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Could you please show me the workings to the following questions which I am struggling with:
1. the current spot rate for the US $ against the £ is $/£1.8420. Interest in the US is 5% pa, whereas it is 4% pa in the UK. What would you expect the 3 month forward rate to be?
Answer = $/£1.8466
I am aware that I need to use the interest rate parity formula but I am unsure whether US represents ib or ic in the formula.
2. AJT Co has a gearing ratio (debt : debt+equity) of 30% and pays corporation tax of 25%. AJT has an asset (ungeared) beta of 1.2. The risk free rate is 5% and the market return is 12%.
What is the cost of equity for AJT
Answer = 16.10%
1. Because the $ is quoted against the GBP, it is US interest (for 3 months) on the top of the formula and UK interest (for 3 months) on the bottom. So 1.8420 x (1.0125)/(1.01) = 1.8466
2. The equity beta determines the cost of equity.
To get the equity beta, use the asset beta formula ‘backwards’ with E = 70; D = 30; and T = 0.25
So 1.2 = (70/(70 + 22.5))x Be
Be = 1.2 x (70+22.5)/70 = 1.586Cost of equity = 5% x 1.586(12%-5%) = 16.10%
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