The cost of capital for a firm is 10 percent. The firm has two possible investme

Question

The cost of capital for a firm is 10 percent. The firm has two possible investments with the following cash inflows:
Years      A         B
1          $300   $200
2          $200   $200
3          $100   $200

a. Each investment costs $480. What investment(s) should the firm make according to net present value?
b. What is the internal rate of return for the two investments? Which investment(s) should the firm make? Is this the same answer you obtained in part a?
c. If the cost of capital rises to 14 percent, which investment(s) should the firm make?

Note:  Can someone please answer this showing what they are getting for 'r' in the IRR equation.  I am not understanding where to get that information from.  Any help!!!  Please!!!

Explanation / Answer

Determination of net present value:

       NPVA =   $300   +   $200     + $100     ? $480

               (1 + .1)    (1 + .1)2    (1 + .1)3

            = $300(.909) + 200(.826) + 100(.751) ? 480

            = $513 ? 480 = $33

       NPVB =   $200   +   $200     + $200     ? $480

               (1 + .1)    (1 + .1)2    (1 + .1)3

            = $200(.909) + 200(.826) + 200(.751) ? 480

            = $497 ? 480 = $17

The firm should make both investments because their net present values are positive.

    b. Determination of the internal rate of return for A:

         $480 = $300 +   $200    + $100

                (1 + r)    (1 + r)2    (1 + r)3

Since this is not an annuity, select an interest rate and attempt to equate both sides of the equation. For example, use 14%:

       $300(.877) + 200(.770) + 100(.675) = $484.60 which is

         approximately equal to $480.

The internal rate of return on investment A is approximately 14% (14.68% using a financial calculator that accepts uneven cash flows).

       Determination of the internal rate of return for B:

       $480 = $200 + $200    + $200     

              (1 + r)    (1 + r)2    (1 + r)3

       $480 = $200(PVAIF for 3 years at ? percent)

       IF = 2.000

       Locate 2.000 in the interest table for 3 years and

       determine the internal rate of return to be 12%.

     (PV = -480; N = 3; I = ?; PMT = 200, and FV = 0.

        I = 12.04.)

Since the internal rates of return exceed the cost of capital (10%), the firm should make both investments. (This is the same answer determined in part a.)

    c. If the cost of capital were to increase to 14%, the

       net present values would be

            A: $484.60 ? 480 = $4.60

            B: $464.20 ? 480 = ($15.80)

The net present values decline in both cases, but the net present value of A is still positive, so the firm should make that investment. (You should point out that the increase in the cost of capital does not change the investments' internal rates of return. However, since investment B's internal rate of return is now less than the cost of capital, that investment should not be made. This is the same conclusion derived from using the net present value.)

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