Question

ABC Limited is seeking for a $10,000,000 finance. Two major investors have put forward two bond terms for ABC’s considerations and ABC can only choose either one. In both bond terms, ABC Limited would raise $10,000,000 up front in exchange for issuing a bond promising a single (and larger) maturity payment from ABC Limited in 15 years at a promised interest rate. The two bond issuance options open to ABC Limited are as follows:

• A 15-year bond to Investor A, promising an annual rate of interest of 10%;

• A 15-year bond to Investor B, promising of interest of 9.72% per year, compounded monthly.

(A) What is the effective annual yield to maturity on each of the bonds terms?

(B) What is the future required payment that ABC will make 15 years later on each bond?

Answer 1

A) Calculating effective annual yield to maturity For Investor A

Nominal Rate = 10 % per annum, No of compounding periods in a year = 1

where n=compounding periods in a year

Effective annual YTM for investor A = (1 + 0.12)¹ - 1 = 1.12 - 1 = 0.12 = 12%

Calculating effective annual yield to maturity for Investor B

Nominal Rate = 9.72% per annum compounded monthly, No of compounding periods in a year = 12

where n=compounding periods in a year

Effective annual YTM for investor B = ( 1 + 0.81%)¹² - 1 = (1.0081)¹² - 1 = 1.101649336 - 1 = 0.101649336 = 10.1649336%

B) Calculating payment to investor A after 15 years

Amount raised = 10000000

Payment to investor A after 15 years = Amount raised (1 + Effective annual yield to maturity)^{no of years}

= 10000000 (1 + 10%)¹ = 10000000 x (1.10)¹⁵ = 10000000 x 4.177248169 = 41772481.69

Calculating payment to investor B after 15 years

Amount raised = 10000000

Payment to investor B after 15 years = Amount raised (1 + Effective annual yield to maturity)^{no of years}

= 10000000 (1 + 10.1649336%)¹² = 10000000 x (1.101649336)¹² = 10000000 x 4.272190946 = 42721909.46