by two (2) methods as follows Example Compute the PV month by month and sum those monthly resuts to find the NPV Ive done this for you as an example A Read through the example provided in the Example tab Expicitly state that you reviewed the example and understand what is happening Then, separately, use Excers NPV function Now recompute the NPV at a MAR of 65 I know that is awfuly high, but see what happens Comment about the difference Compute the FV at the end of month 20 at a MARR of 15 Note I do not know of an Excel function that performs this calculation Example P n 20 A 15 iM 1 17 per year MARRAnnual This is an effective annual interest rate per month MARRMonthly This is an effective monthly interest rate Month Cumulative 10 12 16 18 Undiscounted CF$400 00 700 00 200 00 600 00 300 00 1000 00 1200 00 400 00 300 00 1000 00 1200 00 400 00 300 00 1000 00 1200 00 400 00 300 00 1000 00 1200 00 400 00 300 00 1000 00 00 99 0 98 Discount (or PW) Factors 0 95 0 94 0 93 0 92 0 91 0 90 0 890 88 85 0 84 0 83 0 82 0 81 0 80 0 79 Discounted CFs NPV by summing DCFs $248 84 700 1186 105 586 1853 289 6989 954 481 1132 11 373 002 276 512 911 034 1080 582 356 0233 263 9256 869 5652 1031 4 339 818 251 912 829 9837 984 4477 324 3495 240 4453 792 204 Example

Question

Problem 3  Reconsider the series of cash flows from Problem 2 Cumulative Month Amount 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 CF (1,000s of $) $400 00  700 1200 600 300  1000  1200  400  300  1000 1200 400 300 1000  1200  400  300 1000 1200 400 300  1000 What uniform periodic payment would you need in order to produce the same NPV as you found in Problem 2 if the MARR yields 15   This is an ordinary annuity (or an annuity in arrears), with a monthly payment schedule  Caution Remember to adjust the units for the MARR  Also, watch the signs of your results  A  Use an appropriate equation from Peterson to compute the uniform monthly payment required to produce the same NPV  B  Then, separately, use Excel's PMT function to compute the same value  C  Finally, separately lay out that stream of 20 identical payments and use it to check your results by the same methods as in Problem 2  That is, use the CF stream of that ordinary annuity to compute the NPV  Note The correct result is the same as Peterson's Annual Equivalent method  (Well     the same except that you have computed a Monthly Equivalent here)  Now, what if we change this to an annuity due (or an annuity in advance) and we change the payment schedule to annual  What series of uniform payments would we need to provide the same NPV, given that we have a MARR of 15   D  Rearrange and use an appropriate equation from Peterson to compute the annual payments required to produce the same NPV  E  Separately, use Excel's PMT function to compute the same value  F  Use the CF stream of that annuity due to compute the NPV  Problem 2  Consider the following series of cash flows  Cumulative Month Amount 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 CF (1,000s of $) $400 00  700 1200 600 300  1000  1200  400  300  1000 1200 400 300 1000  1200  400  300 1000 1200 400 300  1000 What is the NPV if the MARR yields 15   Compute your solution by two (2) methods as follows  Example  Compute the PV month by month and sum those monthly results to find the NPV  I've done this for you as an example  A  Read through the example provided in the  Example  tab  Explicitly state that you reviewed the example and understand what is happening  B  Then, separately, use Excel's NPV function  C  Now recompute the NPV at a MARR of 65   I know that is awfully high, but see what happens  Comment about the difference  D  Compute the FV at the end of month 20 at a MARR of 15   Note I do not know of an Excel function that performs this calculation  Example n   20 months i A   15    per year   MARR Annual This is an effective annual interest rate  i M   1 171    per month   MARR Monthly This is an effective monthly interest rate  Month   Cumulative 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Undiscounted CF   $400 00  700 1200 600 300  1000  1200  400  300  1000 1200 400 300 1000  1200  400  300 1000 1200 400 300  1000 Discount (or PW) Factors   1 0 988421 0 976976 0 965663 0 954481 0 943429 0 932505 0 921707 0 911034 0 900485 0 890058 0 879752 0 869565 0 859496 0 849544 0 839707 0 829984 0 820373 0 810874 0 801484 0 792204 Discounted CFs    700 1186 105 586 1853 289 6989  954 481  1132 11  373 002  276 512  911 034 1080 582 356 0233 263 9256 869 5652  1031 4  339 818  251 912 829 9837 984 4477 324 3495 240 4453  792 204 NPV by summing DCFs   $248 84 Example $248 84 Example    Problem 3  Reconsider the series of cash flows from Problem 2 Cumulative Month Amount 9 10 11 12 3 141561718920 CF (1,000s of S) $400 00  700 1200 600 300 1000  1200 400 3001000 00 400300 1000 1200  300 1000 1200 400  1000 what uniform periodic payment would you need in order to produce the same NPV as you found in Problem 2 if the MARR yields 15   This is an ordinary annuity (or an annuity in arrears), with a monthly payment schedule  Caution Remember to adjust the units for the MARR  Also, watch the signs of your results A Use an appropriate equation from Peterson to compute the uniform monthly payment required to produce the same NPV B  Then, separately, use Excel's PMT function to compute the same value C  Finally, separately lay out that stream of 20 identical payments and use it to check your results by the same methods as in Problem 2  That is, use the CF stream of that ordinary annuity to compute the NPV Note The correct result is the same as Peterson's Annual Equivalent method (Well  the same except that you have computed a Monthly Equivalent here)  Now, what if we change this to an annuity due (or an annuity in advance) and we change the payment schedule to annual  What series of uniform payments would we need to provide the same NPV, given that we have a MARR of 15   D  Rearange and use an appropriate equation from Peterson to compute the annual payments required to produce the same NPV E  Separately, use Excel's PMT function to compute the same value F  Use the CF stream of that annuity due to compute the NPV Problem 2  Consider the following series of cash flows 10 12 16 18 CF (1,000s of $) S400 00  7001200 300  1000  1200 300 1000 200 300 1000  200300 1000 200 300 1000 he NPV if the MARR yields 15   Compute your solution by two (2) methods as follows  Example  Compute the PV month by month and sum those monthly resuts to find the NPV  Ive done this for you as an example A  Read through the example provided in the Example  tab  Expicitly state that you reviewed the example and understand what is happening  Then, separately, use Excers NPV function  Now recompute the NPV at a MAR of 65   I know that is awfuly high, but see what happens  Comment about the difference  Compute the FV at the end of month 20 at a MARR of 15   Note I do not know of an Excel function that performs this calculation  Example P n 20 A  15  iM 1 17    per year MARRAnnual  This is an effective annual interest rate   per month   MARRMonthly This is an effective monthly interest rate Month Cumulative 10 12 16 18 Undiscounted CF$400 00  700 00 200 00 600 00 300 00 1000 00 1200 00  400 00  300 00 1000 00 1200 00 400 00 300 00 1000 00 1200 00 400 00  300 00 1000 00 1200 00 400 00 300 00  1000 00 00 99 0 98 Discount (or PW) Factors  0 95 0 94 0 93 0 92 0 91 0 90 0 890 88 85 0 84 0 83 0 82 0 81 0 80 0 79 Discounted CFs  NPV by summing DCFs $248 84  700 1186 105 586 1853 289 6989  954 481 1132 11 373 002 276 512 911 034 1080 582 356 0233 263 9256 869 5652 1031 4 339 818 251 912 829 9837 984 4477 324 3495 240 4453 792 204 Example

