Question

You are CEO of Rivet​ Networks, maker of​ ultra-high performance network cards for gaming​ computers, and you are considering whether to launch a new product. The​ product, the Killer​ X3000, will cost $ 903 comma 000 to develop up front​ (year 0), and you expect revenues the first year of $ 798 comma 000 ​, growing to $ 1.46 million the second​ year, and then declining by 45 % per year for the next 3 years before the product is fully obsolete. In years 1 through​ 5, you will have fixed costs associated with the product of $ 102 comma 000 per​ year, and variable costs equal to 45 % of revenues.    a. What are the cash flows for the project in years 0 through​ 5? b. Plot the NPV profile for this investment using discount rates from​ 0% to​ 40% in​ 10% increments. c. What is the​ project's NPV if the​ project's cost of capital is 9 % ​? d. Use the NPV profile to estimate the cost of capital at which the project would become​ unprofitable; that​ is, estimate the​ project's IRR.

Answer 1

a)

Particulars	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5
Outflow (A)	-9,03,000	-	-	-	-	-
Revenues (B)	-	7,98,000	14,60,000	8,03,000	4,41,650	2,42,908
Fixed Costs (C)	-	1,02,000	1,02,000	1,02,000	1,02,000	1,02,000
Variable Costs (D = 45% of A)	-	3,59,100	6,57,000	3,61,350	1,98,743	1,09,308
Total Cash flow (E = A+B-C-D)	-9,03,000	3,36,900	7,01,000	3,39,650	1,40,908	31,599

As we can see from the table above, the revenues are calculated based on the assumptions given in the question. So from year 3 we have derived revenues as 55% of the previous year (45% reduced revenues each year)

b)

The profile can be drawn based on the inputs provided.

So first we will take the discount rates from 0% to 40% in steps of 10% increments. Then we will use the NPV formula in excel. The NPV formula has following inputs NPV(rate, value1, value2, value3, ...). So here we will input rate as per each step and value1 = Cash flow in year 0 = -903,000 and so on from the table above.

c) Project's NPV if cost of capital is 9%

NPV = CF₀ + (CF₁ / ((1 + r)ⁿ)) + (CF₂ / ((1 + r)ⁿ⁺¹)) + (CF₃ / ((1 + r)ⁿ⁺²)) + (CF₄ / ((1 + r)ⁿ⁺³)) + (CF₅ / ((1 + r)ⁿ⁺⁴))

Here CF₀ = cash flow in year 0 from the table above, CF₁ = cash flow in year 1 from the table above and so on. n = year, r = cost of capital

NPV = -903,000 + (3,36,900 / ((1 + 9%)¹))) + (7,01,000 / ((1 + 9%)²))) + (3,39,650 / ((1 + 9%)³))) + (1,40,908 / ((1 + 9%)⁴))) + (31,599 / ((1 + 9%)⁵)))

NPV = -903,000 + (3,36,900 / 1.09) + (7,01,000 / 1.1881) + (3,39,650 / 1.2950) + (1,40,908 / 1.4116) + (31,599 / 1.5386)

NPV = -903,000 + 3,09,082.57 + 5,90,017.68 + 2,62,272.12 + 99,822.43 + 20,537.26

NPV = 3,78,732.052

d) IRR is the rate at which the NPV of the project is zero.

Using the NPV profile we can find the from the graph that at what discount rate, the NPV is zero.

You can also IRR function in excel to find the discount rate at which the NPV is zero.

In this you just have to input all the cash flows from the table above and it returns you the IRR of the project.

By doing this we can arrive at the discount rate of 28.81%