Question

The net present value (NPV) and Internal rate of retur (IRR) methods of investment analysis are interrelated and are sometimes used together to make capital budgeting decisions. Consider the case of Blue Hamster Manufacturing Inc.: Last Tuesday, Blue Hamster Manufacturing Inc. lost a portion of its planning and financial data when both its main and its backup servers crashed. The company's CFO remembers that the internal rate of return (IRR) of Project Zeta is 13.8%, but he can't recall how much Blue Hamster originally invested in the project nor the project's net present value (NPV). However, he found a note that detailed the annual net cash flows expected to be generated by Project Zeta. They are: Year Year 1 Year 2 Year 3 Year 4 Cash Flow $1,800,000 $3,375,000 $3,375,000 $3,375,000 The CFO has asked you to compute Project Zeta's initial investment using the information currently available to you. He has offered the following suggestions and observations: • A project's IRR represents the return the project would generate when its NPV is zero or the discounted value of its cash inflows equals the discounted value of its cash outflows-when the cash flows are discounted using the project's RR. • The level of risk exhibited by Project Zeta is the same as that exhibited by the company's average project, which means that Project Zeta's net cash flows can be discounted using Blue Hamster's 10% WACC.

Answer 1

NPV is given by:

NPV = L Rt/(1 + i) ,t varies from 1 ton where Rt = Cash flow netted (Inflow - Outflow) during the period "t" i = Discount rate t = number of periods

Now, the discount rate at which NPV = 0 is known as IRR

For project Zeta,

IRR = 13.8%

Hence,

NPV (at i = 13.8%) = 0

Hence,

[ 18,00,000 / ( 1 + 13.8%)^¹ ] + [ 33,75,000 / ( 1 + 13.8%)^² ] + [ 33,75,000 / ( 1 + 13.8%)^³ ] +[ 33,75,000 / ( 1 + 13.8%)^⁴ ] - Initial Investment = 0  

Initial Investment = 1581722.32 + 2606089.06 + 2290060.68 + 2012355.61

Initial Investment = $ 8490227.675 = $ 8490228

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Calculating NPV at i = 10%

Hence,

[ 18,00,000 / ( 1 + 10%)^¹ ] + [ 33,75,000 / ( 1 + 10%)^² ] + [ 33,75,000 / ( 1 + 10%)^³ ] +[ 33,75,000 / ( 1 + 10%)^⁴ ] - Initial Investment = NPV

NPV = 1636363.64 + 2789256.20 + 2535687.45 + 2305170.41 - 8490227.675

NPV = $ 776250.02

SUM X fx =IRR(C3:07) B Discount Rate Year 10% Project A -$84,90,227.68 $18,00,000 $33,75,000 $33,75,000 $33,75,000! =IRR( C3:07) IRR

SUM fx =NPV(C1,C4:C7)+ Discount Rate Year 10%) Project A -$84,90,227.68 $18,00,000 $33,75,000 $33,75,000 $33,75,000 13.80% =NPV(C1, C4:07 )+ C3 3 IRR NPV

09 E Year Bodvouwn , fx =NPV(C1,C4:07)+C3 в C D Discount Rate 10% Project A -$84,90,227.68 $18,00,000 2 $33.75.000 3. $33,75,000 4 $33,75,000 IRR 13.80% $7,76,250.02 AWN NPV

1. Initial Investment = $ 8490227.675 = $ 8490228

2.  NPV (at 10% discount rate) = $ 776250.02

3. Project's IRR will INCREASE is cash inflows increases.