Accepted Answer

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Problem 3. Reconsider the series of cash flows from Problem 2

	Cumulative
Month	Amount	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20

CF (1,000s of $)	$400.00	-700	1200	600	300	-1000	-1200	-400	-300	-1000	1200	400	300	1000	-1200	-400	-300	1000	1200	400	300	-1000

	What uniform periodic payment would you need in order to produce the same NPV as you found in Problem 2 if the MARR yields 15%?
	This is an ordinary annuity (or an annuity in arrears), with a monthly payment schedule. Caution Remember to adjust the
	units for the MARR. Also, watch the signs of your results.
	A.	Use an appropriate equation from Peterson to compute the uniform monthly payment required to produce the same NPV.
	B.	Then, separately, use Excel's PMT function to compute the same value.
	C.	Finally, separately lay out that stream of 20 identical payments and use it to check your results by the same methods as in
		Problem 2. That is, use the CF stream of that ordinary annuity to compute the NPV.

	Note The correct result is the same as Peterson's Annual Equivalent method. (Well ... the same except that you have computed a Monthly Equivalent here).

	Now, what if we change this to an annuity due (or an annuity in advance) and we change the payment schedule to annual? What series
	of uniform payments would we need to provide the same NPV, given that we have a MARR of 15%?
	D.	Rearrange and use an appropriate equation from Peterson to compute the annual payments required to produce the same NPV.
	E.	Separately, use Excel's PMT function to compute the same value.
	F.	Use the CF stream of that annuity due to compute the NPV.


Problem 2. Consider the following series of cash flows:

	Cumulative
Month	Amount	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20

CF (1,000s of $)	$400.00	-700	1200	600	300	-1000	-1200	-400	-300	-1000	1200	400	300	1000	-1200	-400	-300	1000	1200	400	300	-1000

	What is the NPV if the MARR yields 15%? Compute your solution by two (2) methods as follows:
	Example.	Compute the PV month-by-month and sum those monthly results to find the NPV. I've done this for you as an example.
	A.	Read through the example provided in the "Example" tab. Explicitly state that you reviewed the example and understand what is happening.
	B.	Then, separately, use Excel's NPV function.
	C.	Now recompute the NPV at a MARR of 65%. I know that is awfully high, but see what happens. Comment about the difference.
	D.	Compute the FV at the end of month 20 at a MARR of 15%. Note I do not know of an Excel function that performs this calculation.

Example
n =	20	months
i_A =	15%	% per year = MARR_Annual This is an effective annual interest rate.
i_M =	1.171%	% per month = MARR_Monthly This is an effective monthly interest rate.
Month =	Cumulative	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Undiscounted CF =	$400.00	-700	1200	600	300	-1000	-1200	-400	-300	-1000	1200	400	300	1000	-1200	-400	-300	1000	1200	400	300	-1000
Discount (or PW) Factors =		1	0.988421	0.976976	0.965663	0.954481	0.943429	0.932505	0.921707	0.911034	0.900485	0.890058	0.879752	0.869565	0.859496	0.849544	0.839707	0.829984	0.820373	0.810874	0.801484	0.792204
Discounted CFs =		-700	1186.105	586.1853	289.6989	-954.481	-1132.11	-373.002	-276.512	-911.034	1080.582	356.0233	263.9256	869.5652	-1031.4	-339.818	-251.912	829.9837	984.4477	324.3495	240.4453	-792.204
NPV by summing DCFs =	$248.84	Example

Question

Problem 3. Reconsider the series of cash flows from Problem 2 Cumulative Month Amount 0 1 2 3 4 5 6 7 8 9 10

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