Question

A) You are considering the purchase of a $1,000 par value bond with a coupon rate of 5​% (with interest paid​ semiannually) that matures in 12 years. If the bond is priced to yield 9​%, what is the​ bond's current​ price?

The​ bond's current price is ​$__

B) Compute the current yield of​ a(n) 8.5​%, 25​-year bond that is currently priced in the market at ​$1,200. Use annual compounding to find the promised yield on this bond. Repeat the promised yield​ calculation, but this time use semiannual compounding to find​ yield-to-maturity.

The current yield is __ %

C) A bond has a Macaulay duration of 7.50 and is priced to yield 5.5​%. If interest rates go up so that the yield goes to 6.0 % what will be the percentage change in the price of the​ bond? Now, if the yield on this bond goes down to 5​%, what will be the​ bond's percentage change in​ price?

If interest rates go up to 6.0​%, the percentage change in the price of the bond is __%

Answer 1

A). To find the bond's current price, we need to put the following values in the financial calculator:

N = 12*2 = 24;

I/Y = 9/2 = 4.5;

PMT = (5%/2)*1000 = 25;

FV = 1000;

Press CPT, then PV, which gives us -710.09

So, the bond's price is $710.09

B). Current Yield = Annual Coupon Payment / Current Bond Price

= [8.5%*$1000] / $1200 = $85 / $1200 = 0.0708, or 7.08%

C). Modified Duration = Macaulay Duration / [1 + Yield]

= 7.50 / [1 + 0.055] = 7.11

c-1).% change in bond's price = -Duration * Change in Yield

= -7.11 * (0.06 - 0.055) = -0.0355, or -3.55%

c-2).% change in bond's price = -Duration * Change in Yield

= -7.11 * (0.05 - 0.055) = 0.0355, or 3.55%