Question

You are looking at a new project and need to decide if your company will want to go through with this investment.

Initial Investment = -150,000

CF year 1             =    65,000

CF year 2             =    45,000

CF year 3             =    60,000        

CF year 4             =    55,000

The rate of return on this investment is 11%.

What is the IRR & Payback

Answer 1

Solution

Calculation of Internal Rate of Return:

As we know that at IRR, Initial Outflow = Discounted Future Cash Flows.
Now, we will calculate the IRR using trial-and-error method. For our calculation, we will use 15% and 20% as the discounting factors as follows,

Years	Cash Flow	PVIF @ 15%	Discounted Cash Flow	PVIF @ 20%	Discounted Cash Flow
1	65,000.00	0.8696	56,521.74	0.8333	54,166.67
2	45,000.00	0.7561	34,026.47	0.6944	31,250.00
3	60,000.00	0.6575	39,450.97	0.5787	34,722.22
4	55,000.00	0.5718	31,446.43	0.4823	26,523.92
			1,61,445.61		1,46,662.81

Now, at IRR, Total Discounted Cash Flow should be equal to Initial Outflow. Therefore it is clear that the IRR will be somewhere in between the given rates. Assuming the IRR as "x",

(x - 15) / (20 - 15) = (150000 - 161445.61) / (146662.81 - 161445.61)
Or, (x - 15) / 5 = 11445.61 / 14782.80
Or, x - 15 = 3.8713 (Approx.)
Or, x = 18.8713

Therefore, Internal Rate of Return = 18.8713%

Calculation of Payback Period:

Payback Period is that period at which a company will recover its initial investment. Therefore, it shall be calculated as below,

Years	Cash Flow	Cumulative Cash Flow
1	65,000.00	65,000.00
2	45,000.00	1,10,000.00
3	60,000.00	1,70,000.00
4	55,000.00	2,25,000.00

Therefore, it is clear that the company will be able to recover its initial investment of 150000 in 2 to 3 years. To make an accurate calculation,

(PBP - 2) / (3 - 2) = (150000 - 110000) / (170000 - 110000)
Or, PBP - 2 = 40000 / 60000
Or, PBP - 2 = 0.667 (Approx.)
Or, PBP = 2.667

Therefore, Payback Period = 2.667 Years