Question

1. If you have the following information about an investment opportunity:
   1. Initial investment (cash out- required capital) is $ 500,000
   2. Expected operating cash inflows( after considering taxes) in year (1) $ 200,000, in year (2) $ 260,000, in year (3) $ 250,000, & in year (4) $ 150,000

Calculate the payback period, the net present value if the cost of capital is % 15%, & also calculate the internal rate of return?

Answer 1

Project B
Initial Investment		5,00,000
year	Cashflow	Cumulative Cashflow
1	2,00,000	2,00,000
2	2,60,000	4,60,000 (200000 + 260000)
3	2,50,000	7,10,000 (460000 + 250000)
4	1,50,000	8,60,000 (710000 + 150000)

Hence, in year 3 we have earned $ 460,000 of the invested $ 500,000

Remaining amount (500,000 - 460,000) $ 40,000 is to be earned in year 3

In year 3 we earn a total of $ 250,000

TO earn $ 40,000 time required = 40000 / 250000 = 0.16 year

Hence, Payback period = Year 2 + 0.16 (year 3) = 2.16 years

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NPV is given by:

NPV = L Rt/(1 + i) ,t varies from 1 ton where Rt = Cash flow netted (Inflow - Outflow) during the period "t" i = Discount rate t = number of periods

Hence,

NPV = [ 200,000 / (1 + 15%)^1] + [ 260,000 / (1 + 15%)^2] +  [ 250,000 / (1 + 15%)^3] + [ 150,000 / (1 + 15%)^4] - Initial Investment

NPV = 173913.04 + 196597.35 + 164379.06 + 85762.99 - 500,000

NPV = $ 120,652.44

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IRR is the "discount rate" at which NPV = 0

Suppose IRR = r%

so at discount rate =r, NPV = 0

NPV = 0 = [ 200,000 / (1 + r%)^1] + [ 260,000 / (1 + r%)^2] +  [ 250,000 / (1 + r%)^3] + [ 150,000 / (1 + r%)^4] - Initial Investment

0 = [ 200,000 / (1 + r%)^1] + [ 260,000 / (1 + r%)^2] +  [ 250,000 / (1 + r%)^3] + [ 150,000 / (1 + r%)^4] - 500,000

solving for r,

r = 26.81%

Hence, IRR = 26.81%

NPV = L Rt/(1 + i) ,t varies from 1 ton where Rt = Cash flow netted (Inflow - Outflow) during the period "t" i = Discount rate t = number of periods