Question

New Futuristics Company is thinking about marketing a new software product. Upfront costs to market and develop the product are $10 million. Starting in year 1, the product is expected to generate Free Cash Flows of $1.5 million per year for 15 years. The company will have to provide product support expected to cost $200,000 per year in perpetuity, which have not been included in the FCF just mentioned. Assume all cash flows (except for the upfront costs) occur at the end of each year. (a) What is the net present value (NPV) of this investment if the cost of capital is 5%? Should the firm undertake the project? (b) Repeat the analysis for discount rates of 1% and 15%. Should the company undertake the project in these two cases? (c) What is the payback period of the project? (Note: You only need to consider the upfront costs in this calculation) (d) How many IRRs does this investment opportunity have? (Hint: Plot the project NPV as a function of the discount rate, i.e. creating a graph which shows what the NPV is for a broad range of discount rates) (e) Can the IRR rule be used to evaluate this investment? Explain.

Answer 1

S.No.	Given:	Values
1	Initial Investment in year 0 (Cf 0)	$ 1,00,00,000
2	Annual Free Cash Flows for 15 years (Annuity , i.e, Cfn=1-15)	$ 15,00,000
3	Period of Free Cash Flows for evaluation "n"	15
4	Product Support per year Cfn	$ 2,00,000
5	Time frame for Product Support "n"	Perpetuity
Q (a)	Cost of Capital / Discount Rate "r"	5%
A	Formula for assessing Present Value of Profits PV Profits	Cf/r*(1-(1/(1+r)^n))
	and
B	Formula for assessing Present Value of Support Cost PV Support	Cash Flow per year/ r
	Therefore, Net Present Value (NPV) = - Initial Investment + PV Profit +PV Support
	Substituting for values of "n" and "r", we get:
=>	NPV = -10000000+1500000/5%*(1-(1/(1+5%)^15)) - 200000/5%
=>	NPV= -1,0000,000+30,000,000*(1-(1/(2.078928))-4,000,000
=>	NPV= -10,000,000+30,000,000*(1-0.481017)-4,000,000
=>	NPV= -10,000,000+30,000,000*(0.518982902)-4.000,000
=>	NPV= -10,000,000+15,569,487.06-4.000,000
=>	NPV=5,569,487.06 - 4,000,000
=>	NPV = $1,569,487
Answer (a)	Since, the Net Present Value is positive, the project should be accepted.

Q (b)
i.	Cost of Capital "r"	1%
ii.	Cost of Capital "r"	15%
i)	Cost of Capital "r"	1%
	Net Present Value (NPV) = - Initial Investment + PV Profit +PV Support
	Substituting for values of "n" and "r", we get:
=>	NPV = -10000000+1,500,000/1%*(1-(1/(1+1%)^15)) - 200000/1%
=>	NPV= -1,0000,000+150,000,000*(1-(1/(1.160968955))-20,000,000
=>	NPV= -10,000,000+150,000,000*(1-0.861349475)-20,000,000
=>	NPV= -10,000,000+150,000,000*(0.138650525)-20,000,000
=>	NPV= -10,000,000+20,797,578.78-20,000,000
=>	NPV = -9,202,421
ii)	Cost of Capital "r"	15%
	Net Present Value (NPV) = - Initial Investment + PV Profit +PV Support
	Substituting for values of "n" and "r", we get:
=>	NPV = -10000000+1,500,000/15%*(1-(1/(1+15%)^15)) - 200000/15%
=>	NPV= -1,0000,000+10,000,000*(1-(1/(8.137061629))-1,333,333.33
=>	NPV= -1,0000,000+10,000,000*(1-(0.122894485))-1,333,333.33
=>	NPV= -1,0000,000+10,000,000*(0.877105515)-1,333,333.33
=>	NPV= -1,0000,000+8,771,055.148-1,333,333.33
=>	NPV = $ -2,562,278
Q (b) Answer	Since, the Net Present Value (NPV) at Cost of Capital = 1% and 15% are negative, the project should be rejected.

