Question

1. You have just landed your dream summer internship, and your boss asks you to analyze a project that has an investment cost of 3,500,000, to be paid today (t = 0), and will generate a cash-flow of 350,000 in the first year (t = 1). The cash-flow will then grow at 12% per year for the next eight years (the last time the cash-flow grows at 12% is from t = 8 to t = 9). Afterwards, as competition increases, cash-flow growth is expected to be only 4% per year in perpetuity. (The cash-flow grows at 4% from t = 9 to t = 10 and forever thereafter.) The discount rate is 18%.
   1. (3 points) Start by drawing the timeline, showing the cash flows at t = 0, 1, 2, 3, 8, 9, 10, 11 (the amount and how you calculated it).
   2. (10 points) What is the NPV of this project?
   3. (3 points) Do you recommend accepting or rejecting the project? Why? (Three sentences at most.)

D. (4 points) Write down the equation for the IRR of this project. (You don’t have to solve for the IRR, just write the equation whose solution is the IRR.)

Answer 1

a. Draw the timeline for the project showing the cash flows at t = 0,1,2,3,8,9,10,11
Ans.
	t=0	t=1	t=2	t=3	t=8	t=9	t=10	t=11
Cash flows	-35,00,000	3,50,000	3,92,000	4,39,040	7,73,738	8,66,587	9,01,250	9,37,300
			350000*(1+0.12)	350000*((1+0.12)^2)	350000*((1+0.12)^7)	350000*((1+0.12)^8)	866587*(1+0.04)	866587*((1+0.04)^2)
b. What is the NPV of this project?
Ans.
Assuming that the project terminates after 11 years, the NPV can be calculated as follows
Year	Cash flows		Discount rate	18%
0	-35,00,000
1	3,50,000		NPV =	-9,89,746
2	3,92,000
3	4,39,040
4	4,91,725
5	5,50,732
6	6,16,820
7	6,90,838
8	7,73,738
9	8,66,587
10	9,01,250
11	9,37,300
NPV has been calculated using the excel formula taking the rate as 0.18 and the values as calculated above from B13 to B23 and adding the cash outlow at B12 to the formula answer
c. Do you recommend accepting or rejecting the project? Why?
Ans.
If the NPV is to be calculated assuming that the project will generate cash flows till perpetuity, then the
NPV can be calculated as follows
NPV = C/r-g
where C is the cash flow per year, r is the discount rate and g is the growth rate per year
Substituting in the above formula we get
NPV =	61,89,907
866587/(0.18-0.04)
The project can be accepted only if the cash flows are received in perpetuity.
If the project is assumed to have a finite life say 11 years as calculated above then it is having negative NPV
and hence it is not recommended to accept the project.
d. Write down the equation for the IRR of this project.
Ans.
IRR is the discount rate at which the NPV of the project becomes 0.
The equation for obtaining IRR of the given project can be written as follows :-
- 35,00,000 + 350,000/(1.12)^1 + 350,000/(1.12)^2 + ..... + 350,000*(1.12)^8 + 866587*(1.04)^1 + 866587*(1.04)^2 + ............ = 0