Answer:
a. Assuming you hold the bonds until they mature, the rate of return you would probably earn is the YTM of 5.89%.
b. Assuming you hold the bonds until they are called, the rate of return you would probably earn is the YTC of 5.65%.
Explanation:
This can be determined by calculating the YTM and YTC as follows:
a. Calculation of Yield to Maturity (YTM)
The bond's 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 = 30
pmt = annual coupon payment = annual coupon rate * Face value = 7% * $1,000 = $70 = 70
pv = present value = current bond price = $1,155 = 1155
fv = face value or par value of the bond = 1000
Substituting the values into equation (1), we have:
YTM = RATE(30,70,-1155,1000) ............ (2)
Inputting =RATE(30,70,-1155,1000) into excel (Note: as done in the attached excel file), the YTM is obtained as 5.89%.
Therefore, assuming you hold the bonds until they mature, the rate of return you would probably earn is the YTM of 5.89%.
b. Calculation of Yield to Call (YTC)
The bond's Yield to call can be calculated using the following RATE function
in Excel:
YTC = RATE(nper,pmt,-pv,fv) .....................(3)
Where;
YTM = yield to call = ?
nper = number of periods = number of years of call protection = 11
pmt = annual coupon payment = annual coupon rate * Face value = 7% * $1,000 = $70 = 70
pv = present value = current bond price = $1,155 = 1155
fv = future value of the bond or the amount at which the bond can be called = $1,085 = 1085
Substituting the values into equation (3), we have:
YTM = RATE(11,70,-1155,1085) ............ (4)
Inputting =RATE(11,70,-1155,1085) into excel (Note: as done in the attached excel file), the YTM is obtained as 5.65%.
Therefore, assuming you hold the bonds until they are called, the rate of return you would probably earn is the YTC of 5.65%.
