Question

Bonds issued by the Tyler Food chain have a par value of $1,000, are selling for $1,210, and have 20 years remaining to maturity. Annual interest payment is 14.5 percent ($145), paid semiannually. Compute the approximate yield to maturity. (Round the final answer to 2 decimal places.)

Approximate yield to maturity %

Answer 1

Solution:

Given:

Bond’s Par Value or Face Value = $ 1,000

Selling Price or Present Value of Bonds = $ 1,210

Maturity Period = 20 Years

Annual Interest Rate / Coupon Rate = 14.5 % or ($ 145) and is paid semiannually.

To Calculate:

Approximate Yield to Maturity.

Step: Calculation of Approximate Yield to Maturity (AYTM):

Formula:

Approximate Yield to Maturity = ((Interest Rate × Face Value) + ((Face Value – Present Value) / Maturity Period)) / ((60 % × Present Value) + (40 % × Face Value))

On putting the value in the formula, we get,

= ((0.145 × 1000) +( (1000 – 1210) / 20)) / ((0.6 × 1210) + (0.4 × 1000))

= ((145) + (-210 / 20)) / (726 + 400)

= ((145) + (-10.5)) / 1126

= (145 - 10.5) / 1126

= 134.5 / 1126

AYTM = 0.119449 = 11.94 %

Ans: Approximate Yield to Maturity = 11.94 %

Alternative Method of calculating the YTM from YTM semiannually:

Formula:

Yield to Maturity Semiannually = ((F-P/ n) + C/ 2) / ((F + P)/ 2))

Where,

F = Face Value of Bond

P = Present Value of Bond

n= Number of years to maturity

c = Coupon rate in $

= (($ 1000 - $1210) / 20) + $ 145/2) / (($ 1000 + $ 1210) / 2))

= (($ 1000 - $1210) / 20) + $ 72.5) / (($ 1000 + $ 1210) / 2))

= (( -210 / 20) +72.5) / (2210 / 2)

= ( -10.5 + 72.5) / 1105

= 62 / 1105

= 0.05610 = 5.61 %

YTM Semiannually = 5.61 %

Now we calculate Yield to Maturity from Semiannual YTM:

Formula:

1. YTM = 2 × YTM Semiannually

YTM = 0.05610 × 2

= 0.1122 = 11.22 %

YTM = 11.22 %

2. YTM = (1 + YTM Semiannually) ^2 – 1

YTM = (1 + 0.05610) ^2 – 1

= (1.05610) ^2 – 1

= 1.11534721 – 1

= 0.1153 = 11.53 %

YTM = 11.53 %

The actual YTM in this question is 11.94 %. However, our approximate yield to maturity are 11.22 % and 11.53 %. These values are good for approximation and for quick comparisons.