Question

2. William bought a corporate bond for S5.450- The face value of the bond was $7,000 and he received semi- annual coupon payments at a rate of 4% per year until the bond matured (5 years romthe purchase The coupon payment that William received each period and ROR that William earned on his purchase are closest to _a)-$280,4.85%- $280, 9.94%- c) $140, 9.94% d) $140, 4.85% e) $140, 9.82% 4)-$280,-98296- -gr-s 109,4:33%- -_-.h), $ 109,-8.85%- i)-6218,8;77%. ._j)-$218;4.33%-- 4'pen 5,4So

Answer 1

Face value, M = $ 7,000

Coupon rate = 4% per year, semi annually

Coupon, c = 4% of $7000 = $ 280

Semi annually he received, C = $ 140

The present value of cash flow can be written as follows

Price = C(PVIFA,i%,10) + M(PVIF,i%,10)

Mathematically it can be written as follows

$\large P = \frac{C}{i}[1-\frac{1}{(1+i)^{10}}]+\frac{M}{(1+i)^{10}}$

Now we can calculate the RoR through trial and error method

Let us assume i= 10%

$\large P = \frac{140}{0.1}[1-\frac{1}{(1+0.1)^{10}}]+\frac{7000}{(1+0.1)^{10}}$

On solving we will get

P = $ 3,558.80

Since, price is $5450 Thus decrease the rate Let us assume i= 5%

$\large P = \frac{140}{0.05}[1-\frac{1}{(1+0.05)^{10}}]+\frac{7000}{(1+0.05)^{10}}$

P = 140*7.722 + 7000*0.6139

P = $ 5,378.38

Still price is greater than the actual price again decrease i. Let us assume i=4.5%

$\large P = \frac{140}{0.045}[1-\frac{1}{(1+0.045)^{10}}]+\frac{7000}{(1+0.045)^{10}}$

P = 140*7.913 + 7000*0.6439

P= $ 5,615.12

Now we can see the price lies in between 4.5% to 5%. We can determine it using linear interpolation technique as follows

$\large RoR = 4.5 + (5-4.5)*\frac{5615.12-5450}{5615.12-5378.38}$

$\large RoR = 4.5 + 0.5*0.697474$

$\large RoR = 4.5 + 0.3487$

RoR = 4.85%

Here we have calculated RoR for semi annual basis. Thus, the actual RoR for 5 years will be twice of it

Thus, RoR= 9.70%

Answer is e. $ 140, 9.82%

Please contact if having any query. Thank you.