Weighted average cost of capital (WACC) is the minimum return expected from the securities of a company. It is the sum of the weighted costs of the individual components in the capital structure. The product of the cost of capital of a component and the proportion of the component in the capital structure yields the weighted cost of that particular component in the capital structure. The cost of capital for equity is the ratio of the dividend per share and the market price for each share. This is computed as 1.50/15*100=10%. The weighted cost of equity capital is the product of the cost of capital and the proportion of equity in the capital structure. This is computed as 10%*60%=6%. The cost of capital for the debt is the after tax cost of capital which is computed as 30% (1-40%) =18%. The weighted cost is 18%*30%=5.4%. The cost of capital for the preferred stock is the ratio of dividend per share and the market price per share of the preferred stock. This can be computed as (10%*1200) /1200=10%. The weighted average cost of capital is the summation of the weighted costs of the individual components. In this case, WACC is ( 6%+5.4%+10%) *0. 25=6.025%.
The payback period refers to the shortest time taken to recover the initial cost. The payback period is obtained by summing the cash flows for each period. The payback period does not capture the time value of money concept. The annual cash flows obtained after the acquisition of the new machinery would be 10,000+10,000+10,000+50,000+50,000=130,000. The payback period would be 1+ (70,000/130,000*12) = 1 year and 6 months. The required payback period by the firm is 1 year. Therefore, the old machine should be replaced if the payback period criterion is used. The payback criterion uses the cash flows without discounting them to the present value. It is recommended that the cash flows to be discounted to their present terms. This helps to take into consideration the notion of the time value of money.
The discounted payback period, unlike the payback period, takes into consideration the time value of the funds. The discounted payback period criterion involves discounting the cash flows into their present value. The discounted cash flows are accumulated together, and the minimum time taken to recover the initial cost is computed. The discounting of the cash flows is carried out by multiplying the cash flows with the present value interest annuity factor. The discount factor in this case would be (1+0.40) ^-1=0.7142. The present value of the cash stream in the first year would be 0.7142*130,000=92,846. During the second year, the present value of cash stream would be 0.5102*130,000=66,326. The discounted value in the third year would be 0.3644*130,000=47,376. The discounted payback period would be 92,846+66,326+47,376=206,498. The discounted payback period would be 2 years and 1 month. The old machine should be replaced.
Net present value is the difference between the total present value of cash flows and the initial cost. A project is acceptable if the net present value is positive. A project which yields a negative net present value should be rejected. If a project has a zero net present value, the investor has the option of undertaking the project or not undertaking the project. Since the cash flows are the same, the discounting factor to be used is referred to as the annuity discounting factor. The present value of cash inflows would be 1.588*130,000=206,440. The net present value if the new machine is acquired would be 206,440-200,000=6,440. The acquisition of the new machine results to a positive net present value. Therefore, the old machine should be replaced if the net present value criterion method is used.
The internal rate of return method is similar to the net present value method. However, when using the internal rate of return method, we compute the rate of return which equates the net present value to zero. In order to equate the net present value to zero, a higher discount rate than 40% is used. In this case, 60% would be used. Using 60% as the discount factor, the net present value would be 1.2597*130,000=163,761. The net present value would be 163,761-200,000= -36,239. The internal rate of return would be 40 %+ (6,440/42,679)60%-40%=43.02%. The internal rate of return is higher than the required rate of return. The old machine should be replaced.
The modified internal rate of return is a modification of the internal rate of return. Modified internal rate of return is crucial in overcoming the shortcomings which arise when using the internal rate of return method. The formula used in calculating the modified internal rate of return is MIRR = (-Σ FV / Σ PV) 1/ (N-1). FV represents the positive cash flows while PV represents the negative cash flows. The MIRR in this case is (6,440/36,239)1/3-1=33.31%. Modified internal rate of return is always lower than the internal rate of return. The old machine should not be replaced since the modified internal rate of return is lower than the required rate of return, which is 40%.