Question

1. You have joined the Projects division of MaraMore Inc. Your first job is to analyze two projects, which you have code-named “alpha” and “beta”. Both projects will require the same initial investment of $100,000 and are expected to generate the following cash flows over an economic life of 4 years.

Year	Project “Alpha”	Project “Beta”
1	70,000	40,000
2	32,000	40,000
3	32,000	40,000
4	9,000	40,000

Assuming that MaraMore Inc.’s cost of capital for these projects is 10%:

1. Calculate the IRR for each project. Which project would you select using the IRR rule?
2. Calculate the PI for each project and indicate your decision using the rule.
3. Can you think of any situations in which, because of a change in the cost of capital, you might be confronted with conflicting decisions using the NPV and IRR rules? Show how this might happen.

Answer 1

ANSWER: INTERNAL RATE OF RETURN MEANS THE RATE AT WHICH NET PRESENT VALUE OF PROJECT COMES EQUAL TO 0.

NET PRESENT VALUE IS THE DIFFEERNCE BETWEEN PRESENT VALUE OF CASH INFLOW AND PRESENT VALUE OF CASH OUTFLOW.

STATEMNT SHOWING IRR OF "ALPHA"

YEAR	AMOUNT	DISCOUNTED RATE @ 10%	PRESENT VALUE
0	$(100000)	1	$(100000)
1	$70000	.909	63630
2	$32000	.826	26432
3	$32000	.751	24032
4	$9000	.683	6147
		NET PRESENT VALUE	20241

IF WE INCREASES THE RATE OF COST OF CAPITAL THEN NPV REDUCES.

ASSUMING COST OF CAPITAL 25%

YEAR	AMOUNT	DISCOUNTED RATE @25%	PRESENT VALUE
0	$(100000)	1	$(100000)
1	$70000	.8	56000
2	$32000	.64	20480
3	$32000	.512	16384
4	$9000	.41	3690
		NPV	(3446)

IRR OF ALPHA = POSITIVE NPV RATE OF DISCOUNT + POSITIVE NPV / (POSITIVE NPV - NEGATIVE NPV) * DIFERENCE IN BOTH RATES.

IRR = 10% + 20241 / 20241 - (-3446) * 15

= 10% + 12.818% = 22.818%

IRR OF PROJECT BETA

YEAR	AMOUNT	DISCOUNT RATE@10%	AMOUNT
0	$(100000)	1	$100000
1-4	40000	3.17	126800
		NPV	26800

NOW ASSUMING COST OF CAPITAL 25%

YEAR	AMOUNT	DISCOUNT RATE@25%	AMOUNT
0	$100000	1	$100000
1-4	40000	2.36	$94400
		NPV	(5600)

IRR = POSITIVE NPV RATE OF DISCOUNT + POSITIVE NPV / (POSITIVE NPV - NEGATIVE NPV) * DIFERENCE IN BOTH RATES.

IRR = 10% + 26800/32400 * 15

= 22.41%

LOWER THE IRR MEANS LOWER THE RISK , SO BY CONSIDERING THIS RULE THUMB PROJECT BETA IS BETTER DUE TO LOWER IRR

ANSWER 2 . PROFITABILITY INDEX IS CALCULATED BY DIVIDING THE PRESENT VALUE OF FUTURE CASH FLOWS BY INTIAL INVESTMENT.

PI = PRESENT VALUE OF CASH FLOW / INTIAL INVESTMENT

BY USING THE ORIGINAL DATA .

PI OF ALPHA = $120241 / $100000 = 1.20241

PI OF BETA = $126800 / $100000 = 1.268

ON THE BASIS OF PI, PROJECT WITH HIGHER PI SHOULD BE SELECTED TO PROCEED.

HIGHER PI GENERALLY STATES GENERATION OF MORE CASH INFLOW IN FUTURE THAN LOWER PI PROJECT.

IF ANY PROJECT HAVING PI LESS THAN 1 SHOULD NOT BE SELECTED TO PROCEED.

SO PROJECT BETA HAS HIGHER PI AND SHOULD BE SELECTED TO PROCEED.

ANSWER 3. NO THER IS NO CONFLICTION IN DECISION MAKING EVEN IF COST OF CAPITAL CHANGES.

ACTUALLY NPV OF PROJECT BETA IS MORE THAN PROJECT ALPHA WHICH WILL REMAIN HIGHER AT ANY COST OF CAPITAL THAN ALPHA.

ALSO, IRR OF BETA IS LOWER THAN IRR OF ALPHA WHICH WILL REMAIN LOWER AT ANY COST OF CAPITAL.

SO PROJECT BETA ALWAYS BETTER THAN PROJECT ALPHA.

NEW COST OF CAPITAL15%.

                                                              ALPHA

YEAR	AMOUNT	DISCOUNT RATE@15%	PRESENT VALUE
0	$100000	1	100000
1	70000	.87	60900
2	32000	.756	24192
3	32000	.658	21056
4	9000	.572	5148
		NPV	11296

ASSUMING COST OF CAPITAL 25%(FOR CALCULATION OF IRR)

YEAR	AMOUNT	DISCOUNTED RATE @25%	PRESENT VALUE
0	$(100000)	1	$(100000)
1	$70000	.8	56000
2	$32000	.64	20480
3	$32000	.512	16384
4	$9000	.41	3690
		NPV	(3446)

IRR = 15% + 11296/14742* 10

= 22.66%

                                                                        BETA

YEAR	AMOUNT	DISCOUNT RATE@15%	AMOUNT
0	$(100000)	1	$100000
1-4	40000	2.855	114200
		NPV	14200

ASSUMING COST OF CAPITAL 25%(FOR CALCULATION OF IRR)

YEAR	AMOUNT	DISCOUNT RATE@25%	AMOUNT
0	$100000	1	$100000
1-4	40000	2.36	$94400
		NPV	(5600)

IRR = 15% + 14200 / 19800 * 10

IRR = 22.17%

SO IT CAN BE OBSERVED THAT IRR OF BETA AGAIN IS LESS THAN ALPHA IRR.

SO THERE IS NO CONFLICTION IN DECISION MAKING EVEN AFTER CHANGE IN COST OF CAPITAL.