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Corporate finance question  refinancing with tax shield
This comes from Corporate Finance (Berk/Demarzo/Strangeland), the recommended study text:
Richmond Industries plans to issue 1.5 million new shares of equity to raise $50 million to finance a new investment. After making the investment, Richmond expects to earn free cash flows of $10 million each year. Richmond currently has 5 million shares outstanding, and it has no other assets or opportunities. Suppose the appropriate discount rate for Richmond’s future free cash flows is 8%, and the only capital market imperfections are corporate taxes and financial distress costs. a. What is the NPV of Richmond’s investment? b. What is Richmond’s share price today? Suppose Richmond borrows the $50 million instead and thus there are only 3.5 million shares outstanding. The firm will pay interest only on this loan each year, and it will maintain an outstanding balance of $50 million on the loan. Suppose that Richmond’s corporate tax rate is 40%, and expected free cash flows are still $10 million each year. c. What is Richmond’s share price today if the investment is financed with debt? __________________________________________________ ____ a is pretty straightforward. It's just 50 + 10/0.08 = 75 million (present value of perpetuity less initial investment). For b, you divide 75 million by 5 million to get $15/share. I'm having trouble with c. I get that the leveraged value of the firm should be the unleveraged value plus the tax shield. So I add 75 + 0.4 * 50 = 95 million. To get the share price, we subtract the debt from the leveraged value to get the equity, then divide by the number of shares. This gives (95  50)/3.5 = $12.86/share. But it's my understanding that (when there's a tax shield involved) the share price is supposed to go up when debt is increased. In the solutions manual, the solution is (75+0.4 * 50)/5 = $19 per share. This makes no sense to me, as there are only 3.5 million shares in the leverage scenario (not 5 million). Where am I going wrong? 
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