Question

The internal rate of return for an investment with contributions of $3,000 at time 0 and $1,000 at time 1 and returns of $2,000 at time 1 and $4,000 at time 2 can be expressed as 1/ n . Find n.

Answer 1

Solution:

Given:

Contribution for 0 Year = $ 3000

Contribution for 1 Year = $ 1000

Return at 1 Year = $ 2000

Return at 2 Year = $ 4000

Internal Rate of Return (IRR) = 1/n

To Calculate:

The value of ‘n’ using IRR and NPV (Net Present Value) Formula.

Formula:

NPV = ∑         Ct           -     Co

                    (1+ IRR) t

Where:

NPV= Net Present Value of Investment

Ct= Total Net Cash Flows during given time period t

Co= Total Cost of Initial Investment

t = Time Period

IRR= Internal Rate of Return

Tabulation of the given data:

Time Period	Contribution	Returns	Net Cash Flow = Returns - Contribution
0	$ 3000	0	0000 - 3000 = -3000
1	$1000	$ 2000	2000 - 1000 = 1000
2	0	$ 4000	4000 – 0000 = 4000
Total	Total Initial Investment $ 4000	Total Cash Flow $ 6000	Total Net Cash Flow $ 2000

Here, Total Cash Flow = $ 6000

Total Initial Investment = $ 4000

Total Net Cash Flow = $ 2000

t = 2 Years

IRR = 1/n

On putting the value in the following Formula, we get,

NPV = ∑         Ct           -     Co

                    (1+ IRR) t

= 6000     - 4000

(1+ 1/n)2

= 6000/ (n+1/n)2 – 4000

4000n2 = 6000/ n2+2n+1

4000 = 6000/ n2 (2n+1)/n2

4000= 6000/3n

3n = 6000/4000

n = 1.5/3

Ans: n = 0.5 or 50%

Alternate Method:

The value of ‘n’ using Return on Investment (ROI) Formula:

Return on Investment = Total Return – Total Investment × 100

                                              Total Investment

Here,

Total Investment = $ 3000 + $ 1000 = $ 4000

Total Return = $ 2000 + $ 4000 = $ 6000

On putting the value in the Formula, we get,

ROI= $6000-$4000 ×100

              $ 4000

= 2000/4000 × 100

= 0.5 or 50 %

Ans: n = 0.5 or 50%