Question

1. Suppose a 5% coupon, 5-year bond is selling for $1100. The coupon is paid every six months. The principal value is $1000.

2. (1) Calculate the yield to maturity of this bond. . (Hint: Use the Yield function in Excel.)

3. (2) Calculate the price of this bond if the yield to maturity increases by 1% with maturity unchanged. .

4. (3) Calculate the price of this bond if the yield to maturity decreases by 1% with maturity unchanged. .

Answer 1

Solution

Answer :

1) 2.84%

2) $ 1,052.32

3) $ 1,150.29

Note:

The Approximate Yield to Maturity Formula =[Coupon + ( Face Value - Market Price) / Number of years to maturity] / [( Face Value + Market Price)/2 ] *100

= [$ 25+ ( $ 1,000- $ 1100) /10] /[( $ 1,000+ $ 1100)/2] *100

= 15/1050*100

= 1.428571429%

Annual YTM = 1.428571429% *2

= 2.86%

Note : Coupon = Rate * Face Value

= 5%/2 * $ 1,000

= $ 25

Since this formula gives an approximate value, the financial calculators can be used alternatively.

where,

Par Value = $ 1,000

Market Price = $  1,100

Annual rate = 5% and

Maturity in Years = 5 Years

Payments = 2

Hence the yield to maturity = 2.84%

Answer = 2.84%

(2) If YTM is increased by 1%, Interest = 2.84%+1%

= 3.84%

Price of bond = Coupon * PVIFA (n,i)+ face value * PVIF (n,i)

Price of bond= 25* PVIFA (10 , 3.84%/2) + 1000* PVIF (10 ,3.84%)

Price of bond = 25 *9.02029966434857 + 1000 * 0.8268102464445080  

= $ 1,052.32

Hence the correct answer is $ 1,052.32

3)

If YTM is decreased by 1%, Interest = 2.84%-1%

= 1.84%

Price of bond = Coupon * PVIFA (n,i)+ face value * PVIF (n,i)

Price of bond= 25* PVIFA (10 , 1.84%/2) + 1000* PVIF (10 ,1.84%)

Price of bond = 25 *9.51207805720039 + 1000 * 0.9124888818737560

= $ 1,150.29

Hence the correct answer is $ 1,150.29