Question

A wine lover has decided to start a winery. The initial investment will be $5 million on Day 1. The winery will require an additional $1 million dollars investment at very beginning Year 1. The vines will mature over five years. Beginning at the end of year 6, the winery is expected to produce net cash inflows of $2 million, 4 mil in year 7, 6 mil in year 8, 8 mil in year 9 and 10 mil in year 10. What is the NPV, IRR, and Payback (nondiscounted and discounted) assuming a discount rate of 15 percent? Please give IRR, NNPV, Payback Period, Discount Payback Period (show formulas please)

Answer 1

(All figures are in Millions of Dollars)

NPV = present value of all cash flows associated with the project

= -5 -1 + 2/1.15^6 + 4/1.15^7 + 6/1.15^8 + 8/1.15^9+ 10/1.15^10

= 3.07576

So, NPV = $3.07576 million

THe IRR is given by the discount rate (r) for which NPV = 0

-5 -1 + 2/(1+r)^6 + 4/(1+r)^7 + 6/(1+r)^8 + 8/(1+r)^9+ 10/(1+r)^10 = 0

Using hit and trial method

Putting r = 20% =0.2 , the left hand side of the above equation = 0.34704

Putting r= 21% = 0.21, the left hand side of the above equation = -0.07833

So the value of r for which LHS of equation =0 , lies between 0.20 and 0.21

Using Linear approximation method, the approximate value of r is given by

r= 0.20+ (0.34704-0)/(0.34704-(-0.07833)) * (0.21-0.20) = 0.208159

Putting r = 0.208159 , the left hand side of the above equation = -0.00251

Putting r = 0.2081, the left hand side of the above equation = -0.000086

So, IRR = 20.81%

Payback period is the period in which Cumulative cashflows equals/exceeds zero and

discounted Payback period is the period in which discounted Cumulative discounted cashflows equals/exceeds zero

The table below gives the Cumulative Cashflows and Discounted Cumulative Cashflows

year	Cash	Discounted Cash flows	Cumulative Cash flows	Cumulative Discounted Cash flows
0	-6	-6	-6	-6
1	0	0	-6	-6
2	0	0	-6	-6
3	0	0	-6	-6
4	0	0	-6	-6
5	0	0	-6	-6
6	2	0.864655192	-4	-5.135344808
7	4	1.50374816	0	-3.631596648
8	6	1.961410643	6	-1.670186005
9	8	2.274099296	14	0.603913291
10	10	2.471847061	24	3.075760352

From the table, it can be seen that the cumulative Cashflows is 0 in the year 7

So, Payback period = 7 years

From the table, it can be seen that the cumulative Discounted Cashflows exceeds 0 in the year 9

So, Discounted Payback period = 9 years