Question

If the applicable discount rate is 15%, what is the NPV of the following investment? Round to the nearest cent. The project is expected to cost $81,000 immediately, and generate the following annual cash flows: Year 1: $29,000 Year 2: $35,000 Year 3: $64,000 Year 4: $21,000

You want to start an organic garlic farm. The farm costs $300,000, to be paid in full immediately. Year 1 cash flows will be $36,000, and grow at 6% a year into year 5 when you decide to sell the farm at the end of the year for $360,000. Assuming these estimates are all correct, what is the IRR of the garlic farm investment? Round to the tenth of a percent (eg 5.6%=5.6). [Hint: You'll want to solve this in Excel using Goal Seek]

Answer 1

1.

Discount rate	15.000%
Year	0	1	2	3	4
Cash flow stream	-81000.000	29000.000	35000.000	64000.000	21000.000
Discounting factor	1.000	1.150	1.323	1.521	1.749
Discounted cash flows project	-81000.000	25217.391	26465.028	42081.039	12006.818
NPV = Sum of discounted cash flows
NPV 0 =	24770.28
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

2.

IRR is the rate at which NPV =0	0
IRR	16.19%
Year	0	1	2	3	4	5
Cash flow stream	-300000.000	36000.000	38160.000	40449.600	42876.576	405449.171
Discounting factor	1.000	1.162	1.350	1.569	1.823	2.118
Discounted cash flows project	-300000.000	30982.973	28265.036	25785.526	23523.527	191442.938
NPV = Sum of discounted cash flows
NPV 0 =	-1.36119E-07
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	16.19%

Where,

Year 2 cash flow = year 1 cash flow *(1 + growth rate) = 36000*(1+0.06)

Year 3 cash flow = year 2 cash flow *(1 + growth rate) = 36000*(1+0.06)

Year 4 cash flow = year 3 cash flow *(1 + growth rate) = 36000*(1+0.06)

Year 5 cash flow = year 4 cash flow *(1 + growth rate) + proceeds from sale = 36000*(1+0.06)^2 + 360000