A firm is considering Project S and L, whose cash flows are shown below. These p

Question

A firm is considering Project S and L, whose cash flows are shown below. These projects are mutually exclusive. The CEO wants to use the IRR criterion, while the CFO favors the NPV method. You were hired to judge which one is wrong. If the wrong decision criterion is used, how much potential value would the firm lose? W ACC=4% 0 1 2 3 4 CF for project S (0) -1035 (1)380 (2)385 (3)390 (4)395 CF for project L (0) -2165 (1) 765 (2)770 (3)775 (4)780 PLEASE SHOW STEPS ON HOW TO SOLVE USING A FINANCIAL CALCULATOR THANK YOU

Explanation / Answer

WACC: 6%

Year       0              1              2              3              4

CFs         -1025     380         380         380         380

CFl          -2150     765         765         765         765

Diff         -1125     385         385         385         385

Here ,we will first calculate the crossover rate.

Crossover Rate

Crossover rate is the cost of capital at which the net present values of two projects are equal. It is the point at which the net present value profile of one project crosses over (intersects) the net present value profile of the other project.

Assume first project has initial investment A and its cash flows at end of year 1, 2 and 3 are CF1, CF2 and CF3, we can develop its net present value equation as follows:

NPV of First Project =     CF1/ (1+r)            +             CF2/(1+r)2          +             CF3/(1+r)3          A

If second project has initial investment B and its cash flows are CFi and CFii, its net present value equation will be:

NPV of Second Project =              CFi/(1+r)     +   CFii/(1+r)2              B

Since crossover rate is the rate at which NPVs of two projects are equal, we can find it by equating NPV equation for the first project with NPV equation for the second project and then solving it for r.

CF1/(1+r)             +             CF2/(1+r)2          +             CF3/(1+r)3          A =      CFi/(1+r)              +             CFii/(1+r)2           B

From the above ,we will calculate r.

Cross over rate=r- cost of capital

Short cut for calculating cross over rate

1)Determine the cash flows stream of first project and second project.

2) Find the difference between initial investments of both projects and between each periodic cash flows.

3) Develop an IRR equation by equating the net present value equation of the resulting differential cash flows to zero.

Solve the equation for r.

R =13.86%. This is the crossover rate. Project L is preferable when the cost of capital is below 13.86%. However, if the cost of capital exceeds 13.86%, project S will have higher net present value.

Crossover rate=13.86%     As interest rate is less than crossover rate , there is a conflict.

IRR of L =15.781%

IRR of S=17.861%

NPV of L=$550.81

NPV of S=$291.74

Value lost if IRR used= NPV of L-NPV of S=$209.07         

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