15.)ZZZ Best (ZZZ) flows shown below is considering two mutually exclusive proje

Question

15.)ZZZ Best (ZZZ) flows shown below is considering two mutually exclusive projects with the annual cash 300000 200000 100000 75000 -500000 100000 250000 300000 CF 1 CF 2 CF 3 IRR of Project NPV @ 8% Discount Rate NPV @ 1 1% Discount Rate Cross Over Point NPV at Point of Indifference What is the IRR of each project? IRRAIRR B razz's required rate of return for these projects is 8% which project should it choose based on NPV? which project should it choose if the required rate of return is 11% based on NPV? At what required rate of return should it be indifferent to the choice of projects, based solely on their NPV (crossover point)? What is the NPV of each project at the point of indifference? What is the highest discount rate at which at least one of the two projects should not be rejected? 5 of 8

Explanation / Answer

IRR is the rate at which NPV of the project becomes 0.

NPV for project A = 0= -$300000 + $200000/ (1+IRR) + $100000/(1+IRR)2 + $75000/(1+IRR)3 +

Put NPV = 0 and to simplify th eequaion knock off two zeroes from all the numbers

$300 = $200/ (1+IRR) + $100/(1+IRR)2 + $75/(1+IRR)3 +

Value of IRR can only be solved by trial and error if not excel

Excel using function = IRR(cashflows) gives a value of IRR = 14.72% for given cash flow for project A

Let's keep IRR= 10%, 15% and 20% and see at what value both sides almost equalize

At 10% RHS = $320.8

At 15% RHS = $298.8 (this is closer to $300 so we are moving in right direction)

At 20% RHS = $279.51

Since $300 lies between $320.8 and $279.51 and closer to $298.8, we'll check for 14.7% 14.8% and 14.9% to see which one brings us closer to 300

At this point it's safe to say it's 14.72%

You can solve for more decimal points by taking values in between

Do the same for project B

NPV for project A = 0= -$500000 + $100000/ (1+IRR) + $250000/(1+IRR)2 + $300000/(1+IRR)3

Put NPV = 0 and to simplify th eequaion knock off two zeroes from all the numbers

$500 = $100/ (1+IRR) + $250/(1+IRR)2 + $300/(1+IRR)3

Value of IRR can only be solved by trial and error if not excel

Excel using function = IRR(cashflows) gives a value of IRR = 12.21% for given cash flow for project B

Let's keep IRR= 10%, 15% and 20% and see at what value both sides almost equalize

At 10% RHS = $522.9   (this is closer to $500 so we are moving in right direction)

At 15% RHS = $473.247

Since $500 lies between $522.9 and $473.25 and closer to $522.9, we'll check for 11% 12% and 13% to see which one brings us closer to 500

Reiterations will give us 12.21% as the value that balances LHS and RHS correct

You can solve for more decimal points by taking values in between

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Since Project A has higher IRR of 14.72% , company will be inclined to select this project because it gives better returns for given cost of capital.

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NPV for project A = -$300000 + $200000/ (1+8%) + $100000/(1+8%)2 + $75000/(1+8%)3

= $30456.48

NPV for project B = -$500000 + $100000/ (1+8%) + $250000/(1+8%)2 + $300000/(1+8%)3

= $45076.96

At 8% B has has NPV, so ZZZs should choose B.

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NPV for project A = -$300000 + $200000/ (1+11%) + $100000/(1+11%)2 + $75000/(1+11%)3

=$16181.77

NPV for project A = -$500000 + $100000/ (1+11%) + $250000/(1+11%)2 + $300000/(1+11%)3

=$12353.11

NPV of project A is better so company may go with project A

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At crossover rate, that is rate at which NPV of project A and B become equal, companies will be indifferent between these projects

Equate NPV of project A = NPV of project B to calculate crossover rate R

-$300000 + $200000/ (1+R) + $100000/(1+R)2 + $75000/(1+R)3  = -$500000 + $100000/ (1+R) + $250000/(1+R)2 + $300000/(1+R)3

knock off zeroes to simplify,

-$300 + $200/ (1+R) + $100/(1+R)2 + $75/(1+R)3  = -$500 + $100/ (1+R) + $250/(1+R)2 + $300/(1+R)3

$200 + $100/(1+R) -$150/(1+R)2 - $225/(1+R)3 = 0

Follow the same trial and error method

For shortcut you can just take the coefficients and treat them as cashflows and use =IRR(cashflows) function in excel

That gives an answer = 10.35% as crossover rate

10.35%

For 5th question, You can calculate NPV of A and B at 10.35% for each of them

-300000 -500000 200 200000 100000 100 100000 250000 -150 75000 300000 -225 14.72% 12.21%

10.35%

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