Question

How do I calculate finding I/Y manually, I know how to BAII Plus it?

•Debt:

•1 million bonds outstanding

•$1000.00 face value

•Current price = $1100.00

•Coupon rate = 9%, semiannual coupons

•15 years to maturity

Tax Rate is 40%

I know the set up and answer is

-1100 = 45(PVIFA, I/Y, 30) + 1000(PVIF, I/Y, 30)

I/Y = 3.9268 x 2 = 7.85%

Answer 1

Yield to maturity is the rate at which you market price is equal to the present value of all coupon payments and maturity price.

You need to go with hit and trial method And then interpolation.

In hit and trial method you need to guess the rate at which the present value of coupon payments and maturity value is equal to the Market Price. You need to continue guess till you get the two rate. At one rate your Pv is less than market price and at other Pv is more than market price and then Do interpolation to find the rate.

While guessing you need to think smart as to reduce the work because for exact and/or Close approximation answer the difference between the two rate should be minimal.

Given in the question:

market price = 1100, Par value =1000, Coupon rate =9% , Year to maturity =15

Since coupon paid semi annuly you need to revise the Coupon rate and periods.

Coupon rate = 9/2 = 4.5% , No of periods = 15 x 2= 30 years

Coupon payment = 1000 x 0.45 = 45

Now as you know if you calculate price of the bond assuming coupon rate is YTM i.e. 4.50% YTM then the answer you get is exact 1000 and you know there is inverse ration between YTM and price of the bond. You need 1100, so for higher amount you need to reduce the rate.

Calculate the Price of bond at YTM = 4%

PRice of the bond = Coupon payment x Cumulative discounting factor @ 4% for 30 periods + maturity value x discount factor fir 30th years.

[ For Cumulative discount/pv factor refer the tab;e or can calculate as it is sum of (100/104) + (100/104)² ...............(100/104)³⁰ and For 30th year (100/104)³⁰ ]

= (45 x 17.29203294) + (1000 x 0.308318653)

= 778.1414823 + 308.318653

= 1086.460135

We are still short from 1100 so reduce the rate little more to get price more than 1100.

Calculate the price of bond at 3%

Applying same above formula and Put factors for 3%.

= ( 45 x 19.60044098) + (1000 x 0.411986744)

= 882.0198441 + 411.986744

= 1294.006588

Now you have two rates. Do interpolation to get the YTM at which Price of the bond is 1100.

=

= 3 + [(1294.006588 - 1100) / ( 1294.006588 - 1086.460135)] * 1

= 3 + (194.006588 / 207.546453)

= 3 + 0.93476

YTM = 3.9347 Approx

Above YTM is Semi annual basis

So Annual YTM = 3.9347 x 2 = 7.86% apprx

There will always be minor difference in answer with financial calculator and with Interpolation as Interpolation answer is near to approximate.