A firm has three investment opportunities. Each costs $1,000, and the firm's cost of capital is 10 percent. The cash inflow of each investment is as follows:? cash inflow A B C year 1 $300 500 100 2 300 400 200 3 300 200 400 4 300 100 500 ? a. If the net present value method is used, which investment(s) should the firm make? b. What is the internal rate of return of investment A? The internal rate of return of investment B is 10.22% and 6.15% for investment C. Which

Question

investment(s) should the firm make? c. What is the payback period for each investment?

What will be an ideal response?

Answer 1

a.Discount the cash inflows by the cost of capital. For each investment, that is?               A                                          B      $300 x .909 = $272.70    $500 x .909 =  $454.50        300 x .826 =   247.80     400 x .826 =    330.40        300 x .751 =   225.30     200 x .751 =    150.20        300 x .683 =   204.90     100 x .683 =      68.30                           $950.70                        $1,003.40?               C      $100 x .909 = $  90.90        200 x .826 =   165.20        400 x .751 =   300.40        500 x .683 =   341.50                            $898.00.?Since investment A is an annuity, the present value could be determined by using the interest table for the present value of an annuity. That is, $300 x 3.170 = $951, which is essentially the same answer except for rounding.?Next subtract the cost from the present value to determine the net present value:?      A:   $950.70 ? $1,000 = ($49.30)      B: $1,003.40 ? $1,000 =   $3.40      C:   $898.00 ? $1,000 = ($102.00).?Since only B has a net present value that is positive, it is the only investment that covers the firm's cost of capital and hence is the only one that should be selected.?b.Internal rate of return for A:?      $1,000 =  $300  +    300   +     300    +   300                    (1 + r)    (1 + r)2      (1 + r)3    (1 + r)4?Since investment A is an annuity, the annuity table for the present value of an annuity may be used to solve the problem. Restated the equation is        $1,000 = $300X        X = $1,000/$300 = 3.33.3.33 is the interest factor for the present value of an annuity for four years. Find this interest factor in the table to determine the internal rate of return. In this case the internal rate of return is approximately 8 percent, which is less than the firm's cost of capital. (The IRR is 7.7 percent using a financial calculator.) Therefore, the investment should not be made. (This answer is consistent with the answer given by the net present value in the previous question.) The internal rates of return for investments B and C were given. Only the internal rate of return of B exceeds the cost of capital; thus it is the only investment the firm should make.?c.The payback periods for the investments are       A   three and one?third years       B   two and one?half years       C   three and two?thirds years.?Notice that in this case the payback method gives the same ranking of investments as the net present value. However, the payback method does not tell if any of the investments should be made.