A bond of MacKinnons Inc. has face value of $1000, pays 6% coupon semiannually,

Question

A bond of MacKinnons Inc. has face value of $1000, pays 6% coupon semiannually, and has 20 years to maturity. The bond has a quoted price of 102. a) What is the yield to maturity on MacKinnons’ bond? b) What is the current yield? c) By how many percentage points would the price of MacKinnons’ bond change if the market interest rates suddenly increase by 1%? d) What will the market price of this bond be one year from now if the required yield on similar bonds falls to 2% in one year from now? e) If you sell the bond in three and a half years from now at 102.7, what is your holding period yield?

Explanation / Answer

a.

Semiannual interest = 1000 * 6% *6/12 = 30

semiannual months = 20*2 = 40

Yield = [I +(Face value -price)/months] /[(face value +price)/2]

         = [30+ (1000- 102)/ 40 ] /[(1000+102)/2

         = [30+22.45] / 551

           = 52.45 / 551

              = 0.09519 or9.51 % semiannually

Annual YTM= 9.51 *2 =19.02 %    

b.

Current yield = Annual coupon payment/Bond price

                =1000*6%/102 =0.588235 or 58.82%

c.

Calculate PV when I = 7%, PMT = 102, FV = 1000, and N = 40 (assuming annual pay bond)

pvf when i=7%=1359.83

pvf when i=6%=1534.72

Price change = 1534.72-1359.83 = $174.89

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