Q (c )
S.No.	Given:	Values
1	Initial Investment in year 0 (Cf 0)	1,00,00,000
2	Annual Free Cash Flows for 15 years (Annuity , i.e, Cfn=1-15)	15,00,000
4	Product Support per year Cfn	To be ignored
5	Time frame for Product Support "n"	To be ignored
	Payback period = Initial Investment / Annual Cash Flows
=>	10,000,000/1,500,000	6.67
=>	or 10,000,000/1,500,000 * 12	or 80 months
Answer	Pay Back Period	or 6 years and 8 months
	Payback (rounded off)	7 years

Q (d)

The Internal Rate of Return can be defined as the rate at which the Net Present Value (NPV) of Cash Flows equals Zero.

IRR is the value of "r" in the following equation, viz.,

NPV = -10,000,000+1,500,000/ IRR% *(1-(1/(1+IRR%)^15)) - 200,000/ IRR%

Through trial and error, we find that there are two rates (two IRR), i.e,, 2.238561% and 8.7198590% at which the NPV is approximately equal to 0. This has to be done graphically. (Not able to copy the graph on to screen)

Answer : The project has two IRR, viz., 2.238561% and 8.7198590% (See Table pasted below showing value of NPV for different values of IRR)

Q (e)

Since there are two (2) Internal Rate of Return (IRR) for this project (see Q (d) above), the IRR rule cannot be used to evaluate the investment. As per the IRR rule, the project can be accepted if, and only if, the IRR exceeds the project's cost of capital. It can be observed that at 1% and 15%, the NPV is negative (refer question b); and at 5% (refer question a), it is positive. If we plot the values of NPV at different rates of discounts mentioned above on a graph, we will see that the NPV is positive between 2.238561% and 8.7198590%

Answer : The project can be accepted when the Net Present Value (NPV) is positive. In this case, where the IRR is between 2.238561% and 8.7198590% (see working Note below tabulating NPV for different values of IRR/ Discount rate).

Working Note for Questions (d) and (e)

Q (d)	Table of Values showing the value of NPV for different Values of IRR	Discount Rate (IRR)	NPV
	Where, Discount rate "r" is	10.00%	-5,90,880.74
	Where, Discount rate "r" is	9.00%	-1,31,189.58
	Where, Discount rate "r" is	8.85%	-61,039.38
	Where, Discount rate "r" is	8.78%	-28,226.08
	Where, Discount rate "r" is	8.76%	-18,842.75
	Where, Discount rate "r" is	8.74%	-9,456.00
	Where, Discount rate "r" is	8.72%	-65.94
	Where, Discount rate "r" is	8.719%	403.65
	Where, Discount rate "r" is	8.7195%	168.86
	Where, Discount rate "r" is	8.7198590%	0
	Where, Discount rate "r" is	7.00%	8,04,728.15
	Where, Discount rate "r" is	6.00%	12,35,040.15
	Where, Discount rate "r" is	4.00%	16,77,581.15
	Where, Discount rate "r" is	3.50%	15,61,830.63
	Where, Discount rate "r" is	3%	12,40,235.96
	Where, Discount rate "r" is	2.50%	5,72,066.59
	Where, Discount rate "r" is	2.40%	3,76,089.66
	Where, Discount rate "r" is	2.30%	1,52,612.35
	Where, Discount rate "r" is	2.25%	29,359.38
	Where, Discount rate "r" is	2.24%	3,718.94
	Where, Discount rate "r" is	2.238561%	0
	Where, Discount rate "r" is	2.238%	-1,449.89
	Where, Discount rate "r" is	2.235%	-9,228.76
	Where, Discount rate "r" is	2.23%	-22,262.24
	Where, Discount rate "r" is	2.22%	-48,588.94
	Where, Discount rate "r" is	2.21%	-75,266.04
	Where, Discount rate "r" is	2.20%	-1,02,298.51