Question

3.2.The cash flow diagram is shown below, find the unknown value of “A”. For the computation, use an interest rate of 6%. 22,000 1 2 3 4 A) $1,982.57 B) $2,062.55 C) $1,862.55 D) $2,215.69 3.3.Sam invested in a corporate bond at a discounted price of $9,000 when the face value was $10,000. The bond pays a quarterly dividend. If the return on the investment is 10%, what does Sam receive as a quarterly dividend? Please assume the bond matures in 20 years. A) $201 B) $221 C) $190 D) $152

Answer 1

3.2

In this case, NPV of cash flows is given as

NPV=-22000+2A*(P/A,0.06,5)+3A*(P/F,0.06,5)

In balanced state NPV is zero. So,

-22000+2A*(P/A,0.06,5)+3A*(P/F,0.06,5)=0

Now let us calculate the interest factors

(P/F,i,n)=1/(1+0.06)^5=0.747258

$(P/A,i,n)=\frac{1-\frac{1}{(1+i)^{n}}}{i}$

$(P/A,0.06,5)=\frac{1-\frac{1}{(1+0.06)^{5}}}{0.06}=4.212364$

Plug in these value of interest factors in above equation

-22000+2A*4.212364+3A*0.747258=0

A=22000/(2*4.212364+3*0.747258)=$2062.53

Closest option is

B. $2062.55

3.3

Quarterly rate of return=i=10%/4=2.5%

Let the quarterly dividend be D

Number of dividends=20*4=80

Purchase price=$9000

Future value=$10000

We know that fair price of bond is equal to PV of cash flows. So,

9000=D*(P/A,0.025,80)+10000*(P/F,0.025,80)

Let us calculate the interest factors

(P/F,i,n)=1/(1+0.025)^80=0.138705

$(P/A,i,n)=\frac{1-\frac{1}{(1+i)^{n}}}{i}$

$(P/A,0.025,80)=\frac{1-\frac{1}{(1+0.025)^{80}}}{0.025}=34.451817$

Plug in these value of interest factors in above equation

9000=D*34.451817+10000*0.138705

D=(9000-10000*0.138705)/34.451817=$220.97

Closest option is

B) $221