4. Suppose there are two securities, A and B. Security A is a 3 year security, i

Question

4. Suppose there are two securities, A and B. Security A is a 3 year security, interest only, coupon of 9 percent, par value of $10,000. Security B is also a 3 year security, priced at $10,000, and 3 payments of principal and interest of $3,950.55 are to be received annually at the end of each year. a. What is the yield to maturity on each of these securities? b. What is the duration (D) for each of these securities? c. Which has a lower weighted average number of years to realize total cash flows from the investment?

Explanation / Answer

a)Calculation of Pvf for 3 yrs for sec B = 10000/3950.55 =2.53 (by referring to annuity table we get 9%)

Since Bond A issued at par and given no nformation about redemption price ,it is assumed that bond A is redeemed at par then YTM of bond is coupon rate i.e 9%

For security B , we have calculated YTM i.e 9%

Calculation of duration of these two bonds :

Duration of bond A 2.76 yrs and Bond B 1.94 yrs

C) Security B has the lower weighted average number of years to realize total cash flows from investment.

Cash Flows Pv of cash flows Period * Pv of c f Year PVF @ 9% Security A Security B Sec A Sec B Sec A Sec B 1 0.91743119 900 3950.55 825.69 3624.4 825.6880734 3624.4 2 0.84167999 900 3950.55 757.51 3325.1 1515.023988 6650.2 3 0.77218348 10900 3950.55 8416.8 3050.5 25250.3998 9151.5 27591.11186 19426.1 Duration 27591.11/10000 19426.1/10000 2.759111186 1.94261

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