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Consider the following projects, X and Y where the firm can only choose one. Project X costs $600 and has cash flows of $400 in each of the next 2 years. Project Y also costs $600, and generates cash flows of $500 and $275 for the next 2 years, respectively. Sketch a net present value profile for each of these projects. Which project should the firm choose if the cost of capital is 10 percent? What if the cost of capital is 25 percent? Show all work.

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Answer:

If the cost of capital is 10 percent, firm should choose project X

If the cost of capital is 25%, choosing project X or Y is similar and not profitable.

Explanation:

  • The formula to calculate the present value of the project in year n is:

+) PVn = Cash flow/ [(1 + k)^n]

In which, k is the cost capital

  • The net present value of project at year n is calculated as following

+) NPV = PV1 - Initial investment (cost of project) + PV2 +... + PVn

(PV1 - present value in year 1; PVn - prsent value in year n)

1) Cost of capital is 10 percent => k = 0.1

Project X:

+ In Year 1, the cash flow is $400

=> The present value of project X in year 1 is: PV1 = 400/ (1 + 0.1)^1 = $363.64

+ In Year 2, the cash flow is $400

=> The present value of project X in year 2 is: PV2 = 400/[(1+0.1)^2]= $330.58

+ The net present value of project X in year 2 is:

NPVx = PV1 - Cost + PV2 = 363.64 - 600 + 330.58 = $94.22

Project Y:

+ In Year one, the cash flow is $500

=> The present value in year 1 is: PV1 = 500/ (1 + 0.1)^1 = $454.55

+ In Year 2, the cash flow is $275

=> The present value in year 2 is: PV2 = 275/[(1+0.1)^2]= $227.27

+ The net present value of project X in year 2 is:

NPVy = PV1 - Cost + PV2 =  454.55 - 600 + 227.27 = $81.82 < NPVx

=> If the cost of capital is 10 percent, firm should choose project X

2) Cost of capital is 25 percent => k = 0.25

Project X:

+ In Year 1, the cash flow is $400

=> The present value in year 1 is: PV1 = 400/ (1 + 0.25)^1 = $320

+ In Year 2, the cash flow is $400

=> The present value in year 2 is: PV2 = 400/[(1+0.25)^2]= $256

+ The net present value of project X in year 2 is:

NPVx = PV1 - Cost + PV2 = 320 - 600 + 256 = - $24

Project Y:

+ In Year one, the cash flow is $500

=> The present value in year 1 is: PV1 = 500/ (1 + 0.25)^1 = $400

+ In Year 2, the cash flow is $275

=> The present value in year 2 is: PV2 = 275/[(1+0.25)^2]= $176

+ The net present value of project X in year 2 is:

NPVy = PV1 - Cost + PV2 =  400 - 600 + 176 = -$24 = NPVx

=> If the cost of capital is 25%, choosing project X or Y is similar and not profitable.

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