Could someone please explain to me how we arrive at the Weight of Debt in the first step of the solution below? Why is the weight of debt not 40% and equity 60% since the d/e ratio is 0.4? Also, in the calculation they give, how are they arriving at this: wd = 0.40 x (1 - wd) wd = 0.40 - 0.40wd 1.40wd = 0.40 Thanks for help! ******************************** A company is considering a $10,000 project that will last 5 years. Annual after tax cash flows are expected to be $3,000 Target debt/equity ratio is 0.4 Cost of equity is 12% Cost of debt is 6% Tax rate 34% What is the project’s net present value (NPV)? A) -$1,460. B) +1,460. C) +1,245 Your answer: B was correct! First, calculate the weights for debt and equity wd + we = 1 we = 1 - wd wd / we = 0.40 wd = 0.40 x (1 - wd) wd = 0.40 - 0.40wd 1.40wd = 0.40 wd = 0.286, we = 0.714 ******************************** Second, calculate WACC WACC = (wd ~ kd) ~ (1 − t) + (we ~ ke) = (0.286 ~ 0.06 ~ 0.66) + (0.714 ~ 0.12) = 0.0113 + 0.0857 = 0.0970 Third, calculate the PV of the project cash flows N = 5, PMT = -3,000, FV = 0, I/Y = 9.7, CPT ¨ PV = 11,460 And finally, calculate the project NPV by subtracting out the initial cash flow NPV = $11,460 − $10,000 = $1,460 ********************************
There is a need to be careful in reading what they are providing. If they give debt as 40% and Equity as 60%, then Yes, you can use .4 and .6 as their respective weights. But if they provide d/e ratio, then you will need to do some calculation to get respective weights. In the above question, assume debt weight as x and then calculate for x. 1. If weight of debt is x, then weight of equity would be 1 - x 2. And it is given that x / (1 - x) = 0.4 3. Solving this equation for x, you get x = 0.4 / 1.4 = weight of debt 4. And weight of equity would be 1 - x.