The AIF Company issued a 10-year bond at par (F = $1000) that pays a coupon of 1

Question

The AIF Company issued a 10-year bond at par (F = $1000) that pays a coupon of 11% on an annual basis, and is callable at $1100. Suppose you bought the bond when it was issued, and at the time of your purchase suppose the yield curve was flat and continued to remain at that level during years 1-4. However, at the start of year 5 (or end of year 4), suppose the yield curve dropped to 8% and AIF called the bond.  Assume you reinvest your investment funds in a new six-year bond at par and the yield curve remains flat at 8%. What is your ARR for the call period? What is your ARR for the 10-year period? How do the ARRs compare to the YTM when you purchased the bond?

Explanation / Answer

. Formula to calculate Average Rate of Return (also known as the Accounting rate of return) of an investment as follow,

ARR = (Average Profit / Average Investment)


2. Formula to calculate Payback Period of an investment as follow,

Payback Period = Initial Investment / Cash Inflow per Period

ARR is an acronym for Annual Recurring Revenue and a metric used by SaaS or subscription businesses with Term subscriptions. ARR is the value of the contracted recurring revenue components of your term subscriptions normalized to a one year period. ARR excludes one-time and variable fees. There are no defined rules for the determination of ARR. Typically, ARR will include only committed and fixed subscription fees. ARR always excludes one-time fees and usually excludes any subscription consumption or variable fees.

Simple ARR Calculations:

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