Question

Please show and explain work- simplified

3. Your division is considering two investment projects, each of which requires an up-front expenditure of 20 million. You estimate that the investment will produce the following net cash flows: Year Project A Project B 1 $5,000,000 $20,000,000 2 10,000,000 10,000,000 3 20,000,000 6,000,000 a. What are the two project’s net present values, assuming the cost of capital is 5%? 10%? 15%? b. What are the two projects’ IRRs at these same costs of capital? Show your work.

Answer 1

Project A:

Cash Flows:
Year 0 = -$20,000,000
Year 1 = $5,000,000
Year 2 = $10,000,000
Year 3 = $20,000,000

Calculation of Net Present Value:

If Cost of Capital is 5%:

NPV = -$20,000,000 + $5,000,000/1.05 + $10,000,000/1.05^2 + $20,000,000/1.05^3
NPV = $11,108,951.52

If Cost of Capital is 10%:

NPV = -$20,000,000 + $5,000,000/1.10 + $10,000,000/1.10^2 + $20,000,000/1.10^3
NPV = $7,836,213.37

If Cost of Capital is 15%:

NPV = -$20,000,000 + $5,000,000/1.15 + $10,000,000/1.15^2 + $20,000,000/1.15^3
NPV = $5,059,587.41

Calculation of Internal Rate of Return:

Let IRR be i%

NPV = -$20,000,000 + $5,000,000/(1+i) + $10,000,000/(1+i)^2 + $20,000,000/(1+i)^3
0 = -$20,000,000 + $5,000,000/(1+i) + $10,000,000/(1+i)^2 + $20,000,000/(1+i)^3

Using financial calculator, i = 26.73%

IRR = 26.73%

Project B:

Cash Flows:
Year 0 = -$20,000,000
Year 1 = $20,000,000
Year 2 = $10,000,000
Year 3 = $6,000,000

Calculation of Net Present Value:

If Cost of Capital is 5%:

NPV = -$20,000,000 + $20,000,000/1.05 + $10,000,000/1.05^2 + $6,000,000/1.05^3
NPV = $13,300,939.42

If Cost of Capital is 10%:

NPV = -$20,000,000 + $20,000,000/1.10 + $10,000,000/1.10^2 + $6,000,000/1.10^3
NPV = $10,954,169.80

If Cost of Capital is 15%:

NPV = -$20,000,000 + $20,000,000/1.15 + $10,000,000/1.15^2 + $6,000,000/1.15^3
NPV = $8,897,838.42

Calculation of Internal Rate of Return:

Let IRR be i%

NPV = -$20,000,000 + $20,000,000/(1+i) + $10,000,000/(1+i)^2 + $6,000,000/(1+i)^3
0 = -$20,000,000 + $20,000,000/(1+i) + $10,000,000/(1+i)^2 + $6,000,000/(1+i)^3

Using financial calculator, i = 47.63%

IRR = 47.63%