1. **Problem Statement:** IBM's German affiliate is considering two bonds: a 10-year, 100 million euro-denominated bond yielding 4% and a 100 million dollar bond yielding 2.7%. The euro is forecasted to depreciate by 1.7% annually. 2. **Calculate the expected dollar cost of the euro-denominated bond:** The effective dollar yield includes the euro yield adjusted for currency depreciation: $$ \text{Expected dollar yield} = (1 + \text{euro yield})(1 + \text{currency change}) - 1 $$ $$ = (1 + 0.04)(1 - 0.017) - 1 = 1.04 \times 0.983 - 1 = 1.02272 - 1 = 0.02272 \text{ or } 2.272\% $$ The dollar cost of the euro bond is thus approximately 2.272%, which is lower than the dollar bond's 2.7% rate. 3. **Find the depreciation rate that equalizes the dollar cost of both bonds:** Let $x$ be the annual depreciation rate of the euro (expressed as a decimal, negative for depreciation). We set: $$ (1 + 0.04)(1 + x) - 1 = 0.027 $$ Solve for $x$: $$ 1.04 (1 + x) = 1.027 $$ $$ 1 + x = \frac{1.027}{1.04} = 0.9875 $$ $$ x = 0.9875 - 1 = -0.0125 = -1.25\% $$ So, if the euro depreciates by 1.25% annually, the dollar costs are equal. 4. **Calculate the after-tax dollar cost of the euro-denominated bond:** The before-tax dollar cost is 2.272% from step 2. After tax, with a 35% corporate tax rate: $$ \text{After-tax cost} = \text{Before-tax cost} \times (1 - 0.35) = 0.02272 \times 0.65 = 0.014768 \text{ or } 1.4768\% $$ **Final answers:** - Expected dollar cost of euro bond: about 2.272% - Depreciation rate to equalize costs: -1.25% per year - After-tax dollar cost of euro bond: about 1.477%