What is the payback period of this investment?
The cash flow timeline for this problem is shown below: Year 0 1 2 3 4 5 6 Cash Flow ($million) -10.4 0 4.6 2.1 2.1 2.1 2.1 The payback period is 4.8 years. Based on the payback period requirement, would you make this movie? No What is the NPV of the movie if the cost of capital is 10.2%? The NPV of the project is: C2 1 1 1 NPV = -Co + ------------ + C x ----- 1 - -------------- x ------------- (1 + r)2 r (1+r)4 (1 + r)2 The NPV is -1.54. Problem 7 ou are deciding between two mutually exclusive investment opportunities. Both require the same initial investment of $10.3 million. Investment A will generate $2.16 million per year (starting at the end of the first year) in perpetuity. Investment B will generate $1.52 million at the end of the first year, and its revenues will grow at 2.9% per year for every year after that. a. Which investment has the higher IRR? b. Which investment has the higher NPV when the cost of capital is 6.8%? a. Which investment has the higher IRR? Here is the cash flow timeline: Year 0 1 2 3 Cash Flow A ($M) -10.3 2.16 2.16 2.16 Cash Flow B ($M) -10.3 1.52 1.52(1.029) 1.52(1.029)^2 To calculate the IRR we solve r . C NPV =0= ----------- - Co r-g The IRR of investment A is 21% The IRR of investment B is 17% Which Project has the higher IRR? A
b. Which investment has the higher NPV when the cost of capital is 6.8%? The NPV is given by: C NPV = --------- - Co r -g The NPV of investment A is $21.46 million. The NPV of investment B is 28.67 million. You should pick investment B. Problem 8 Ranking by IRR will work in this case so long as the project have the same risk Problem 9 AOL is considering two proposals to overhaul its network infrastructure. They have received two bids. The first bid from Huawei will require a $20 million upfront investment and will generate $20 million in savings for AOL each year for the next 3 years. The second bid from Cisco requires a $83 million upfront investment and will generate $60 million in savings each year for the next 3 years. a. What is the IRR for AOL associated with each bid? b. If the cost of capital for each investment is 18%, what is the net present value (NPV) of each bid? Suppose Cisco modifies its bid by offering a lease contract instead. Under the terms of the lease, AOL will pay $25 million upfront, and $35 million per year for the next 3 years. AOL's savings will be the same as with Cisco's original bid. c. What is the IRR of the Cisco bid now? d. What is the new NPV? e. What should AOL do? a. What is the IRR for AOL associated with each bid? Modeling the cash flows with a timeline, we have: Time 0 1 2 3 CF Huawei -20 20 20 20 And for Cisco we have: Time 0 1 2 3 CF Cisco -83 60 60 60
The net present value (NPV) is the sum of the discounted cash flows at time 0. To find the internal rate of return (IRR), set the NPV equal to 0 and solving for r : n Ct NPV = 0 = ∑ --------------- t=0 (1+R)t where C t is the cash flow at time t. The IRR associated with the first bid from Huawei is 84%. The IRR associated with the Cisco opportunity is 51.5%.
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