Explanation

First, we need to calculate the discount factors from the zero-coupon bond prices:

• 3-month bond:

  • Market price = USD 97.8012
  • Face value = USD 100
  • Discount factor = 97.8012 / 100 = 0.978012

• 6-month bond:

  • Market price = USD 95.2375
  • Face value = USD 100
  • Discount factor = 95.2375 / 100 = 0.952375

• 9-month bond:

  • Market price = USD 92.3805
  • Face value = USD 100
  • Discount factor = 92.3805 / 100 = 0.923805

Now, apply these discount factors to the corresponding cash flows from the coupon bond:

• 3-month cash flow: USD 67,500 × 0.978012 = 66,015.81
• 6-month cash flow: USD 67,500 × 0.952375 = 64,285.31
• 9-month cash flow: USD 4,567,500 × 0.923805 = 4,219,479.34

Total present value = 66,015.81 + 64,285.31 + 4,219,479.34 = 4,349,780.46

This matches option C (USD 4,349,780).

Key Concepts:

• Discount factors represent the present value of $1 received at a future date
• Zero-coupon bonds provide the purest measure of discount factors since they have only one cash flow
• Pricing coupon bonds involves discounting each cash flow using the appropriate discount factor for its timing