Question

1.Suppose you are faced with the following spot rates:

y₁ = 9%

_y2 = 10%

_y3 = 11%

Now consider a bond with a $100 face value maturing in 3 years. The bond pays annual coupon payments at a 6% coupon rate. What is the bond price?

Select one:

a. $92.63

b. $87.97

c. $80.86

d. $85.49

e. $100

2.A bond will sell at a discount when

Select one:

a. the coupon rate is greater than the current yield, and the current yield is greater than yield to maturity.

b. the coupon rate is greater than yield to maturity.

c. the coupon rate is less than the current yield, and the current yield is greater than the yield to maturity.

d. the coupon rate is less than the current yield, and the current yield is less than yield to maturity.

e. None of the options are true.

Answer 1

Answer-1

Current Bond Price =

CF1 = Cashflow at year 1 = $100*6% = $6

CF2 = Cash Flow at year 2= $100*6% = $6

CF3 = Cash Flow at year3= $6+$100 = $106 [ interest +maturity amount]

r1 = interest rate at Year 1=9% or 0.09

r2 = interest rate at Year 2=10% or 0.10

r3 = interest rate at Year 3 = 11% or 0.11

Current Bond Price =

=>Current Bond Price = $87.97

Hence Correct answer = $87.97 (Option -b)

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Answer-2

A bond will sell at discount when Coupon rate is less than the YTM or yield to maturity.

For example,

Face vale of the bond = $1000

year to maturity = 1 year

Coupon rate = 10%

Currently the bond is selling at $982.143

Let YTM be r %

hence

$982.143 = value to be recived after 1 year / (1+r)

=>$982.143= $1100/(1+r)

=>1+r= 1.12

=>r = 0.12 or 12%

hence YTM = 12 % WHICH IS MORE THAN THE COUPON RATE 10%.

Here Current Yield is = Next Year Interest/ Current price *100

=> Current yield = $100/$982.143 *100 = 10.18%

Coupon rate < current yield< YTM.

=> 10% < 10.18%< 12%

hence correct option is

-(d.) the coupon rate is less than the current yield, and the current yield is less than yield to maturity.

Coupon rate < current yield< YTM.

Ultimately Coupon rate < YTM.