Question

The Pennington corporation issued bonds on January 1, 1987. The bonds were sold at par had 12% annual coupon paid semi-annually and mature December 31, 2016. a) What was the Yield-to-Maturity (YTM) on the date the bonds were issued? b) What was the price on January 1, 1992, assuming interest rates have fallen to 10%? c) Find the current yield, capital gains/losses yield and total yield on January 1, 1992?

Answer 1

a) Time to Maturity = 30 years or 60half years

Selling Price of the bonds (at par) = $100

Face Value of the bonds = $100

Coupon Rate = 12%

So, Coupon Interest = Coupon Rate * Face Value of the bond

Or, Coupon Interest = 12% * $100 = $12 (full year) or $6 (half year)

Or, Selling Price of the bond = Coupon Interest* pvifa(r%, 60) + Face Value* pvif (r%, 60)

Or, $100= $6* pvifa (r%, 60) + $100* pvif (r%, 60)

Now interpolating the results

Let r = 5%

$100= $6*18.9293 + $100*0.0535= $118.93

Let r = 7%

$100= $6*14.0392 + $100*0.0173= $85.97

Or (7-5)% (7-r)% = (85.97-118.93)/ (85.97-100)

Or, 2/(7-r) = -32.965/ -14.03

Or, 0.85= 7-r

Or, r = 6.15%

So for full year YTM% = 6.15%*2= 12.30%

b) In 1992, time to maturity will be = 5 years

Interest rate will be 10% (full year) so half yearly it will be 5%

Coupon Rate will be 6% (half yearly)

So Price = Coupon Interest* pvifa(r%, 5*2) + Face Value* pvif (r%, 5*2)

Or, Price = $100*0.06* pvifa (5%, 10) + $100* pvif (5%, 10)

Or, Price = $6* 7.7217 + $100* 0.6139= $107.72

c) Current Yield % = Coupon Interest + (Closing Value – Face Value)/ Face Value*100

Or, Current Yield % = $6+ ($107.72- $100)/ $100*100=

Or Current Yield % = 13.72%

Capital Gain Loss Yield % = Selling Price – Face Value Price/ Face Value Price* 100

Or, Capital Gain Loss Yield % = ($107.72-$100/ $100)*100= 7.72%

Total Yield % = Current Yield + Capital Gain Loss Yield

Or, Total Yield% = 13.72% + 7.72% = 21.44%