Garage Inc. has identified the following two mutually exclusive (i.e. it can onl

Question

Garage Inc. has identified the following two mutually exclusive (i.e. it can only do one or the other but not both) projects with cash flows as outlined below. Y

Year Cash Flow(A) Cash Flow (B)

0 -$43,500 -$43,500

1 21,400 6,400

2 18,500 14,700

3 13,800 22,800

4 7,600 25,200

Without using excel-------What is the IRR for each project? Using the IRR decision rule, which project should the company select? IS this necessarily correct? If cost of capital (e.g. required return hurdle rate) is 11%, what is the NPV for each of these projects? Using the NPV rule, which project would the company select? Over what range of discount rates would the company choose project A? Project B? At what discount rate would the company be indifferent between these two projects? Explain.

Explanation / Answer

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

NPV for project A = 0= -$43500 + $21400/ (1+IRR) + $18500/(1+IRR)2 + $13800/(1+IRR)3 + $7600/ (1+IRR)4

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

$435 = $214/ (1+IRR) + $185/(1+IRR)2 + $138/(1+IRR)3 + $76/ (1+IRR)4

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

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

At 10% RHS = $503

At 15% RHS = $468.6 (this is closer to $435 so we are moving in right direction)

At 20% RHS = $423.3

Since $435 lies between $468.6 and $423.3 and closer to $423.3, we'll check for 19%, 18% 17% and 16%

At 19% RHS = $430.3

At 18% RHS = $437.4

Since $435 lies between $430.3 and $437.4 and closer to $437.4, we'll check for 18.2%, 18.4%

At 18.2% RHS = 435.96

At 18.4% RHS = 434.53

At this point it's safe to say it's 18.3%

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

DO the same for project B

NPV for project B = -$43500 + $6400/ (1+IRR) + $14700/(1+IRR)2 + $22800/(1+IRR)3 + $25200/ (1+IRR)5

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

$435 = $64/ (1+IRR) + $147/(1+IRR)2 + $228/(1+IRR)3 + $252/ (1+IRR)4

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

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

At 10% RHS = $523

At 15% RHS = $460.8 (this is closer to $435 so we are moving in right direction)

At 20% RHS = $408.8

Since $435 lies between $460.8 and $408.8 and closer to $460.8 we'll check for 16%, 17% 18%

At 16% RHS = $449.66

At 17% RHS = $438.92

Since $435 lies between $438.92 and $449.66 and closer to $438.92, we'll check for 17.2%, 17.4%

At 17.2% RHS = 436.82

At 17.4% RHS = 434.73

At this point it's safe to say it's 17.4% (17.37%)

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

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Since Project A has higher IRR of 18.3% (18.33%), 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 = -$43500 + $21400/ (1+11%) + $18500/(1+11%)2 + $13800/(1+11%)3 + $7600/ (1+11%)4

= $5891.1

NPV for project B = -$43500 + $6400/ (1+11%) + $14700/(1+11%)2 + $22800/(1+11%)3 + $25200/ (1+11%)4

=$7467.80

NPV of project B is better so company may go with project B as most firms use NPV more than IRR as NPV can take multiple discount rates unlike IRR which uses just one rate.

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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 t0 calculate crossover rate R

-$43500 + $21400/ (1+R) + $18500/(1+R)2 + $13800/(1+R)3 + $7600/ (1+R)4 = -$43500 + $6400/ (1+R) + $14700/(1+R)2 + $22800/(1+R)3 + $25200/ (1+R)4

$15000/(1+R) + 3800/(1+R)2 = 9000/(1+R)3 + 17600/(1+R)4

knock off zeroes to simplify,

$150/(1+R) + 38/(1+R)2 = 90/(1+R)3 + 176/(1+R)4

Follow the same trial and error method

at arounf 15% ~ 15.2%

Precisely at 15.1876%

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