Question

(a) Calculate the IRR, NPV, Annual Percentage Rate and Payback Period for the following projects:

PROJECT	A	B	C	D
Inicial Investment	1,000,000	2,000,000	2,000,000	1,000,000

(b) Consider the cash flow projection for the next four years. Compare the projects and determine what is the best option for an investor that wants a 10% minimum aceptable rate of return.

Years	Project A	Project B	Project C	Project D
1	300,000	400,000	400,000	1,000,000
2	400,000	200,000	200,000	1,000,000
3	500,000	100,000	100,000	-2,000,000
4	600,000		1,200,000	2,000,000

Answer 1

IRR is calculted by Excel formula.

Cumulative PV of Cash flows (PV of current year+PV of all previous years) PV of Cash Flows(cash flows*discounting factor) Cash Flows Discountin g Factor [1/(1.1 yea Year Project A D B D A -1000000 272727.273 363636.3636 330578.512 165289.2562 375657.4 75131.48009 C C B D -1000000 300000 400000 500000 600000 -2000000 -2000000 363636,364 165289.256 826446.281 -2000000 -2000000 -1000000 909090.909 1000000 1000000 0.909091 1000000 -2000000 2000000 0 363636.364 272727.273 363636.364 909090.9091 528925.62 604057.1 232907.5883 1423673.25 1598934.499 400000 200000 100000 400000 200000 100000 1200000 1 1735537.19 0.826446 0.751315 0.683013 409808.073 NPV 603305.785 -1502629.6 978963.186 1388771.26 528925.62 75131.4801 604057.1 819616.146 4 0 1366026.91 604057. 0.248883 388771.259 -1395942.9 IRR -0.01632 0.414214 -576326.75 598934.499 #NUM!

For project B and C, even the initial investment is not recovered. Therefore IRR is not available or its negative.

For A = 24.89% & D = 41.42%

NPV is simply the sum of PV of all cash flows(which also includes the initial investment as -ve figure)

It is, A = 388,771.26, B = -1,395,942.9, C = -576,326.75 & D = 598,934.5

Payback Period

= (The year in which cumulative PV crosses the initial investment-1) + Proportionate time in that year taken to recover upto initial investment

Therefore,

A = (4-1) + [(1000000-978963.19)/409808.07] = 3.05 years

B = NOT APPLICABLE (because initial investment is not recovered fully)

C = NOT APPLICABLE (because initial investment is not recovered fully)

D = (2-1) + [(1000000-909090.91)/826446.28] = 1.1 years

Annual Percentage Rate

(Assumed Simple average approach)

= (Total Return in all years/Initial Investment)/4

Therefore,

A = (1800000/1000000)/4 = 45%

B = (700000/2000000)/4 = 8.75%

C = (1900000/2000000)/4 = 23.75%

D = (2000000/1000000)/4 = 25%

From above, it can be said that project B and C should be COMPLETELY AVOIDED because of negative NPV and also nkt even the investment is recovered fully.

As far as A and C is concerned, C has more favourble NPV, IRR and Payback.

But that is because of higher payments in the initial years.

Although, C is favourable, it seems to be a HIGH RISK project, because in 3rd year outflow was as much as initial investment.

Therefore, decision should be taken considering the risks of both the project.

BEST OPTION SHOULD BE TO DIVERSIFY INTO BOTH PROJECTS, IF IT IS POSSIBLE.

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