Question

Mumbai
Operating income	1,100,000
Depreciation	250,000	(5,000,000/20yr)
Net income b4 tax	850,000
Taxes @ 40%	340,000	(850,000*.40)
Net income	510,000
ROI	20%	(510000/2500000)
Mumbai	Year 0	Year 1	Year 2
Cashflow		510,000	510,000
Present Value	4,655,558	4,564,559	4,465,369
Initial Investment	(5,000,000)	(5,000,000)	(5,000,000)
NPV	(344,442)	(435,441)	(534,631)
	Year 0	Year 1	Year 2
Cashflow	(5,000,000)	510,000	510,000
IRR	8%	?	?
help w/IRRR & NPV for yr 1 & 2

Answer 1

Solution:-

IRR can be calculated manually without the use of software or excel then you must use the trial and error method. As per the theory, it says that the rate of return that will give an NPV is also equal to zero.

As mentioned in the question, IRR for Year 0 is 8%. So we are guessing the IRR for year 1 should nearly 8%. Still to confirm the exact IRR for Year 1. We will calculate IRR by using the following formula.

0 = NPV = CF₀ - T∑(t-1)CF_n

(1+r)ⁿ

NPV = Net present vaue.

CF₀ = Initial Investment.

CF_n = Cash Inflow for n no. of the period.

r = IRR

n = No. of the project years (As per the question, it is 20 years)

a. Calculate of IRR for Year 1

From the above theory, we are considering NPV =0 while calculating IRR

Let's guess IRR= 8%

0 = 5,000,000- t∑(t-1)(510,000)

(1+.08)²⁰

= 5,000,000- 5007255 (Please consider Note 1 for the calculation of $ 5,007,225)

=7,255

$7,255 is not close to zero, thus 8% is not IRR.

Let's guess IRR=8.02%

0= 5,000,000- t∑(t-1)(510000)

(1+.0802)²⁰

= 5,000,000- 4999811.54 (Please consider Note 1 for the calculation of $ 4,999,881.54)

=188.46

$ 188.46 is very close to zero, thus we are considering 8.02% as IRR for Year 1.

a. Calculate of IRR for Year 2

Let's guess IRR= 9.00%

0= 5,000,000-510000 - t∑(t-1)(510000)

(1+0.802)¹ (1+.09)¹⁹

0 = 5,000,000- 472134 - t∑(t-1)(510000)

   (1+.09)¹⁹

0 = 4527865 - t∑(t-1)(510000)

   (1+.09)¹⁹

= 4527865 - 4564558 ((Please consider Note 1 for the calculation of $ 4,564,558)

= 36693

$36,693 is not close to zero, thus, 9 % is not IRR.

Let's guess, IRR = 9.13%

0= 5,000,000-510000 - t∑(t-1)(510,000)

(1+0.802)¹ (1+.0913)¹⁹

0 = 5,000,000- 472134 - t∑(t-1)(510,000)

   (1+.0913)¹⁹

0 = 4527865 - t∑(t-1)(510,000)

   (1+.0913)¹⁹

= 4527865 -4523892 (Please consider Note 1 for the calculation of $ 4,523,892)

= 3972

$3,972 is very close to zero, thus 9.13% is IRR for year 2.

Working Notes

1:- Calculation of how we calculate $ $ 5,007,225.

= t∑(t-1)(510,000)

(1+.08)²⁰

^{We have to calculate the factor of 8% which is equal to 9.8181147}

^{Then we have multiple 510,000 with the Pv factor of 8% i.e 9.8181147}

^{= 510000* 9.8181147}

^=5,007,255

Similarily we have calculated the factor of 8.02%, 9% & 9.13% and get the figure of $ 4,999,881.54,$ 4,564,558 & $ 4,523,892 respectively.

Formula to calculate PV Factor= ∑ 1

   (1+r)ⁿ