Question

1. Your division is considering two investment projects, each of which requires an up-front expenditure of $14 million. You estimate that the investments 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

1. What are the two project’s NPVs assuming the cost of capital is 4%, 11%, 16%?
2. What are the two projects’ IRRs at those same costs of capital?

Answer 1

Project A:

Cash Flows:
Year 0 = -$14,000,000
Year 1 = $5,000,000
Year 2 = $10,000,000
Year 3 = $20,000,000

Calculation of NPV:

If interest rate is 4%:

NPV = -$14,000,000 + $5,000,000/1.04 + $10,000,000/1.04^2 + $20,000,000/1.04^3
NPV = $17,833,181.16

If interest rate is 11%:

NPV = -$14,000,000 + $5,000,000/1.11 + $10,000,000/1.11^2 + $20,000,000/1.11^3
NPV = $13,244,556.46

If interest rate is 16%:

NPV = -$14,000,000 + $5,000,000/1.16 + $10,000,000/1.16^2 + $20,000,000/1.16^3
NPV = $10,555,127.31

Calculation of IRR:

Let IRR be i%

NPV = -$14,000,000 + $5,000,000/(1+i) + $10,000,000/(1+i)^2 + $20,000,000/(1+i)^3
0 = -$14,000,000 + $5,000,000/(1+i) + $10,000,000/(1+i)^2 + $20,000,000/(1+i)^3

Using financial calculator, i = 48.54%

IRR of Project A = 48.54%

Project B:

Cash Flows:
Year 0 = -$14,000,000
Year 1 = $20,000,000
Year 2 = $10,000,000
Year 3 = $6,000,000

Calculation of NPV:

If interest rate is 4%:

NPV = -$14,000,000 + $20,000,000/1.04 + $10,000,000/1.04^2 + $6,000,000/1.04^3
NPV = $19,810,309.51

If interest rate is 11%:

NPV = -$14,000,000 + $20,000,000/1.11 + $10,000,000/1.11^2 + $6,000,000/1.11^3
NPV = $16,521,390.64

If interest rate is 16%:

NPV = -$14,000,000 + $20,000,000/1.16 + $10,000,000/1.16^2 + $6,000,000/1.16^3
NPV = $14,516,954.36

Calculation of IRR:

Let IRR be i%

NPV = -$14,000,000 + $20,000,000/(1+i) + $10,000,000/(1+i)^2 + $6,000,000/(1+i)^3
0 = -$14,000,000 + $20,000,000/(1+i) + $10,000,000/(1+i)^2 + $6,000,000/(1+i)^3

Using financial calculator, i = 91.76%

IRR of Project B = 91.76%