Question

A $10,000​, 7.5% bond with quarterly coupons redeemable at par on October​ 15, 2032, was purchased on May​ 5, 2020, at 98.75. What is the approximate yield realized if the bond was sold on August​ 7, 2025, at​ 92?

Answer 1

Calculation of Bond Yield:

A bond's yield is the return to an investor from the bond's coupon and maturity cash flow.

Here, Total Value = $ 10,000, Coupon Rate = 7.5%, Redeemable at par on October 15, 2032.

Purchase on May 5, 2020, at 98.75.

Sold on August 7, 2025, at 92.

So, from the above information, we can say,

Annual Coupon Amount = $ 10,000 * 7.5% = $ 750

Purchase Amount = $ 10,000 * 98.75% = $9,875

Sales Amount = $ 10,000 * 92% = $ 9,200

No. of Years for which Bonds are Hold = May 5, 2020 to August 7, 2025 = 5 Years, 3 Months, 2 Days = 5.25 Years

Formula:

Bond Yield = Average Annual Return / Average Investment

= Annual Coupon Rate + ((Sales Price-Purchase Price)/No. of Years for which Bonds are Hold)

(Sales Price+Purchase Price)/2 i.e. Average Investment

= $ 750 + (($ 9,200 - $ 9,875)/5.25) / (($ 9,200 + $ 9,875)/2)

= 6.52%