It is now January 1, 2018, and you are considering the purchase of an outstanding bond that was issued on January 1, 2016. It has a 9% annual coupon and had a 20-year original maturity. (It matures on December 31, 2035.) There is 5 years of call protection (until December 31, 2020), after which time it can be called at 109-that is, at 109% of par, or $1,090. Interest rates have declined since it was issued, and it is now selling at 114.12% of par, or $1,141.20. What is the yield to maturity

YTM is 7.54%.

Explanation:

The yield to maturity can be calculated using the following RATE function in Excel:

YTM = RATE(nper,pmt,-pv,fv) (1)

Where;

YTM = yield to maturity = ?

nper = number of periods = number of years to maturity = original maturity number of years - number of years between January 1, 2016 and January 1, 2018 = 20 - 2 = 18

pmt = annual coupon payment = face value * annual coupon rate = 1000 * 9% = 90 (Note: This is an inflow to the bondholder and it is therefore a positive figure).

pv = present value = current bond price = -1141.20 (Note: This is an outflow to the buyer of the bond and it is therefore a negative figure).

fv = face value of the bond = 1000 (Note: This is an inflow to the bondholder and it is therefore a positive figure).

Substituting the values into equation (1), we have:

YTM = RATE(18,90,-1141.20,1000) (2)

Inputting =RATE(18,90,-1141.20,1000) into excel (Note: as done in the attached excel file), the YTM is obtained as 7.54%.

Therefore,  YTM is 7.54%.

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