Question

Deep mining and precious metals are separate firms that are both considering a silver mining project. Deep mining is in the actual mining business and has an Aftertax cost of capital of 16.2 percent. Precious metals is in the precious gem retail business and has an Aftertax cost of capital of 13.4 percent. The project under consideration has initial costs of $950,000 and anticipated annual cash flows of $165,000 a year for 12 years. Which firms, if either, should accept this project?

A) deep mining only

B) precious metals only

C) both deep mining and precious metals

D) neither deep mining nor precious metals

E) cannot be determined without further information

Answer 1

Project Silver mining project Deep mining after-tax cost of capital 16.2% Precious metals after-tax cost of capital-13.4% Project's inital cost- $950,000 Annual cash inflows165,000 Num ber of years (Project's life)- 12 Years Note: The deep mining is in actual mining business and precious metals in in precious gems retail business, that's why both has different after-tax cost of capital For this project, the after-tax cost of capital should be adjusted for precious metals As deep mining in in same mining business. Therefore, the applicable discount 1 1 6 .2 % | rate/after-tax cost of capital for both the firms will be Present Value of Cash flows muin Annuity Net present value - -Initial investment Number of periods 1 + Periodic interest rate Annual cash flows AnnsityX Periodicinterest rate -Initial investment 12 (1 +16.2%) - |-$950.000 | $165,000 x 16.2% (0.162 $950,000 -$165,000 x 0.162

12 1.162)$950,000 $165,000 x 0.162 6.06001273253036 -| $165.000 х S950,000 0.162 1- 0.165016154938415 $165,000 x S950,000 = 0.162 $16.0-(0 0.834983845061585 S950,000 | $165,000 x 0.162 = ($165.000 х (5.15422126581225)-$950.000) = $850. 446.51-$950.000 -$99. 553.49 Therefore, the net present value of this mining project at the applicable discount rate for both the firms (16.2%), is negative that is-S99, 553.49 Hence, this project is not beneficial for either firms. Therefore, the correct option is tion (D) neither deep mining nor precious metals Note: If Precious metals were in the mining business then it's after-tax cost of capital would be used to calculate the NPV of cash flows, which is positive at 13.4%, then in that case the project would be beneficial for the Precious metals. However, its not in the same business, so applicable discount rate for both the firms will be 16.2% and this project is not profitable for any of these firms.