question archive In 2020, country G sold a zero coupon bond with a maturity of 5 years and a face value of €100

In 2020, country G sold a zero coupon bond with a maturity of 5 years and a face value of €100

Subject:FinancePrice:2.86 Bought10

In 2020, country G sold a zero coupon bond with a maturity of 5 years and a face value of €100. The country is rated AAA, hence the opportunity cost of capital is 7%. For a B rating, the risk adjusted discount rate is 12%, and for junk bonds, it will be 20%. a) Calculate the price of the bond in 2020. b) In 2022 the country is down rated to B, which may reflect a probability of default during the next 3 years of about 20%. What would be the value in 2022? c) What will be the price of a bond with the same characteristics sold in 2020? d) Calculate b) and c) for a probability of default of 50% (junk bond). e) Identify and discuss all components of the “risk premium required by the financial market.”

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Part (a)

Price of the bond = Face value / (1 + r)n = 100 / (1 + 7%)5 = 71.30

Part (b)

Time to maturity now = 5 - 2 = 3 years.

Hence, Price of the bond = (1 - probability of default) x Face value / (1 + r)n = (1 - 20%) x 100 / (1 + 7%)5 = 57.04

Part (c)

Price of the bond = Face value / (1 + r)n = 100 / (1 + 12%)5 = 56.74

Part (d)

Hence, Price of the bond = (1 - probability of default) x Face value / (1 + r)n = (1 - 50%) x 100 / (1 + 7%)5 = 35.65

Price of the bond in 2020 = Face value / (1 + r)n = 100 / (1 + 20%)5 = 40.19

Part (e)

Risk premium required by the financial markets includes but not limited to:

  • Inflation risk premium
  • Liquidity risk premium
  • Maturity risk premium
  • Exchange rate risk premium
  • Interest rate ris premium