Question

Jamaica Corp. is adding a new assembly line at a cost of $8.5 million. The firm expects the project to generate cash flows of $2 million, $3 million, $4 million, and $5 million over the next four years. Its cost of capital is 16 percent. What is the internal rate of return (IRR) that Jamaica can earn on this project and should the project be accepted? (Round to the nearest percent)?

A. 18 percent, yes because IRR > r

B. 18 percent, no because IRR > r

C. 20 percent, yes because IRR > r

D. 22 percent, yes because IRR > r

Answer 1

Given

cost of investment = $8,500,000

The cash flows for each year

Firstly we need to calculate Present Value Cash Flows (PVCF) for each cash flow

Formula PVCF = CF/(1+ r)^t

r= required rate of return = cost of capital = 16%

t= time period

For year 1

CF = $2,000,000

PVCF = 2,000,000/ (1+ 0.16)^1 = $1,724,137.93

For year 2

CF = $3,000,000

PVCF = 3,000,000/ (1+ 0.16)^2 = $2,229,488.70

For year 3

CF = $4,000,000

PVCF = 4,000,000/ (1+ 0.16)^3 = $2,562,630.69

For year 4

CF = $5,000,000

PVCF =5,000,000/ (1+ 0.16)^4 = $2,761,455.49

Let us calculate NPV at r = 16%

NPV = sum of present value of cash inflows – cost of investment

NPV = $1,724,137.93+ $2,229,488.70 + $2,562,630.69 + $2,761,455.49 - $8,500,000 = 777,712.81

IRR is the internal rate of return at which the NPV = 0

So, we can calculate IRR by trial and error method.

IRR = ra + [ NPVa/ (NPVa – NPVb)] * [rb-ra]

ra= lower discount rate chosen

rb =higher discount rate chosen

NPVa = NPV at ra

NPVb = NPV at rb

Now, we can see that NPV is positive at r = 16%

So we need to choose a rate where NPV is negative

Let us choose r= 30% and see if NPV is negative

For year 1

CF = $2,000,000

PVCF = 2,000,000/ (1+ 0.30)^1 = $1,538,461.54

For year 2

CF = $3,000,000

PVCF = 3,000,000/ (1+ 0.30)^2 = $1,775,147.93

For year 3

CF = $4,000,000

PVCF = 4,000,000/ (1+ 0.30)^3 = $1,820,664.54

For year 4

CF = $5,000,000

PVCF =5,000,000/ (1+ 0.30)^4 = $1,750,638.98

Let us calculate NPV at r = 30%

NPV = sum of present value of cash inflows – cost of investment

NPV = $1,538,461.54 + $1,775,147.93 + $1,820,664.54 + $1,750,638.98 - $8,500,000 = -1,615,087.01

For 30% NPV is negative

Thefore IRR is a rate in between 16% and 30%

IRR = ra + [ NPVa/ (NPVa – NPVb)] * [rb-ra]

ra= lower discount rate chosen = 16%

rb =higher discount rate chosen = 30%

NPVa = NPV at ra = 777,712.81

NPVb = NPV at rb = -1,615,087.01

Now substituting values in the formula

IRR = 16% + [777,712.81/ (777,712.81 - (-1,615,087.01))] * [30%-16%]

IRR = 16% +0.3250220948 *14%

=16% + 4.55

=20.55%

Also, IRR is greater than 16% the cost of capital, so according to IRR rule we can accept the projects which give higher return than cost of capital

Answer: option C. 20 percent, yes because IRR > r