Question

​(​Time-disparity problem​)

The State Spartan Corporation is considering two mutually exclusive projects. The free cash flows associated with these projects are shown in the popup​ window:

	PROJECT A		PROJECT B
Initial outlay	−​$50,000		−​$50,000
Inflow year 1	15,625		0
Inflow year 2	15,625		0
Inflow year 3	15,625		0
Inflow year 4	15,625		0
Inflow year 5	15,625		100,000

The required rate of return on these projects is 10

percent.

a. What is each​ project's payback​ period?

b. What is each ​project's

NPV​?

c. What is each​ project's

IRR​?

d. What has caused the ranking​ conflict?

e. Which project should be​ accepted? Why?

NEED ANSWER TO THESE QUESTIONS

a. What is the payback period of project​ A? _____years  ​(Round to two decimal​ places.)

What is the payback period of project​ B? ______years  ​(Round to two decimal​ places.)

b. What is the NPV of project​ A? ​$_____ ​(Round to the nearest​ cent.)

What is the NPV of project​ B? $_____ ​(Round to the nearest​ cent.)

C. What is the IRR of project​ A? ​______% ​(Round to two decimal​ places.)

What is the IRR of project​ B? _____​% ​(Round to two decimal​ places.)

d. What has caused the ranking​ conflict?  ​(Select the best choice​ below.)

A.

The projects evaluated have the same initial cash outlay.

B.

The two projects are independent.

C.

The free cash flows genearted by the projects are different.

D.

The NPV and IRR decision criteria have different reinvestment assumptions.

e. Which project should be​ accepted? Why?  ​(Select the best choice​ below.)

A.Project B should be chosen because it has higher NPV. The NPV criterion is preferred because it makes the most acceptable reinvestment assumption for the​ wealth-maximizing firm.

B. Neither project A nor B should be chosen because ranking conflict exists among different decision criteria. Different decision criteria should yield the same result.

C.Project A should be chosen because it has higher IRR.

The IRR criterion is preferred because it makes the most acceptable reinvestment assumption for the​ wealth-maximizing firm.

D.

Project A should be chosen because it has lower payback period. The payback period is preferred because it can be easily computed.

Answer 1

Payback period:

Payback period is the period in which initial investment is recovered.

PBP = Year in which least +ve Closing Balance + [ Closing balance at that year / Cash flow in Next Year ]
If Actual PBP > Expected PBP - Project will be rejected
Actual PBP </= Expected PBP - Project will be accepted

Project A:

Particulars	Amount
Initial Investment	$    50,000.00
Cash Flow per period	$    15,625.00
Payback period	3.2

PBP = Initial Investment / Cash Flow per Anum
= $ 50000 / $ 15625
= 3.2
Payback period is 3.2 Years

Project B:

Year	Opening Balance	Cash Flow	Closing Balance
1	$          50,000.00	$                     -	$       50,000.00
2	$          50,000.00	$                     -	$       50,000.00
3	$          50,000.00	$                     -	$       50,000.00
4	$          50,000.00	$                     -	$       50,000.00
5	$          50,000.00	$    100,000.00	$      -50,000.00

PBP = Year in which least +ve Closing Balance + [ Closing balance at that year / Cash flow in Next Year ]
= 4 Years + [ $ 50000 / $ 100000 ]
= 4 Years + 0.5 Years
= 4.5 Years

Payback Period is 4.5 Years
Project A is selected as it has lesser payback period.

NPV :
NPV is the difference between Present value of Cash Inflows and Present value of cash outflows.

NPV = PV of Cash Inflows - PV of Cash Outflows
If NPV > 0 , Project can be accepted
NPV = 0 , Indifference point. Project can be accepted/ Rejected.
NPV < 0 , Project will be rejected.
Project A:

Year	CF	PVF @10 %	Disc CF
0	$        (50,000.00)	1.0000	$        (50,000.00)
1	$          15,625.00	0.9091	$          14,204.55
2	$          15,625.00	0.8264	$          12,913.22
3	$          15,625.00	0.7513	$          11,739.29
4	$          15,625.00	0.6830	$          10,672.09
5	$          15,625.00	0.6209	$            9,701.90
NPV			$            9,231.04

Project B:

Year	CF	PVF @10 %	Disc CF
0	$        (50,000.00)	1.0000	$        (50,000.00)
1	$                        -	0.9091	$                        -
2	$                        -	0.8264	$                        -
3	$                        -	0.7513	$                        -
4	$                        -	0.6830	$                        -
5	$        100,000.00	0.6209	$          62,092.13
NPV			$          12,092.13

Project B is selected as it has higher NPV.

IRR :
IRR is the Rate at which PV of Cash Inflows are equal to PV of Cash Outflows or Rate of growth is expected from project/ Investment. At IRR, NPV of Project/ Investment will be Zero. It assumes that intermediary Cfs are reinvested at IRR only.

IRR = Rate at which least +ve NPV + [ NPV at that Rate / Change in NPV due to 1% inc in disc rate ] * 1%

If IRR > Cost of Capital - Project can be accepted
IRR = Cost of Capital - Indifferebce Point - Project will be accepted / Rejected
IRR < Cost of Capital - Project will be erejected

Project A:

Year	CF	PVF @16 %	Disc CF	PVF @17 %	Disc CF
0	$      (50,000.00)	1.0000	$      -50,000.00	1.0000	$      -50,000.00
1	$        15,625.00	0.8621	$        13,469.83	0.8547	$        13,354.70
2	$        15,625.00	0.7432	$        11,611.92	0.7305	$        11,414.27
3	$        15,625.00	0.6407	$        10,010.28	0.6244	$          9,755.79
4	$        15,625.00	0.5523	$          8,629.55	0.5337	$          8,338.28
5	$        15,625.00	0.4761	$          7,439.27	0.4561	$          7,126.74
NPV			$          1,160.84		$              -10.22

IRR = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 16 % + [ 1160.84 / ( 1160.84 - ( -10.22) ) ] * 1 %
= 16 % + [ 1160.84 / ( 1171.06) ] * 1 %
= 16 % + [ 0.99 ] * 1 %
= 16 % + 0.99 %
= 16.99 %

Project B:

Year	CF	PVF @14 %	Disc CF	PVF @15 %	Disc CF
0	$      (50,000.00)	1.0000	$      -50,000.00	1.0000	$      -50,000.00
1	$                      -	0.8772	$                      -	0.8696	$                      -
2	$                      -	0.7695	$                      -	0.7561	$                      -
3	$                      -	0.6750	$                      -	0.6575	$                      -
4	$                      -	0.5921	$                      -	0.5718	$                      -
5	$      100,000.00	0.5194	$        51,936.87	0.4972	$        49,717.67
NPV			$          1,936.87		$            -282.33

IRR = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 14 % + [ 1936.87 / ( 1936.87 - ( -282.33) ) ] * 1 %
= 14 % + [ 1936.87 / ( 2219.2) ] * 1 %
= 14 % + [ 0.87 ] * 1 %
= 14 % + 0.87 %
= 14.87 %
Project A is selected as it has higher IRR.

Part D:

IRR assumes the intermediary CFs are reinvested at IRR only, where as NPV assume the intermediary CFs are reinvested at COst of Capital.

OPtion D is correct.

Part E:

In case of conflict and the projects are mutually exclusive, Select the project withh higher NPV.

Project B is selected as it has higher NPV compared to Project A.