Question

1. What is the present value of a $10 billion bond paying 8%, expiring in 5 years when market yields are 10%?

2. What is the present value of a $10 billion bond paying 8% semiannually, expiring in 5 years when market yields are 10%?

Answer 1

The present value is computed as shown below:

Present value = Future value / (1 + r)ⁿ

The present value of the bond is computed as follows:

= $ 0.80 billion / 1.10¹ + $ 0.80 billion / 1.10² + $ 0.80 billion / 1.10³ + $ 0.80 billion / 1.10⁴ + $ 0.80 billion / 1.10⁵ + $ 10 billion / 1.10⁵

= $ 9.24 billion Approximately

The present value of the bond is computed as follows:

The coupon payment will be as follows:

= 8% / 2 x $ 10 billion (Since the payments are semi annual, hence divided by 2)

= $ 0.40 billion

The market yield is computed as follows:

= 10% / 2 (Since the payments are semi annual, hence divided by 2)

= 5% or 0.05

N is computed as follows:

= 5 x 2 (Since the payments are semi annual, hence multiplied by 2)

= 10

So, the price of the bond will be as follows:

= $ 0.40 billion / 1.05¹ + $ 0.40 billion / 1.05² + $ 0.40 billion / 1.05³ + $ 0.40 billion / 1.05⁴ + $ 0.40 billion / 1.05⁵ + $ 0.40 billion / 1.05⁶ + $ 0.40 billion / 1.05⁷ + $ 0.40 billion / 1.05⁸ + $ 0.40 billion / 1.05⁹ + $ 0.40 billion / 1.05¹⁰ + $ 10 billion / 1.05¹⁰

= $ 9.23 billion Approximately

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