Question

timco bonds are currently valued atb1010. they have 4 years until maturity and the coupon rate is 4%. what is the yield?

Answer 1

Price = 1010 | Par value = 1000

Time to maturity = 4 years

Coupon rate = 4%

Annual coupon payment = 4% * 1000 = 40

Since coupon payment remains same for 4 years, therefore, we can consider it as an annuity

PV of Annuity formula = (C / YTM) * (1 - (1+YTM)^-n)

PV of final Principal payment = Principal / (1+YTM)ⁿ

Price of Bond = (40 / YTM) * (1 - (1+YTM)^-4) + 1000 / (1+YTM)⁴

=> 1010 = (40 / YTM) * (1 - (1+YTM)^-4) + 1000 / (1+YTM)⁴

Since equation is complex to solve because Power of 4. Therefore, we will create a cashflow series on Excel and use IRR function for determining the Yield. The yield will be the return rate at which Price and PV of all cashflows will be equal.

Below are the series of cashflows on Excel:

Now using the IRR function, we can get the Yield to maturity.

Below is how IRR function looks like:

The result of the function is 3.73%

Hence, the yield to maturity of the bond is 3.73%

In case the question needed Current Yield of the bond, then below formula can be used

Current Yield = Annual Coupon Payment / Current Market Price of the bond

Current Yield = 40 / 1010 = 3.96%

Hence, current yield of the bond is 3.96%