Question

Emerson Electronic Inc has a 9.5% semi-annual coupon bond that matures on March 28, 2040.
If the market rate for these bonds is YTM=7.5%, what is the value of this bond (face value =
1,000, today is March 28, 2020)?

Please show work and formulas for a better understanding (no excel) if possible, please show TVM keys work as well. That would really help.

Answer 1

Number of years = 2040 - 2020 = 20

There are 2 payments in a year since coupons are paid semi annually.

Semi annual rate = 7.5% / 2 = 3.75%

Semi annual coupon = (9.5% of 1000) / 2 = 47.5

Number of periods = 20 * 2 = 40

Value of bond = Coupon * [1 - 1 / (1 + r)^n] /r + FV / (1 + r)^n

Value of bond = 47.5 * [1 - 1 / (1 + 0.0375)^40] / 0.0375 + 1000 / (1 + 0.0375)^40

Value of bond= 47.5 * [1 - 0.229338] / 0.0375 + 229.337875

Value of bond = 47.5 * 20.55099 + 229.337875

Value of bond = $1,205.51

Keys to use in a financial calculator:

FV 1000

PMT 47.5

I/Y 3.75

N 40

CPT PV