Calculation:

1. Current book value per share:

   \text{Current BVPS} = \frac{\`$6`,000 \text{ million}}{100 \text{ million}} = \`$60`

2. Shares repurchased:

   \text{Shares repurchased} = \frac{\`$400` \text{ million}}{\`$50`} = 8 \text{ million shares}

3. New shares outstanding:

   $$\text{New shares} = 100 \text{ million} - 8 \text{ million} = 92 \text{ million}$$

4. New book value of equity:

   \text{New BVE} = \`$6`,000 \text{ million} - \`$400` \text{ million} = \`$5`,600 \text{ million}

5. New book value per share:

   \text{New BVPS} = \frac{\`$5`,600 \text{ million}}{92 \text{ million}} = \`$60.87`

Since the market price ($50) is less than the current BVPS ($60), the buyback increases BVPS. The closest option is $61.